Aminet 6/Aminet 6 - June 1995.iso/Aminet/gfx/3d/irit50src.lha/irit5/docs/irit.src

LaTeX Document | 1995-03-15 | 281.1 KB | 6,914 lines

;This is the source file to create documentation for the IRIT solid modeler.
;First character in line specifies the action to take for this line/next block
;as follows:
; ';' - a comment that is always ignored.
; '#' - all lines following this line until next '#' are indented as an array.
;       Four integers follow specifying indentations, # of elements per
;       line, whether or not to put an internal vertical separator, and
;       if entries are row ordered (1) or column ordered (2).
; '@' - latex only manual. Latex commands can appear within this line.
; '^' - text/hlp only manual. Opposite of '@'.
; '!' - plain text and irit docs only manual - keywords/headers.
; '&' - plain text only manual - headers.
; '$' - terminator for current block.
; '*' - prints line in all modes but without any latex filtering on the line.
; '%' - copied verbatim to all output types.
; latex commands can appear in regular text limited to a single line as
; {\command *}. For plain text the {\command } will be filtered out.
; Escaped characters via '\' (i.e. \#) will be left escaped (\#) in the
; latex output but unescaped (#) in the plain output.
;                       IRIT solid modeler (C) Gershon Elber 1991.
@% Irit Solid modeler latex manual.
@% Authors:     Gershon Elber
@% Date:        Thu April 15, 1993
@% Copyright (c) 1991/92/93 Gershon Elber
@\documentstyle[11pt]{article}
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@\textwidth 6.75in
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@\textheight 9.5in
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@\begin{document}
@\pagestyle{empty}
@   \rule{0in}{3in}
@   \begin{center}
@       {\huge\bf _IRIT_VERSION_ User's Manual}\\
@       \vspace{3cm}
@       {\Large A Solid modeling Program}\\
@       \vspace{2cm}
@       {\large Copyright (C) 1989, 1990-1995 Gershon Elber}\\
@       \vspace{1cm}
@       {\large EMail: [e-mail] }\\
@       \vspace{2cm}
@       {\large Join {\em IRIT} mailing list: [e-mail] }\\
@       {\large Mailing list: [e-mail] }\\
@       {\large Bug reports: [e-mail] }\\
@       \vfill
@       {\small This manual is for IRIT _IRIT_VERSION_.}
@   \end{center}
@\newpage
@\tableofcontents
@\newpage
@\setcounter{page}{1}
@\markright{{\em {\bf Irit Solid modeler}}\hfil G. Elber}
@\pagestyle{myheadings}
@\newpage
! IRIT _IRIT_VERSION_ User's Manual
! A Solid modeling Program
^ Copyright (C) 1989, 1990-1995 Gershon Elber
^ EMail: [e-mail]
^ Join IRIT mailing list: [e-mail]
^ Mailing list: [e-mail]
^ Bug reports: [e-mail]
@%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@\section{Introduction}
!INTRODUCTION
   {\em IRIT} is a solid modeler developed for educational purposes. Although
 small, it is now powerful enough to create quite complex scenes.
   {\em IRIT} started as a polygonal solid modeler and was originally developed
 on an IBM PC under MSDOS. Version 2.0 was also ported to X11 and version 3.0
 to SGI 4D systems. Version 3.0 also includes quite a few free form curves
 and surfaces tools. See the UPDATE.NEW file for more detailed update
 information. In Version 4.0, the display devices were enhanced, freeform
 curves and surfaces have further support, functions can be defined, and
 numerous improvement and optimizations are added.
@\section{Copyrights}
!COPYRIGHTS
   BECAUSE {\em IRIT} AND ITS SUPPORTING TOOLS AS DOCUMENTED IN THIS DOCUMENT
 ARE LICENSED FREE OF CHARGE, I PROVIDE ABSOLUTELY NO WARRANTY, TO THE EXTENT
 PERMITTED BY APPLICABLE STATE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING, I
 GERSHON ELBER PROVIDE THE {\em IRIT} PROGRAM AND ITS SUPPORTING TOOLS "AS IS"
 WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT
 LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
 PARTICULAR PURPOSE.
 THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THESE PROGRAMS IS WITH
 YOU. SHOULD THE {\em IRIT} PROGRAMS PROVE DEFECTIVE, YOU ASSUME THE COST OF
 ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
   IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW WILL GERSHON ELBER,
 BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY LOST PROFITS, LOST MONIES,
 OR OTHER SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
 USE OR INABILITY TO USE (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR A
 FAILURE OF THE PROGRAMS TO OPERATE WITH PROGRAMS NOT DISTRIBUTED BY GERSHON
 ELBER) THE PROGRAMS, EVEN IF YOU HAVE BEEN ADVISED OF THE POSSIBILITY OF
 SUCH DAMAGES, OR FOR ANY CLAIM BY ANY OTHER PARTY.
@\smallskip
   {\em IRIT} is a freeware solid modeler. It is not public domain since I
 hold copyrights on it. However, unless you are to sell or attempt to make
 money from any part of this code and/or any model you made with this solid
 modeler, you are free to make anything you want with it.
   {\em IRIT} can be compiled and executed on numerous Unix systems as well
 as OS2, Windows NT and AmigaDOS. However, beware the MSDOS support is fading
 away.
   You are not obligated to me or to anyone else in any way by using {\em IRIT}.
   You are encouraged to share any model you made with it, but the models
 you made with it are {\em yours}, and you have no obligation to share them.
   You can use this program and/or any model created with it for non
 commercial and non profit purposes only. An acknowledgement on the way the
 models were created would be nice but is {\em not} required.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\section{Command Line Options and Set Up of {\em IRIT}}
!SETUP
   The {\em IRIT} program reads a file called {\bf irit.cfg} each time it is executed.
   This file configures the system. It is a regular text file with comments, so
 you can edit it and properly modify it for your environment.
   This file is being searched for in the directory specified by the
 IRIT\_PATH environment variable.
   For example 'setenv IRIT\_PATH /u/gershon/irit/bin/'.
   Note IRIT\_PATH must terminate with '/'. If the variable is not set only
 the current directory is being searched for {\bf irit.cfg}.
   In addition, if it exists, a file by the name of {\bf iritinit.irt} will be
 automatically executed before any other '.irt' file. This file may contain
 any {\em IRIT} command. It is the proper place to put your predefined
 functions and procedures if you have some.
   This file will be searched much the same way {\bf IRIT.CFG} is. The
 name of this initialization file may be changed by setting the StartFile
 entry in the configuration file.
   This file is far more important starting at version 4.0, because of the new
 function and procedure definition that has been added, and which is used
 to emulate BEEP, VIEW, and INTERACT for example.
   The solid modeler can be executed in text mode (see the .cfg and the -t
 flag below) on virtually any system with a C compiler.
  Under all systems the following environment variables must be set
 and updated:
# 14 2 0 1
 path
  Add to path the directory where {\em IRIT}'s binaries are.
 IRIT\_PATH
  Directory with config., help and {\em IRIT}'s binary files.
 IRIT\_DISPLAY
  The graphics driver program/options. Must be in path.
 IRIT\_BIN\_IPC
  If set, uses binary Inter Process Communication.
 For example,
@\begin{verbatim}
   set path = ($path /u/gershon/irit/bin)
   setenv IRIT_PATH  /u/gershon/irit/bin/
   setenv IRIT_DISPLAY "xgldrvs -s-"
   setenv IRIT_BIN_IPC 1
@\end{verbatim}
 to set /u/gershon/irit/bin as the binary directory and to use the sgi's
 gl driver. If IRIT\_DISPLAY is not set, the server (i.e., the {\em IRIT}
 program) will prompt and wait for you to run a client (i.e., a display
 driver). if IRIT\_PATH is not set, none of the configuration files, nor
 the help file will be found.
 If IRIT\_BIN\_IPC is not set, text based IPC is used, which is far
 slower. No real reason not to use IRIT\_BIN\_IPC, unless it does not
 work for you.
  In addition, the following optional environment variables may be set.
# 17 2 0 1
 IRIT\_MALLOC
  If set, apply dynamic memory consistency testing.
  Programs will execute much slower in this mode.
 IRIT\_NO\_SIGNALS
  If set, no signals are caught by IRIT.
 IRIT\_SERVER\_HOST
  Internet Name of IRIT server (used by graphics driver).
 IRIT\_SERVER\_PORT
  Used internally to the TCP socket number. Should not
  be set by users.
 For example,
@\begin{verbatim}
   setenv IRIT_MALLOC 1
   setenv IRIT_NO_SIGNALS 1
   setenv IRIT_SERVER_HOST irit.cs.technion.ac.il
@\end{verbatim}
 IRIT\_MALLOC is useful for programmers, or when reporting a memory
 fatal error occurrence. IRIT\_NO\_SIGNALS is also useful for debugging
 when contorl-C is used within a debugger. The IRIT\_SERVER\_HOST/PORT
 controls the server/client ({\em IRIT}/Display device) communication.
 IRIT\_SERVER\_HOST and IRIT\_SERVER\_PORT are used in the unix and
 Window NT ports of {\em IRIT}.
   See the section on the graphics drivers for more details.
   A session can be logged into a file as set via LogFile in the configuration
 file. See also the LOGFILE command.
   The following command line options are available:
@\begin{verbatim}
   IRIT [-t] [-z] [file.irt]
@\end{verbatim}
# 10 2 1 1
   Puts {\em IRIT} into text mode. No graphics will be displayed and
   the display commands will be ignored. Useful when one needs to
   execute an irt file to create data on a tty device...
   Prints usage message and current configuration/version
   information.
 file.irt
   A file to invoke directly instead of waiting to input from
   stdin.
@\subsection{IBM PC OS2 Specific Set Up}
 Under OS2 the IRIT\_DISPLAY environment variable must be set (if set) to
 os2drvs.exe without any option (-s- will be passed automatically).
 os2drvs.exe must be in a directory that is in the PATH environment
 variable. IRIT\_BIN\_IPC can be used to signal binary IPC which is faster.
 Here is a complete example:
@\begin{verbatim}
%set IRIT_PATH=c:\irit\bin\
 set IRIT_DISPLAY=os2drvs.exe
 set IRIT_BIN_IPC=1
@\end{verbatim}
 assuming the directory specified by IRIT\_PATH holds the executables of
 IRIT and is in PATH.
 If IRIT\_BIN\_IPC is not set, text based IPC is used which is far
 slower. No real reason not to use IRIT\_BIN\_IPC unless it does not
 work for you.
@\subsection{IBM PC Window NT Specific Set Up}
 The NT port uses sockets and is, in this respect, similar to the unix port.
 The envirnoment variables IRIT\_DISPLAY, IRIT\_SERVER\_HOST,
 IRIT\_BIN\_IPC should all be set in a similar way to the Unix specific setup.
 As a direct result, the server (IRIT) and the display device may be running
 on different hosts. For example the server might be running on an NT system
 while the display device will be running on an SGI4D exploiting the graphic's
 hardware capabilities.
@\subsection{Unix Specific Set Up}
   Under UNIX using X11 (x11drvs driver) add the following options to
 your .Xdefaults. Most are self explanatory. The Trans attributes control
 the transformation window, while the View attributes control the view window.
 SubWin attributes control the subwindows within the Transformation window.
# 33 2 0 1
 \#if COLOR
 irit*Trans*BackGround:
  NavyBlue
 irit*Trans*BorderColor:
  Red
 irit*Trans*BorderWidth:
 irit*Trans*TextColor:
  Yellow
 irit*Trans*SubWin*BackGround:
  DarkGreen
 irit*Trans*SubWin*BorderColor:
  Magenta
 irit*Trans*Geometry:
  =150x500+500+0
 irit*Trans*CursorColor:
  Green
 irit*View*BackGround:
  NavyBlue
 irit*View*BorderColor:
  Red
 irit*View*BorderWidth:
 irit*View*Geometry:
  =500x500+0+0
 irit*View*CursorColor:
  Red
 irit*MaxColors:
 \#else
 irit*Trans*Geometry:
  =150x500+500+0
 irit*Trans*BackGround:
  Black
 irit*View*Geometry:
  =500x500+0+0
 irit*View*BackGround:
  Black
 irit*MaxColors:
 \#endif
@\section{First Usage}
!FIRSTUSAGE
   Commands to {\em IRIT} are entered using a textual interface, usually
 from the same window the program was executed from.
   Some important commands to begin with are,
   1. include("file.irt"); - will execute the commands in file.irt. Note
      include can be recursive up to 10 levels. To execute the demo
      (demo.irt) simply type 'include("demo.irt");'. Another way to run
      the demo is by typing demo(); which is a predefined procedure defined
      in iritinit.irt.
   2. help(""); - will print all available commands and how to get help on
      them. A file called irit.hlp will be searched as irit.cfg is
      being searched (see above), to provide the help.
   3. exit(); - close everything and exit {\em IRIT}.
   Most operators are overloaded. This means that you can multiply
 two scalars (numbers), or two vectors, or even two matrices, with the same
 multiplication operator ($*$). To get the on-line help on the
 operator '$*$' type 'help("$*$");'
   The best way to learn this program (like any other program...) is by
 trying it. Print the manual and study each of the commands available.
   Study the demo programs ($*$.irt) provided as well.
   The "best" mode to use irit is via the emacs editor. With this distribution
 an emacs mode for irit files (irt postfix) is provided (irit.el). Make your
 .emacs load this file automatically. Loading file.irt will switch emacs into
 Irit mode that supports the following three keystrokes:
# 18 2 1 1
 Meta-E
  Executes the current line
 Meta-R
  Executes the current Region (Between Cursor and Mark)
 Meta-S
  Executes a single line from input buffer
   The first time one of the above keystrokes is hit, emacs will fork an Irit
 process so that Irit's stdin is controlled via the above commands.
   This emacs mode was tested under various unix environments and under OS2
 2.x.
@\section{Data Types}
!DATATYPES
  These are the Data Types recognized by the solid modeler. They are also
 used to define the calling sequences of the different functions below:
# 18 2 1 1
 {\bf ConstantType}
  Scalar real type that cannot be modified.
 {\bf NumericType}
  Scalar real type.
 {\bf VectorType}
  3D real type vector.
 {\bf PointType}
  3D real type point.
 {\bf CtlPtType}
  Control point of a freeform curve or surface.
 {\bf MatrixType}
  4 by 4 matrix (homogeneous transformation matrix).
 {\bf PolygonType}
  Object consists of polygons.
 {\bf PolylineType}
  Object consists of polylines.
 {\bf CurveType}
  Object consists of curves.
 {\bf SurfaceType}
  Object consists of surfaces.
 {\bf TrimSrfType}
  Object consists of trimmed surfaces.
 {\bf TrivarType}
  Object consists of trivariate function.
 {\bf GeometricType}
  One of Polygon/lineType, CurveType, SurfaceType,
  TrimSrfType, TrivarType.
 {\bf GeometricTreeType}
  A list of GeometricTypes or GeometricTreeTypes.
 {\bf StringType}
  Sequence of chars within double quotes - "A string".
  Current implementation is limited to 80 chars.
 {\bf AnyType}
  Any of the above.
 {\bf ListType}
  List of (any of the above type) objects. List
  size is dynamically increased, as needed.
  Although points and vectors are not the same, {\em IRIT} does not
 destinguish between them, most of the time. This might change in the future.
@\section{Commands summary}
!COMMANDS
 These are all the commands and operators supported by the {\em IRIT} solid
 modeler:
# 11 6 1 0
 \verb+^+
 $==$
 $!=$
 $<=$
 $>=$
 ACOS
 ADAPISO
 AREA
 ASIN
 ATAN
 ATAN2
 ATTRIB
 AOFFSET
 BOOLONE
 BOOLSUM
 BSP2BZR
 BZR2BSP
 CBEZIER
 CBSPLINE
 CCINTER
 CCRVTR
 CDERIVE
 CDIVIDE
 CEDITPT
 CEVAL
 CEVOLUTE
 CEXTREMES
 CHDIR
 CINFLECT
 CINTERP
 CIRCLE
 CIRCPOLY
 CLNTCLOSE
 CLNTEXEC
 CLNTREAD
 CLNTWRITE
 CMESH
 CMORPH
 CMULTIRES
 COERCE
 COLOR
 COMMENT
 CON2
 CONE
 CONVEX
 COORD
 COMPOSE
 CPOLY
 CRAISE
 CREFINE
 CREGION
 CREPARAM
 CROSSEC
 CRVLNDST
 CRVPTDST
 CSURFACE
 CTANGENT
 CTLPT
 CTRIMSRF
 CYLIN
 CZEROS
 ERROR
 EXIT
 EXTRUDE
 FFCOMPAT
 FFEXTREME
 FREE
 FUNCTION
 GBOX
 GETLINE
 GPOLYGON
 GPOLYLINE
 HELP
 HOMOMAT
 INCLUDE
 INTERACT
 IRITSTATE
 LIST
 LOAD
 LOFFSET
 LOGFILE
 MERGEPOLY
 MESHSIZE
 MOMENT
 MSLEEP
 OFFSET
 PAUSE
 PCIRCLE
 PDOMAIN
 POLY
 PRINTF
 PRISA
 PROCEDURE
 RANDOM
 RMATTR
 ROTX
 ROTY
 ROTZ
 RULEDSRF
 SAVE
 SBEZIER
 SBSPLINE
 SCALE
 SCRVTR
 SDERIVE
 SDIVIDE
 SEDITPT
 SEVAL
 SFROMCRVS
 SINTERP
 SIZEOF
 SMERGE
 SMORPH
 SNOC
 SNORMAL
 SNRMLSRF
 SPHERE
 SQRT
 SRAISE
 SREFINE
 SREGION
 SREPARAM
 STANGENT
 STRIMSRF
 STRIVAR
 SURFPREV
 SURFREV
 SWEEPSRF
 SWPSCLSRF
 SYMBCPROD
 SYMBDIFF
 SYMBDPROD
 SYMBPROD
 SYMBSUM
 SYSTEM
 TBEZIER
 TBSPLINE
 TDERIVE
 TEVAL
 TIME
 TINTERP
 THISOBJ
 TORUS
 TRANS
 TREFINE
 TREGION
 TRIMSRF
 TSUBDIV
 VARLIST
 VECTOR
 VIEW
 VIEWOBJ
 VOLUME
@\section{Functions and Variables}
!FUNCTIONS
@ This section lists all the functions supported by the {\em IRIT} system
@ according to their classes - mostly, the object type they return.
 Functions that return a {\bf NumericType}:
# 11 5 1 0
 ACOS
 AREA
 ASIN
 ATAN
 ATAN2
 CLNTEXEC
 CPOLY
 MESHSIZE
 RANDOM
 SIZEOF
 SQRT
 THISOBJ
 VOLUME
 Functions that return a {\bf GeometricType}:
# 11 6 1 0
 ADAPISO
 AOFFSET
 BOOLONE
 BOOLSUM
 BSP2BZR
 BZR2BSP
 CBEZIER
 CBSPLINE
 CCINTER
 CCRVTR
 CDERIVE
 CDIVIDE
 CEDITPT
 CEVAL
 CEVOLUTE
 CEXTREMES
 CINFLECT
 CINTERP
 CIRCLE
 CIRCPOLY
 CLNTREAD
 CMESH
 CMORPH
 CMULTIRES
 COERCE
 COMPOSE
 CON2
 CONE
 CONVEX
 COORD
 CPOLY
 CRAISE
 CREFINE
 CREGION
 CREPARAM
 CROSSEC
 CRVLNDST
 CRVPTDST
 CSURFACE
 CTANGENT
 CTRIMSRF
 CTLPT
 CYLIN
 CZEROS
 EXTRUDE
 FFCOMPAT
 FFEXTREME
 GBOX
 GETLINE
 GPOLYGON
 GPOLYLINE
 LOFFSET
 MERGEPOLY
 MOMENT
 OFFSET
 PCIRCLE
 PDOMAIN
 POLY
 PRISA
 PROCEDURE
 RULEDSRF
 SBEZIER
 SBSPLINE
 SCRVTR
 SDERIVE
 SDIVIDE
 SEDITPT
 SEVAL
 SFROMCRVS
 SINTERP
 SMERGE
 SMORPH
 SNORMAL
 SNRMLSRF
 SPHERE
 SRAISE
 SREFINE
 SREGION
 SREPARAM
 STANGENT
 STRIMSRF
 STRIVAR
 SURFPREV
 SURFREV
 SWEEPSRF
 SWPSCLSRF
 SYMBCPROD
 SYMBDIFF
 SYMBDPROD
 SYMBPROD
 SYMBSUM
 TBEZIER
 TBSPLINE
 TDERIVE
 TEVAL
 TINTERP
 TORUS
 TREFINE
 TREGION
 TRIMSRF
 TSUBDIV
 Functions that create linear transformation matrices:
# 11 6 1 0
 HOMOMAT
 ROTX
 ROTY
 ROTZ
 SCALE
 TRANS
 Miscellaneous functions:
# 11 6 1 0
 ATTRIB
 CHDIR
 CLNTCLOSE
 CLNTWRITE
 COLOR
 COMMENT
 ERROR
 EXIT
 FREE
 FUNCTION
 HELP
 INCLUDE
 INTERACT
 IRITSTATE
 LIST
 LOAD
 LOGFILE
 MSLEEP
 PAUSE
 PRINTF
 PROCEDURE
 RMATTR
 SAVE
 SNOC
 SYSTEM
 TIME
 VARLIST
 VECTOR
 VIEW
 VIEWOBJ
 Variables that are predefined in the system:
# 18 4 1 0
 AXES
 DRAWCTLPT
 FLAT4PLY
 MACHINE
 POLY\_APPROX\_OPT
 POLY\_APPROX\_UV
 POLY\_APPROX\_TOL
 PRSP\_MAT
 RESOLUTION
 VIEW\_MAT
 Constants that are predefined in the system:
# 13 5 1 0
 AMIGA
 APOLLO
 BLACK
 BLUE
 CTLPT\_TYPE
 CURVE\_TYPE
 CYAN
 DEPTH
 FALSE
 GREEN
 IBMOS2
 IBMNT
 KV\_FLOAT
 KV\_OPEN
 LIST\_TYPE
 MAGENTA
 MATRIX\_TYPE
 MSDOS
 NUMERIC\_TYPE
 PARAM\_CENTRIP
 PARAM\_CHORD
 PARAM\_UNIFORM
 PLANE\_TYPE
 POINT\_TYPE
 POLY\_TYPE
 STRING\_TYPE
 SURFACE\_TYPE
 TRIMSRF\_TYPE
 TRIVAR\_TYPE
 TRUE
 UNDEF\_TYPE
 UNIX
 VECTOR\_TYPE
 WHITE
 YELLOW
@\section{Language description}
!LANGUAGE
    The front end of the {\em IRIT} solid modeler is an infix parser that
 mimics some of the C language behavior. The infix operators that are supported
 are plus (+), minus (-), multiply (*), divide (/), and power (\verb+^+), for
 numeric operators, with the same precedence as in C.
    However, unlike the C language, these operators are overloaded,
@\footnote{In fact the C language does support overloaded operators to some
@extent: '1 + 2' and '1.0 + 2.0' implies invocation of two different
@actions.}
 or different action is taken, based upon the different operands.
   This means that one can write '1 + 2', in which the plus sign denotes a
 numeric addition, or one can write 'PolyObj1 + PolyObj2', in which case the
 plus sign denotes the Boolean operation of a union between two geometric
 objects.
   The exact way each operator is overloaded is defined below.
   In this environment, reals, integers, and even Booleans, are all represented
 as real types. Data are automatically promoted as necessary.
   For example, the constants TRUE and FALSE are defined as 1.0 and 0.0
 respectively.
   Each expression is terminated by a semicolon. An expression can be as
 simple as 'a;' which prints the value of variable a, or as complex as:
@\begin{verbatim}
    for ( t = 1.1, 0.1, 1.9,
            cb1 = csurface( sb, COL, t ):
            color( cb1, green ):
            snoc( cb1, cb_all )
        );
@\end{verbatim}
   While an expression is terminated with a semicolon, a colon is used to
 terminate mini-expressions within an expression.
   Once a complete expression is read in (i.e., a semicolon is detected)
 and parsed correctly (i.e. no syntax errors are found), it is executed.
   Before each operator or a function is executed, parameter type matching
 tests are made to make sure the operator can be applied to these
 operand(s), or that the function gets the correct set of arguments.
   The parser is totally case insensitive, so Obj, obj, and OBJ will refer
 to the same object, while MergePoly, MERGEPOLY, and mergePoly will refer
 to the same function.
   Objects (Variables if you prefer) need not be declared. Simply use them
 when you need them. Object names may be any alpha-numeric (and underscore)
 string of at most 30 characters. By assigning to an old object, the old
 object will be automatically deleted and if necessary its type will be
 modified on the fly.
 Example:
@\begin{verbatim}
    V = sin( 45 * pi / 180.0 );
    V = V * vector( 1, 2, 3 );
    V = V * rotx( 90 );
    V = V * V;
@\end{verbatim}
 will assign to V a NumericType equal to the sine of 45 degrees, the VectorType
 ( 1, 2, 3 ) scaled by the sine of 45, rotate that vector around the X axis
 by 90 degrees, and finally a NumericType which is the dot (inner) product of
 V with itself.
   The parser will read from stdin, unless a file is specified on the command
 line or an INCLUDE command is executed. In both cases, when the end of file
 is encountered, the parser will again wait for input from stdin. In order
 to execute a file and quit in the end of the file, put an EXIT command as
 the last command in the file.
@\section{Operator overloading}
@ The basic operators $+$, $-$, $*$, $/$, and \verb+^+ are overloaded.
@ This section describes what action is taken by each of these operators
@ depending on its arguments.
@\subsection{Overloading $+$}
 The $+$ operator is overloaded above the following domains:
@\begin{verbatim}
  NumericType + NumericType -> NumericType
  VectorType  + VectorType  -> VectorType   (Vector addition)
  MatrixType  + MatrixType  -> MatrixType   (Matrix addition)
  PolygonType + PolygonType -> PolygonType  (Boolean UNION operation)
  CurveType   + CurveType   -> CurveType    (Curve curve profiling)
  CurveType   + CtlPtType   -> CurveType    (Curve control point profiling)
  CtlPtType   + CtlPtType   -> CurveType    (Control points profiling)
  ListType    + ListType    -> ListType     (Append lists operator)
  StringType  + StringType  -> StringType   (String concat)
  StringType  + RealType    -> StringType   (String concat, real as int string)
@\end{verbatim}
 Note: Boolean UNION of two disjoint objects (no common volume) will result
 with the two objects combined. It is the USER responsibility to make sure that
 the non intersecting objects are also disjoint - this system only tests for
 no intersection.
@\subsection{Overloading $-$}
 The $-$ operator is overloaded above the following domains:
 As a binary operator:
@\begin{verbatim}
  NumericType - NumericType -> NumericType
  VectorType  - VectorType  -> VectorType   (Vectoric difference)
  MatrixType  - MatrixType  -> MatrixType   (Matrix difference)
  PolygonType - PolygonType -> PolygonType  (Boolean SUBTRACT operation)
@\end{verbatim}
 As a unary operator:
@\begin{verbatim}
  - NumericType -> NumericType
  - VectorType  -> VectorType    (Scale vector by -1)
  - MatrixType  -> MatrixType    (Scale matrix by -1)
  - PolygonType -> PolygonType   (Boolean NEGATION operation)
  - CurveType   -> CurveType     (Curve parameterization is reversed)
  - SurfaceType -> SurfaceType   (Surface parameterization is reversed)
@\end{verbatim}
 Note: Boolean SUBTRACT of two disjoint objects (no common volume) will result
 with an empty object. For both a curve and a surface parameterization, reverse
 operation (binary minus) causes the object normal to be flipped as a side
 effect.
@\subsection{Overloading $*$}
 The $*$ operator is overloaded above the following domains:
@\begin{verbatim}
  NumericType * NumericType   -> NumericType
  VectorType  * NumericType   -> VectorType    (Vector scaling)
  VectorType  * VectorType    -> NumericType   (Inner product)
  MatrixType  * NumericType   -> MatrixType    (Matrix Scaling)
  MatrixType  * PointType     -> PointType     (Point transformation)
  MatrixType  * CtlPtType     -> CtlPtType     (Ctl Point transformation)
  MatrixType  * VectorType    -> VectorType    (Vector transformation)
  MatrixType  * MatrixType    -> MatrixType    (Matrix multiplication)
  MatrixType  * GeometricType -> GeometricType (Object transformation)
  MatrixType  * ListType      -> ListType      (Object hierarchy transform.)
  PolygonType * PolygonType   -> PolygonType   (Boolean INTERSECTION operation)
@\end{verbatim}
 Note: Boolean INTERSECTION of two disjoint objects (no common volume) will
 result with an empty object. Object hierarchy transform transforms any
 transformable object (GeometricType) found in the list recursively.
@\subsection{Overloading $/$}
 The $/$ operator is overloaded above the following domains:
@\begin{verbatim}
  NumericType / NumericType -> NumericType
  PolygonType / PolygonType -> PolygonType   (Boolean CUT operation)
@\end{verbatim}
 Note: Boolean CUT of two disjoint objects (no common volume) will result
 with an empty object.
@\subsection{Overloading \^{\ }}
 The \verb+^+ operator is overloaded above the following domains:
@\begin{verbatim}
  NumericType ^ NumericType -> NumericType
  VectorType  ^ VectorType  -> VectorType  (Cross product)
  MatrixType  ^ NumericType -> MatrixType  (Matrix to the (int) power)
  PolygonType ^ PolygonType -> PolygonType (Boolean MERGE operation)
  StringType  ^ StringType  -> StringType  (String concat)
  StringType  ^ RealType    -> StringType  (String concat, real as real string)
@\end{verbatim}
 Note: Boolean MERGE simply merges the two sets of polygons without any
 intersection tests. Matrix powers must be positive integers or -1, in which
 case the matrix inverse (if it exists) is computed.
@\subsection{Assignments}
   Assignments are allowed as side effects, in any place in an expression.
 If "Expr" is an expression, then "var = Expr" is the exact same expression
 with the side effect of setting Var to that value. There is no guarantee
 on the order of evaluation, so using Vars that are set within the same
 expression is a bad practice. Use parentheses to force the order of
 evaluation, i.e., "( var = Expr )".
@\subsection{Comparison operators $==$, $!=$, $<$, $>$, $<=$, $>=$}
&Comparison operators ==, !=, <, >, <=, >=
 The conditional comparison operators can be applied to the following
 domains (o for a comparison operator):
@\begin{verbatim}
  NumericType o NumericType -> NumericType
  StringType  o StringType  -> NumericType
  PointType   o PointType   -> NumericType
  VectorType  o VectorType  -> NumericType
  PlaneType   o PlaneType   -> NumericType
@\end{verbatim}
 The returned NumericType is non-zero if the condition holds, or zero if
 not.
   For PointTypes, VectorTypes, and PlaneTypes, only $==$ and $!=$ comparisons
 are valid. This is either the same or different.
   For NumericTypes and StringTypes (uses strcmp) all comparisons are valid.
@\subsection{Logical operators $\&\&$, $\|\|$, !}
&Logical operators &&, ||, !
 Complex logical expressions can be defined using the logical {\em and} ($\&\&$),
 logical {\em or} ($\|\|$) and logical {\em not} (!). These operators can be applied
 to NumericTypes that are considered Boolean results. That is, true for a
 non-zero value, and false otherwise.
   The returned NumericType is true if both operands are true for the {\em and}
 operator, at least one is true for the {\em or} operator, and the operand is
 false for the {\em not} operator. In all other cases, a false is returned.
   To make sure Logical expressions are readable, the {\em and} and {\em or}
 operators are defined to have the {\em same} priority. Use parentheses to
 disambiguate a logical expression and to make it more readable.
@\subsection{Geometric Boolean Operations}
&Geometric Boolean Operations
   The {\em IRIT} solid modeling system supports Boolean operations between
 polyhedra objects. Freeform objects will be automaticaly converted to
 a polygonal representation when used in Boolean operations.
   The $+$, $*$, and $-$ are overloaded to denote Boolean union, intersection
 and subtraction when operating on geometric entities. $-$ can also be
 used as an unary operator to reverse the object orientation inside out.
   Example:
@\begin{verbatim}
    resolution = 20;
    B = box(vector(-1, -1, -0.25), 2, 1.2, 0.5);
    C = con2(vector(0, 0, -1.5), vector(0, 0, 3), 0.7, 0.3);
    D = convex(B - C);
    E = convex(C - B);
    F = convex(B + C);
    G = convex(B * C);
    tr = rotx( -90 ) * roty( 40 ) * rotx( -30 );
    All = list( D * tr * trans( vector(  0.6,  0.5, 0.0 ) ),
                E * tr * trans( vector(  3.0,  0.0, 0.0 ) ),
                F * tr * trans( vector( -2.0,  0.0, 0.0 ) ),
                G * tr * trans( vector(  0.7, -1.0, 0.0 ) ) )
            * scale( vector( 0.25, 0.25, 0.25 ) )
            * trans( vector( -0.1, -0.3, 0.0 ) );
    view_mat = rotx( 0 );
    view( list( view_mat, All ), on );
    save( "booleans", list( view_mat, All ) );
@\end{verbatim}
    A complete example to compute the union, intersection and both
 differences of a box and a truncated cone.
@The result of this example can be seen in Figure~\ref{fig-booleans}
@with its hidden lines removed.
@\begin{figure}
@\vspace{3in}
@\special{psfile=user_man/booleans.ps hscale=100 vscale=100 hoffset=-40 voffset=-130}
@\caption{Geometric Boolean operatioms between a box and a truncated cone.
@         Shown are union (left), intersection (bottom center), box minus
@         the cone (top center), and cone minus the box (right).}
@\label{fig-booleans}
@\end{figure}
    There are several flags to control the Boolean operations. See
 IRITSTATE command for the "InterCrv", "Coplanar", and "PolySort"
 states.
@\subsection{Priority of operators}
&Priority of operators
   The following table lists the priority of the different operators.
# 19 3 0 1
 Lowest
 Operator
 Name of operator
 priority
 comma
 colon
 $\&\&$, $\|\|$
 logical and, logical or
 $=,==,!=,<=,>=,<,>$
 assignment, equal, not equal, less
 equal, greater equal, less, greater
 +, -
 plus, minus
 *, /
 multiply, divide
 Highest
 \verb+^+
 power
 priority
 -, !
 unary minus, logical not
@\subsection{Grammar}
&Grammar
   The grammar of the {\em IRIT} parser follows similar guidelines as
 the C language for simple expressions. However, complex statements differ.
   See the IF, FOR, FUNCTION, and PROCEDURE below for the usage of these
 clauses.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\section{Function Description}
&Function Description
@ The description below defines the parameters and returned values of the
@ predefined functions in the system, using the notation of functions
@ in ANSI C. Listed are all the functions in the system, in alphabetic
@ order, according to their classes.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{NumericType returning functions}
&NumericType returning functions
@\subsubsection{ABS}
@\begin{verbatim}
 NumericType ABS( NumericType Operand )
@\end{verbatim}
   Returns the absolute value of the given {\bf Operand}.
@\subsubsection{ACOS}
!ACOS
@\begin{verbatim}
 NumericType ACOS( NumericType Operand )
@\end{verbatim}
   Returns the arc cosine value (in radians) of the given {\bf Operand}.
@\subsubsection{AREA}
!AREA
@\begin{verbatim}
 NumericType AREA( PolygonType Object )
@\end{verbatim}
   Returns the area of the given {\bf Object} (in object units). Returned is
 the area of the polygonal object, not the area of the primitive it might
 approximate.
   This means that the area of a polygonal approximation of a sphere will be
 returned, not the exact area of the sphere.
@\subsubsection{ASIN}
!ASIN
@\begin{verbatim}
 NumericType ASIN( NumericType Operand )
@\end{verbatim}
   Returns the arc sine value (in radians) of the given {\bf Operand}.
@\subsubsection{ATAN}
!ATAN
@\begin{verbatim}
 NumericType ATAN( NumericType Operand )
@\end{verbatim}
   Returns the arc tangent value (in radians) of the given {\bf Operand}.
@\subsubsection{ATAN2}
!ATAN2
@\begin{verbatim}
 NumericType ATAN2( NumericType Operand1, NumericType Operand2 )
@\end{verbatim}
   Returns the arc tangent value (in radians) of the given ratio:
 {\bf Operand1} / {\bf Operand2}, over the whole circle.
@\subsubsection{COS}
@\begin{verbatim}
 NumericType COS( NumericType Operand )
@\end{verbatim}
   Returns the cosine value of the given {\bf Operand} (in radians).
@\subsubsection{CLNTEXEC}
!CLNTEXEC
@\begin{verbatim}
 NumericType CLNTEXEC( StringType ClientName )
@\end{verbatim}
   Initiate communication channels to a client named {\bf ClientName}.
 {\bf ClientName} is executed by this function as a sub process and
 two communication channels are opened between the IRIT server and the
 new client, for read and write. See also CLNTREAD, CLNTWRITE, and
 CLNTCLOSE. if {\bf ClientName} is an empty string, the user is provided
 with the new communication port to be used and the server blocks for the
 user to manualy executed the client after setting the proper
 IRIT\_SERVER\_HOST/PORT environment variables.
 Example:
@\begin{verbatim}
   h1 = CLNTEXEC( "" );
   h2 = CLNTEXEC( "nuldrvs -s-" );
@\end{verbatim}
 executes two clients, one is named {\bf nuldrvs} and the other one is
 prompted for by the user. As a result of the second invokation of
 CLNTEXEC, the user will be prompted with a message similar to,
@\begin{verbatim}
    Irit: Startup your program - I am waiting...
    setenv IRIT_SERVER_PORT 2182
@\end{verbatim}
 and he/she will need to set the proper environment variable and execute
 their client manually.
@\subsubsection{CPOLY}
!CPOLY
@\begin{verbatim}
 NumericType CPOLY( PolygonType Object )
@\end{verbatim}
   Returns the number of polygons in the given polygonal {\bf Object}.
@\subsubsection{EXP}
@\begin{verbatim}
 NumericType EXP( NumericType Operand )
@\end{verbatim}
   Returns the natural exponent value of the given {\bf Operand}.
@\subsubsection{LN}
@\begin{verbatim}
 NumericType LN( NumericType Operand )
@\end{verbatim}
   Returns the natural logarithm value of the given {\bf Operand}.
@\subsubsection{LOG}
@\begin{verbatim}
 NumericType LOG( NumericType Operand )
@\end{verbatim}
   Returns the base 10 logarithm value of the given {\bf Operand}.
@\subsubsection{MESHSIZE}
!MESHSIZE
@\begin{verbatim}
 NumericType MESHSIZE( SurfaceType Srf, ConstantType Direction )
@\end{verbatim}
   Returns the size of {\bf Srf}'s mesh in {\bf Direction}, which
 is one of COL or ROW.
 Example:
@\begin{verbatim}
   RSize = MESHSIZE( Sphere, ROW );
   CSize = MESHSIZE( Sphere, COL );
@\end{verbatim}
@\subsubsection{RANDOM}
!RANDOM
@\begin{verbatim}
 NumericType RANDOM( NumericType Min, NumericType Max )
@\end{verbatim}
   Returns a randomized value between {\bf Min} and {\bf Max}.
@\subsubsection{SIN}
@\begin{verbatim}
 NumericType SIN( NumericType Operand )
@\end{verbatim}
   Returns the sine value of the given {\bf Operand} (in radians).
@\subsubsection{SIZEOF}
!SIZEOF
@\begin{verbatim}
 NumericType SIZEOF( ListType List | PolyType Poly | CurveType Crv )
@\end{verbatim}
   Returns the length of a list, if {\bf List}, the number of polygons
 if {\bf Poly}, or the length of the control polygon if {\bf Crv}.
   If, however, only one polygon is in {\bf Poly}, it returns the number
 of vertices in that polygon.
 Example:
@\begin{verbatim}
   len = SIZEOF( list( 1, 2, 3 ) );
   numPolys = SIZEOF( axes );
   numCtlpt = SIZEOF( circle( vector( 0, 0, 0 ), 1 ) );
@\end{verbatim}
 will assign the value of 3 to the variable {\bf len}, set {\bf numPolys}
 to the number of polylines in the axes object, and set numCtlPt to 9, the
 number of control points in a circle.
@\subsubsection{SQRT}
!SQRT
@\begin{verbatim}
 NumericType SQRT( NumericType Operand )
@\end{verbatim}
   Returns the square root value of the given {\bf Operand}.
@\subsubsection{TAN}
@\begin{verbatim}
 NumericType TAN( NumericType Operand )
@\end{verbatim}
   Returns the tangent value of the given {\bf Operand} (in radians).
@\subsubsection{THISOBJ}
!THISOBJ
@\begin{verbatim}
 NumericType THISOBJ( StringType Object )
@\end{verbatim}
   Returns the object type of the given name of an {\bf Object}. This can
 be one of the constants  UNDEF\_TYPE, NUMERIC\_TYPE, STRING\_TYPE,
 VECTOR\_TYPE, POINT\_TYPE, CTLPT\_TYPE, MATRIX\_TYPE, POLY\_TYPE,
 CURVE\_TYPE, SURFACE\_TYPE, TRIMSRF\_TYPE, or TRIVAR\_TYPE.
   This is also a way to ask if an object by a given name do exist (if the
 returned type is UNDEF\_TYPE or not).
@\subsubsection{VOLUME}
!VOLUME
@\begin{verbatim}
 NumericType VOLUME( PolygonType Object )
@\end{verbatim}
   Returns the volume of the given {\bf Object} (in object units). It returns
 the volume of the polygonal object, not the volume of the object it might
 approximate.
   This routine decomposes all non-convex polygons to convex ones as a side
 effect (see CONVEX).
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{GeometricType returning functions}
&GeometricType returning functions
@\subsubsection{ADAPISO}
!ADAPISO
@\begin{verbatim}
 CurveType ADAPISO( SurfaceType Srf, NumericType Dir, NumericType Eps,
                    NumericType FullIso, NumericType SinglePath )
@\end{verbatim}
 Constructs a {\em coverage} to {\bf Srf} using isocurve in the {\bf Dir} direction,
 so that for any point p on surface {\bf Srf}, there exists a point on one of
 the isocurves that is close to p within {\bf Eps}. If {\bf FullIso}, the
 extracted isocurves span the entire surface domain, otherwise they may
 span only a subset of the domain. If {\bf SinglePath}, an approximation to
 a single path (Hamiltonian path) that visits all isocurves is constructed.
@\begin{verbatim}
    srf = sbezier( list( list( ctlpt( E3, -0.5, -1.0,  0.0 ),
                               ctlpt( E3,  0.4,  0.0,  0.1 ),
                               ctlpt( E3, -0.5,  1.0,  0.0 ) ),
                         list( ctlpt( E3,  0.0, -0.7,  0.1 ),
                               ctlpt( E3,  0.0,  0.0,  0.0 ),
                               ctlpt( E3,  0.0,  0.7, -0.2 ) ),
                         list( ctlpt( E3,  0.5, -1.0,  0.1 ),
                               ctlpt( E3, -0.4,  0.0,  0.0 ),
                               ctlpt( E3,  0.5,  1.0, -0.2 ) ) ) );
    aiso = ADAPISO( srf, COL, 0.1, FALSE, FALSE );
@\end{verbatim}
 Constructs an adaptive isocurve approximation with tolerance of {\bf 0.1} to
 surface {\bf srf} in direction {\bf COL}. Isocurves are allowed to span a
 subset of the surface domain. No single path is needed.
 The {\bf SinglePath} option is currently not supported.
@\subsubsection{ARC}
@\begin{verbatim}
 CurveType ARC( VectorType StartPos, VectorType Center, VectorType EndPos )
@\end{verbatim}
 Constructs an arc between the two end points {\bf StartPos} and {\bf EndPos},
 centered at {\bf Center}. Arc will always be less than 180 degrees, so the
 shortest circular path from {\bf StartPos} to {\bf EndPos} is selected. The
 case where {\bf StartPos}, {\bf Center}, and {\bf EndPos} are collinear is
 illegal, since it attempts to define a 180 degrees arc. Arc is constructed
 as a single rational quadratic Bezier curve.
 Example:
@\begin{verbatim}
    Arc1 = ARC( vector( 1.0, 0.0, 0.0 ),
                vector( 1.0, 1.0, 0.0 ),
                vector( 0.0, 1.0, 0.0 ) );
@\end{verbatim}
 constructs a 90 degrees arc, tangent to both the X and Y axes at coordinate 1.
@See Figure~\ref{fig-arc}.
@\begin{figure}
@\vspace{2.4in}
@\special{psfile=user_man/arc1cnst.ps hscale=100 vscale=100 hoffset=-40 voffset=-200}
@\caption{A 90 degree arc constructed using the ARC constructor.}
@\label{fig-arc}
@\end{figure}
@\subsubsection{AOFFSET}
!AOFFSET
@\begin{verbatim}
 CurveType AOFFSET( CurveType Crv, NumericType OffsetDistance,
                    NumericType Epsilon, NumericType TrimLoops )
 SurfaceType AOFFSET( SurfaceType Srf NumericType OffsetDistance,
                      NumericType Epsilon, NumericType TrimLoops )
@\end{verbatim}
 Computes an offset of {\bf OffsetDistance} with globally bounded error
 (controlled by {\bf Epsilon}). The smaller {\bf Epsilon} is, the better
 the approximation to the offset. The bounded error is achieved by adaptive
 refinement of the {\bf Crv}.
   If {\bf TrimLoops} is TRUE or on, the regions of the object that
 self-intersect as a result of the offset operation are trimmed away.
 Example:
@\begin{verbatim}
    OffCrv1 = AOFFSET( Crv, -0.4, 0.01, TRUE );
    OffCrv2 = AOFFSET( Crv, -0.4, 0.01, FALSE );
@\end{verbatim}
 computes an adaptive offset to {\bf Crv} with {\bf OffsetDistance} of
 0.5 and {\bf Epsilon} of 0.03 and trims the self-intersection loops.
 See also OFFSET and LOFFSET.
@See Figure~\ref{fig-caoffset}.
@\begin{figure}
@\vspace{1.6in}
@\special{psfile=user_man/caoffset.ps hscale=100 vscale=100 hoffset=-60 voffset=-220}
@\caption{Adaptive offset approximation (thick) of a Bspline curve (thin).
@        On the left, the self intersections in the offset computed in the
@        right are eliminated. Both offsets were computedusing AOFFSET.
@        (See also Figure~\protect\ref{fig-coffset}.)}
@\label{fig-caoffset}
@\end{figure}
@\subsubsection{BOOLONE}
!BOOLONE
@\begin{verbatim}
 SurfaceType BOOLONE( CurveType Crv )
@\end{verbatim}
 Given a closed curve, the curve is subdivided into four segments equally
 spaced in the parametric space that are fed into BOOLSUM. Useful if
 a surface should "fill" the area enclosed by a closed curve.
 Example:
@\begin{verbatim}
 Srf = BOOLONE( circle( vector( 0.0, 0.0, 0.0 ), 1.0 ) );
@\end{verbatim}
 Creates a disk surface containing the area enclosed by the unit circle.
@See Figure~\ref{fig-boolsum-one}.
@\begin{figure}
@\vspace{3.5in}
@\special{psfile=user_man/boolone.ps hscale=70 vscale=70 hoffset=-80 voffset=-90}
@\special{psfile=user_man/boolsum.ps hscale=70 vscale=70 hoffset=170 voffset=-70}
@\caption{A boolean sum of a circle creates a disk (left) using BOOLONE and
@        a general boolean sum of four curves (right).}
@\label{fig-boolsum-one}
@\end{figure}
@\subsubsection{BOOLSUM}
!BOOLSUM
@\begin{verbatim}
 SurfaceType BOOLSUM( CurveType Crv1, CurveType Crv2,
                      CurveType Crv3, CurveType Crv4 )
@\end{verbatim}
 Construct a surface using the provided four curves as its four boundary
 curves. Curves do not have to have the same order or type, and will be
 promoted to their least common denominator. The end points of the four
 curves should match as follows:
# 30 2 0 1
 {\bf Crv1} start point,
  to {\bf Crv3} start point.
 {\bf Crv1} end point,
  to {\bf Crv4} start point.
 {\bf Crv2} start point,
  to {\bf Crv3} end point.
 {\bf Crv2} end point,
  to {\bf Crv4} end point.
 where {\bf Crv1} and {\bf Crv2} are the two boundaries in one parametric
 direction, and {\bf Crv3} and {\bf Crv4} are the two boundaries in the other
 parametric direction.
 Example:
@\begin{verbatim}
    Cbzr1 = cbezier( list( ctlpt( E3, 0.1, 0.1, 0.1 ),
                           ctlpt( E3, 0.0, 0.5, 1.0 ),
                           ctlpt( E3, 0.4, 1.0, 0.4 ) ) );
    Cbzr2 = cbezier( list( ctlpt( E3, 1.0, 0.2, 0.2 ),
                           ctlpt( E3, 1.0, 0.5, -1.0 ),
                           ctlpt( E3, 1.0, 1.0, 0.3 ) ) );
    Cbsp3 = cbspline( 4,
                      list( ctlpt( E3, 0.1,  0.1, 0.1 ),
                            ctlpt( E3, 0.25, 0.0, -1.0 ),
                            ctlpt( E3, 0.5,  0.0, 2.0 ),
                            ctlpt( E3, 0.75, 0.0, -1.0 ),
                            ctlpt( E3, 1.0,  0.2, 0.2 ) ),
                      list( KV_OPEN ) );
    Cbsp4 = cbspline( 4,
                      list( ctlpt( E3, 0.4,  1.0, 0.4 ),
                            ctlpt( E3, 0.25, 1.0, 1.0 ),
                            ctlpt( E3, 0.5,  1.0, -2.0 ),
                            ctlpt( E3, 0.75, 1.0, 1.0 ),
                            ctlpt( E3, 1.0,  1.0, 0.3 ) ),
                      list( KV_OPEN ) );
    Srf = BOOLSUM( Cbzr1, Cbzr2, Cbsp3, Cbsp4 );
@\end{verbatim}
@\subsubsection{BOX}
@\begin{verbatim}
 PolygonType BOX( VectorType Point,
                  NumericType Dx, NumericType Dy, NumericType Dz )
@\end{verbatim}
   Creates a BOX polygonal object, whose boundary is coplanar with the
 $XY$, $XZ$, and $YZ$ planes. The BOX is defined by {\bf Point} as
 base position, and {\bf Dx, Dy, Dz} as BOX dimensions. Negative dimensions
 are allowed.
 Example:
@\begin{verbatim}
    B = BOX( vector( 0, 0, 0 ), 1, 1, 1);
@\end{verbatim}
 creates a unit cube from 0 to 1 in all axes.
@\subsubsection{BZR2BSP}
!BZR2BSP
@\begin{verbatim}
 CurveType BZR2BSP( CurveType Crv )
 SurfaceType BZR2BSP( SurfaceType Srf )
@\end{verbatim}
   Creates a Bspline curve or a Bspline surface from the given Bezier curve or
 Bezier surface. The Bspline curve or surface is assigned open end knot
 vector(s) with no interior knots, in the parametric domain of zero to one.
 Example:
@\begin{verbatim}
    BspSrf = BZR2BSP( BzrSrf );
@\end{verbatim}
@\subsubsection{BSP2BZR}
!BSP2BZR
@\begin{verbatim}
 CurveType | ListType BSP2BZR( CurveType Crv )
 SurfaceType | ListType BSP2BZR( SurfaceType Srf )
@\end{verbatim}
   Creates Bezier curve(s) or surface(s) from a given Bspline curve or a
 Bspline surface. The Bspline input is subdivided at all internal knots to
 create Bezier curves or surfaces. Therefore, if the input Bspline does have
 internal knots, a list of Bezier curves or surfaces is returned. Otherwise,
 a single Bezier curve or surface is returned.
 Example:
@\begin{verbatim}
    BzrCirc = BSP2BZR( circle( vector( 0.0, 0.0, 0.0 ), 1.0 ) );
@\end{verbatim}
 would subdivide the unit circle into four 90 degrees Bezier arcs returned
 in a list.
@\subsubsection{CBEZIER}
!CBEZIER
@\begin{verbatim}
 CurveType CBEZIER( ListType CtlPtList )
@\end{verbatim}
   Creates a Bezier curve out of the provided control point list. {\bf CtlPtList}
 is a list of control points, all of which must be of type (E1-E5, P1-P5),
 or regular PointType defining the curve's control polygon. Curve's point type
 will be of a space which is the union of the spaces of all points.
@The created curve is the polynomial (or rational),
@\begin{equation}
@     C(t) = \sum_{i=0}^k P_i B_i(t),
@\end{equation}
@where $P_i$ are the control points {\bf CtlPtList}, and k is the degree of
@the curve, which is one less than the number of points.
 Example:
@\begin{verbatim}
    s45 = sin(pi / 4);
    Arc90 = CBEZIER( list( ctlpt( P2, 1.0, 0.0, 1.0 ),
                           ctlpt( P2, s45, s45, s45 ),
                           ctlpt( P1, 1.0, 1.0 ) ) );
@\end{verbatim}
 constructs an arc of 90 degrees as a rational quadratic Bezier curve.
@\subsubsection{CBSPLINE}
!CBSPLINE
@\begin{verbatim}
 CurveType CBSPLINE( NumericType Order, ListType CtlPtList,
                                                        ListType KnotVector )
@\end{verbatim}
   Creates a Bspline curve out of the provided control point list, the
 knot vector, and the specified order. {\bf CtlPtList} is a list of control
 points, all of which must be of type (E1-E5, P1-P5), or regular PointType
 defining the curve's control polygon. Curve's point type will be of a space
 which is the union of the spaces of all points.
   The length of the {\bf KnotVector} must be equal to the number of control
 points in {\bf CtlPtList} plus the {\bf Order}. If, however, the length of
 the knot vector is equal to {\bf \#CtlPtList + Order + Order - 1} the curve
 is assumed {\em periodic.}
   The knot vector list may be specified as either {\bf list( KV\_OPEN )} or
 {\bf list( KV\_FLOAT )} or {\bf list( KV\_PERIODIC )} in which a uniform
 open, uniform floating or uniform periodic knot vector with the appropriate
 length is automatically constructed.
@The created curve is the piecewise polynomial (or rational),
@\begin{equation}
@     C(t) = \sum_{i=0}^k P_i B_{i,\tau}(t),
@\end{equation}
@where $P_i$ are the control points {\bf CtlPtList} and k is the degree of
@the curve, which is one less than the {\bf Order} or number of points.
@$\tau$ is the knot vector of the curve.
 Example:
@\begin{verbatim}
    s45 = sin(pi / 4);
    HalfCirc = CBSPLINE( 3,
                         list( ctlpt( P3,  1.0,  1.0,  0.0, 0.0 ),
                               ctlpt( P3,  s45,  s45,  s45, 0.0 ),
                               ctlpt( P3,  1.0,  0.0,  1.0, 0.0 ),
                               ctlpt( P3,  s45, -s45,  s45, 0.0 ),
                               ctlpt( P3,  1.0, -1.0,  0.0, 0.0 ) ),
                         list( 0, 0, 0, 1, 1, 2, 2, 2 ) );
@\end{verbatim}
 constructs an arc of 180 degrees in the XZ plane as a rational quadratic
 Bspline curve.
 Example:
@\begin{verbatim}
    c = CBSPLINE( 4,
                  list( ctlpt( E2,  0.5,  0.5 ),
                        ctlpt( E2, -0.5,  0.5 ),
                        ctlpt( E2, -0.5, -0.5 ),
                        ctlpt( E2,  0.5, -0.5 ) ),
                  list( KV_PERIODIC ) );
    color( c, red );
    viewobj( c );
    c1 = cregion( c, 3, 4 );
    color( c1, green );
    c2 = cregion( c, 4, 5 );
    color( c2, yellow );
    c3 = cregion( c, 5, 6 );
    color( c3, cyan );
    c4 = cregion( c, 6, 7 );
    color( c3, magenta );
    viewobj( list( c1, c2, c3, c4 ) );
@\end{verbatim}
 creates a periodic curve and extracts its four polynomial domains as four
 {\em open} end Bspline curves.
@See Figure~\ref{fig-cperiodic}.
@\begin{figure}
@\vspace{2.5in}
@\special{psfile=user_man/cperiod.ps hscale=100 vscale=100 hoffset=-40 voffset=-230}
@\caption{A cubic periodic curve created using KV\_PERIODIC end conditions.}
@\label{fig-cperiodic}
@\end{figure}
@\subsubsection{CCINTER}
!CCINTER
@\begin{verbatim}
 ListType CCINTER( CurveType Crv1, CurveType Crv2, NumericType Epsilon,
                                                       NumericType SelfInter )
 SurfaceType CCINTER( CurveType Crv1, CurveType Crv2, NumericType Epsilon,
                                                       NumericType SelfInter )
@\end{verbatim}
   Computes the intersection point(s) of {\bf Crv1} and {\bf Crv2} in the
 $XY$ plane. Since this computation involves numeric operations, {\bf Epsilon}
 controls the accuracy of the parametric values of the result.
   It returns a list of PointTypes, each containing the parameter of {\bf Crv1}
 in the X coordinate, and the parameter of {\bf Crv2} in the Y coordinate.
   If, however, {\bf Epsilon} is negative, a scalar field surface representing
 the square of the distance function is returned instead.
   If {\bf SelfInter} is TRUE, {\bf Crv1} and {\bf Crv2} can be the same
 curve, and self-intersection points are searched instead.
 Example:
@\begin{verbatim}
 crv1 = cbspline( 3,
                  list( ctlpt( E2, 0, 0 ),
                        ctlpt( E2, 0, 0.5 ),
                        ctlpt( E2, 0.5, 0.7 ),
                        ctlpt( E2, 1, 1 ) ),
                  list( KV_OPEN ) );
 crv2 = cbspline( 3,
                  list( ctlpt( E2, 1, 0 ),
                        ctlpt( E2, 0.7, 0.25 ),
                        ctlpt( E2, 0.3, 0.5 ),
                        ctlpt( E2, 0, 1 ) ),
                  list( KV_OPEN ) );
 inter_pts = CCINTER( crv1, crv2, 0.0001, FALSE );
@\end{verbatim}
 Computes the parameter values of the intersection point of {\bf crv1} and
 {\bf crv2} to a tolerance of 0.0001.
@See Figure~\ref{fig-cci}.
@\begin{figure}
@\vspace{2.5in}
@\special{psfile=user_man/cci.ps hscale=100 vscale=100 hoffset=-60 voffset=-200}
@\caption{A intersection point of two freeform curve computed using CCINTER.}
@\label{fig-cci}
@\end{figure}
@\subsubsection{CCRVTR}
!CCRVTR
@\begin{verbatim}
 NumericType CCRVTR( CurveType Crv, NumericType Epsilon )
 CurveType CCRVTR( CurveType Crv, NumericType Epsilon )
@\end{verbatim}
   Computes the extreme curvature points on {\bf Crv} in the $XY$ plane.
 This set includes not only points of maximum (convexity) and mimumum
 (concavity) curvature, but also points of zero curvature such as
 inflection points.
   Since this operation is partially numeric, {\bf Epsilon} is used to set
 the needed accuracy. It returns the parameter value(s) of the location(s)
 with extreme curvature along the {\bf Crv}.
   If, however, {\bf Epsilon} is negative, the curvature scalar field
 curve is returned as a two dimensional rational vector field curve, for
 which the first dimension is equal to the parameter, and the second is the
 curvature value at that parameter.
@   This function computes the curvature scalar field for planar curves as,
@\begin{equation}
@      \kappa(t) = \frac{x'(t) y''(t) - x''(t) y'(t)}
@             {\left( (x'(t))^2 + (y'(t))^2\ \right)^{\frac{3}{2}}},
@\end{equation}
@ and computes kN for three dimensional curves as the following vector field,
@\begin{equation}
@      \kappa(t) N(t) = \kappa(t) B(t) \times T(t) =
@       \frac{C' \times C''}{\| C' \| ^ 3} \times \frac{C'}{\| C' \|} =
@       \frac{(C' \times C'') \times C'}{\| C' \| ^ 4}.
@\end{equation}
^   This function computes the curvature scalar field for planar curves as,
^          x' y'' - x'' y'
^   k(t) = ----------------
^               2     2  3/2
^           ( x'  + y'  )
^ and computes kN for three dimensional curves as the following vector field,
^                                  C' x C''     C'    (C' x C'') x C'
^   k(t) N(t) = K(t) B(t) x T(t) = -------- x ----- = ---------------
^                                        3    | C' |            4
^                                   | C'|                 | C' |
 The extremum values are extracted from the computed curvature field.
 This curvature field is a high order curve, even if the input geometry is
 of low order. This is especially true for rational curves, for which the
 quotient rule for differentiation is used and almost doubles the degree
 in every differentiation.
 See also CZEROS, CEXTREMES, and SCRVTR.
 Example:
@\begin{verbatim}
 crv = cbezier( list( ctlpt( E2, -1.0,  0.5 ),
                      ctlpt( E2, -0.5, -2.0 ),
                      ctlpt( E2,  0.0,  1.0 ),
                      ctlpt( E2,  1.0,  0.0 ) ) ) * rotz( 30 );
 crvtr = CCRVTR( crv, 0.001 );
 pt_crvtr = nil();
 pt = nil();
 for ( i = 1, 1, sizeof( crvtr ),
     ( pt = ceval( crv, nth( crvtr, i ) ) ):
     snoc( pt, pt_crvtr )
 interact( list( crv, pt_crvtr ) );
@\end{verbatim}
 finds the extreme curvature points in {\bf Crv} and displays them all
 with the curve.
@See Figure~\ref{fig-ccrvtr}.
@\begin{figure}
@\vspace{2.3in}
@\special{psfile=user_man/ccrvtr.ps hscale=100 vscale=100 hoffset=-40 voffset=-220}
@\caption{Extreme curvature locations on a freeform curve computed using CCRVTR.}
@\label{fig-ccrvtr}
@\end{figure}
@\subsubsection{CDERIVE}
!CDERIVE
@\begin{verbatim}
 CurveType CDERIVE( CurveType Curve )
@\end{verbatim}
   Returns a vector field curve representing the differentiated curve,
 also known as the Hodograph curve.
 Example:
@\begin{verbatim}
 Circ = circle( vector( 0.0, 0.0, 0.0 ), 1.0 );
 Hodograph = CDERIVE( Circ );
@\end{verbatim}
@See Figure~\ref{fig-cderive}.
@\begin{figure}
@\vspace{3.5in}
@\special{psfile=user_man/cderive.ps hscale=100 vscale=100 hoffset=-40 voffset=-210}
@\caption{The hodograph (thick) of a bspline circle (thin) constructed as four
@        90 degrees rational bezier arcs, computed using CDERIVE.}
@\label{fig-cderive}
@\end{figure}
@\subsubsection{CDIVIDE}
!CDIVIDE
@\begin{verbatim}
 ListType CDIVIDE( CurveType Curve, NumericType Param )
@\end{verbatim}
   Subdivides a curve into two sub-curves at the specified parameter value.
 {\bf Curve} can be either a Bspline curve in which {\bf Param} must be
 within the Curve's parametric domain, or a Bezier curve in which {\bf Param}
 must be in the range of zero to one.
   It returns a list of the two sub-curves. The individual curves may be
 extracted from the list using the NTH command.
 Example:
@\begin{verbatim}
 CrvLst = CDIVIDE( Crv, 1.3 );
 Crv1 = nth( CrvLst, 1 );
 Crv2 = nth( CrvLst, 2 );
@\end{verbatim}
 subdivides the curve {\bf Crv} at the parameter value of 0.5.
@See Figure~\ref{fig-cdivide}.
@\begin{figure}
@\vspace{2.7in}
@\special{psfile=user_man/cdivide.ps hscale=80 vscale=80 hoffset=30 voffset=-140}
@\caption{A Bspline curve is subdivided into two distinct regions using CDIVIDE.}
@\label{fig-cdivide}
@\end{figure}
@\subsubsection{CEDITPT}
!CEDITPT
@\begin{verbatim}
 CurveType CEDITPT( CurveType Curve, CtlPtType CtlPt, NumericType Index )
@\end{verbatim}
   Provides a simple mechanism to manually modify a single control point number
 {\bf Index} (base count is 0) in {\bf Curve}, by substituting {\bf CtlPt}
 instead. {\bf CtlPt} must have the same point type as the control points of
 the  {\bf Curve}. Original curve {\bf Curve} is not modified.
 Example:
@\begin{verbatim}
    CPt = ctlpt( E3, 1, 2, 3 );
    NewCrv = CEDITPT( Curve, CPt, 1 );
@\end{verbatim}
 constructs a {\bf NewCrv} with the second control point of {\bf Curve} being
 {\bf CPt}.
@\subsubsection{CEVAL}
!CEVAL
@\begin{verbatim}
 CtlPtType CEVAL( CurveType Curve, NumericType Param )
@\end{verbatim}
   Evaluates the provided {\bf Curve} at the given {\bf Param} value.
 {\bf Param} should be in the curve's parametric domain if {\bf Curve} is
 a Bspline curve, or between zero and one if {\bf Curve} is a Bezier curve.
 The returned control point has the same point type as the control points
 of the {\bf Curve}.
 Example:
@\begin{verbatim}
    CPt = CEVAL( Crv, 0.25 );
@\end{verbatim}
 evaluates {\bf Crv} at the parameter value of 0.25.
@\subsubsection{CEVOLUTE}
!CEVOLUTE
@\begin{verbatim}
 CurveType CEVOLUTE( CurveType Curve )
@\end{verbatim}
   Computes the evolute of a curve. The evolute is defined as,
@\begin{equation}
@  E(t) = C(t) + \frac{N(t)}{\kappa(t)},
@\end{equation}
@ where $N(t)$ is the unit normal of $C(t)$ and $k(t)$ is its curvature.
@  $E(t)$ is computed symbolically as the symbolic sum of $C(t)$ and
@ $\frac{N(t)}{\kappa(t)}$ where the latter is,
@\begin{eqnarray}
@  \frac{N(t)}{\kappa(t)}
@ & = & \frac{\kappa(t) N(t)}{k^2(t)} \nonumber \\
@ & = & \frac{(C'(t) \times C''(t)) \times C'(t)}
@             {\| C'(t) \|^4}
@       \frac{\|C'(t)\|^6}
@            {(C'(t) \times C''(t))^2}  \nonumber \\
@ & = & \frac{\left( {(C'(t) \times C''(t)) \times C'(t)} \right)
@                                        \| C'(t) \|^2}
@             {(C'(t) \times C''(t))^2}
@\end{eqnarray}
^               N(t)
^ E(t) = C(t) + ----
^               k(t)
^ where N(t) is the unit normal of C(t) and k(t) is its curvature.
^ E(t) is computed symbolically as the symbolic sum of C(t) and
^ N(t) / k(t).
 The result of this symbolic computation is exact (upto machine precision)
 unlike a similar operation which is only approximated, the OFFSET or the
 AOFFSET.
 Example:
@\begin{verbatim}
    crv = cbspline( 3,
                    list( ctlpt( E3, -1.0,  0.1,  0.2 ),
                          ctlpt( E3, -0.1,  1.0,  0.1 ),
                          ctlpt( E3,  0.1,  0.1,  1.0 ),
                          ctlpt( E3,  1.0,  0.1,  0.1 ),
                          ctlpt( E3,  0.1,  1.0,  0.2 ) ),
                    list( KV_OPEN ) );
    cev = CEVOLUTE( Crv );
@\end{verbatim}
@See Figure~\ref{fig-cevolute}.
@\begin{figure}
@\vspace{2in}
@\special{psfile=user_man/cevolute.ps hscale=100 vscale=100 hoffset=-20 voffset=-260}
@\caption{The evolute (thick) of a freeform curve (thin) can be computed using
@        CEVOLUTE.}
@\label{fig-cevolute}
@\end{figure}
@\subsubsection{CEXTREMES}
!CEXTREMES
@\begin{verbatim}
 ListType CEXTREMES( CurveType Crv, NumericType Epsilon, NumericType Axis )
@\end{verbatim}
   Computes the extreme set of the given {\bf Crv} in the given axis (1 for X,
 2 for Y, 3 for Z). Since this computation is numeric, an {\bf Epsilon} is
 also required to specify the desired tolerance. It returns a list of
 all the parameter values (NumericType) in which the curve takes an extreme
 value.
 Example:
@\begin{verbatim}
    extremes = CEXTREMES( Crv, 0.0001, 1 );
@\end{verbatim}
 Computes the extreme set of curve {\bf crv}, in the {\bf X} axis, with
 error tolerance of {\bf 0.0001}. See also CZERO.
@See Figure~\ref{fig-cextreme}.
@\begin{figure}
@\vspace{2in}
@\special{psfile=user_man/cextreme.ps hscale=100 vscale=100 hoffset=-40 voffset=-330}
@\caption{The X local extremums of a freeform curve are isolated using CEXTREMES.}
@\label{fig-cextreme}
@\end{figure}
@\subsubsection{CINFLECT}
!CINFLECT
@\begin{verbatim}
 ListType CINFLECT( CurveType Crv, NumericType Epsilon )
 CurveType CINFLECT( CurveType Crv, NumericType Epsilon )
@\end{verbatim}
   Computes the inflection points of {\bf Crv} in the $XY$ plane.
 Since this computation is numeric, an {\bf Epsilon} is also required
 to specify the desired tolerance. It returns a list of all the
 parameter values (NumericType) in which the curve has an inflection point.
   If, however, {\bf Epsilon} is negative, a scalar field curve representing
 the sign of the curvature of the curve is returned instead.
@ The sign of curvature scalar field is equal to,
@\begin{equation}
@      \sigma(t) = x'(t) y''(t) - x''(t) y'(t).
@\end{equation}
^ The sign of curvature scalar field is equal to
^       s(t) = x' y'' - x'' y'
 Example:
@\begin{verbatim}
    inflect = CINFLECT( crv, 0.001 );
    pt_inflect = nil();
    pt = nil();
    for ( i = 1, 1, sizeof( inflect ),
            pt = ceval( crv, nth( inflect, i ) ):
            snoc( pt, pt_inflect )
        );
    interact( list( axes, crv, pt_inflect ), 0);
@\end{verbatim}
 Computes the set of inflection points of curve {\bf crv} with error
 tolerance of {\bf 0.001}. This set is then scanned in a loop and
 evaluated to the curve's locations which are then displayed with the {\bf crv}.
 See also CZEROS, CEXTREMES, and CCRVTR.
@See Figure~\ref{fig-cinflect}.
@\begin{figure}
@\vspace{1.2in}
@\special{psfile=user_man/cinflect.ps hscale=100 vscale=100 hoffset=-40 voffset=-310}
@\caption{The Inflection points of a freeform curve can be isolated using CINFLECT.}
@\label{fig-cinflect}
@\end{figure}
@\subsubsection{CINTERP}
!CINTERP
@\begin{verbatim}
 CurveType CINTERP( ListType PtList, NumericType Order, NumericType Size,
                                                        ConstantType Param)
@\end{verbatim}
   Computes a Bspline polynomial curve that interpolates or approximates
 the list of points in {\bf PtList}. The Bspline curve will have order
 {\bf Order} and {\bf Size} control points. The knots will be spaced
 according to {\bf Param} which can be one of PARAM\_UNIFORM,
 PARAM\_CHORD or PARAM\_CENTRIP. The former prescribes a uniform knot
 sequence and the latters specify knot spacing according to the chord
 length and a square root of the chord length.
   All points in {\bf PtList} must be of type (E1-E5, P1-P5) control point,
 or regular PointType. If {\bf Size} is equal to the number of points in
 {\bf PtList} the resulting curve will {\em interpolate} the data set.
 Otherwise, if {\bf Size} is less than the number of points in {\bf PtList}
 the point data set will be least square approximated. In no time can {\bf Size}
 be larger that the number of points in {\bf PtList} or lower than {\bf Order}.
 {\bf Size} of zero forces interpolation by setting {\bf Size} to the
 data set size.
   All interior knots will be distinct preserving maximal continuity.
 The resulting Bspline curve will have open end conditions.
 Example:
@\begin{verbatim}
    pl = nil();
    for ( x = 0, 1, 100,
          snoc(point(cos(x / 5), sin(x / 5), x / 50 - 1), pl)
    );
    c = CINTERP( pl, 3, 21, PARAM_UNIFORM );
@\end{verbatim}
 Samples a helical curve at 100 points and least square fit a quadratic
 Bspline curve with 21 point to the data set. The curve will have a uniform
 knot spacing.
@See Figure~\ref{fig-cinterp}.
@\begin{figure}
@\vspace{2.6in}
@\special{psfile=user_man/cinterp.ps hscale=100 vscale=100 hoffset=-40 voffset=-150}
@\caption{A Helix is sampled at 100 locations is least square fit using CINTERP
@        by a quadratic Bspline curve and 21 control points.}
@\label{fig-cinterp}
@\end{figure}
@\subsubsection{CIRCLE}
!CIRCLE
@\begin{verbatim}
 CurveType CIRCLE( VectorType Center, NumericType Radius )
@\end{verbatim}
   Constructs a circle at the specified {\bf Center} with the specified
 {\bf Radius}. The returned circle is a Bspline curve of four piecewise Bezier
 90 degree arcs. The construced circle is always parallel to the $XY$ plane.
 Use the linear transformation routines to place the circle in the appropriate
 orientation and location.
@\subsubsection{CIRCPOLY}
!CIRCPOLY
@\begin{verbatim}
 PolygonType CIRCPOLY( VectorType Normal, VectorType Trans, NumericType Radius )
@\end{verbatim}
   Defines a circular polygon in a plane perpendicular to {\bf Normal} that
 contains the {\bf Trans} point. Constructed polygon is centered at
 {\bf Trans}. RESOLUTION vertices will be defined with {\bf Radius} from
 distance from {\bf Trans}.
   Alternative ways to construct a polygon are manual construction of the
 vertices using POLY, or the construction of a flat ruled surface using
 RULEDSRF.
@\subsubsection{CLNTREAD}
!CLNTREAD
@\begin{verbatim}
 AnyType CLNTREAD( NumericType Handler, NumericType Block )
@\end{verbatim}
   Reads one object from a communication channel of a client.
 {\bf Handler} contains the index of the communication channel opened via
 CLNTEXEC. If no data is available in the communication channel, this
 function will block for at most {\bf Block} millisecond until data is found
 or timeout occurs. In the latter, a single StringType object is returned
 with the content of "no data (timeout)".  See also CLNTWRITE, CLNTCLOSE,
 and CLNTEXEC.
 Example:
@\begin{verbatim}
   h2 = clntexec( "xmtdrvs -s-" );
       .
       .
   Model = CLNTREAD( h2 );
       .
       .
   clntclose( h2,TRUE );
@\end{verbatim}
 reads one object from client through communication channel h2 and save it
 in variable Model.
@\subsubsection{CMORPH}
!CMORPH
@\begin{verbatim}
 CurveType CMORPH( CurveType Crv1, CurveType Crv2,
                   NumericType Method, NumericType Blend )
 ListType CMORPH( CurveType Crv1, CurveType Crv2,
                  NumericType Method, NumericType Blend )
@\end{verbatim}
 Creates a new curve which is a {\em metamorph} of the two given curves.
 The two given curves must be compatible (see FFCOMPAT) before this blend
 is invoked. Very useful if a sequence that "morphs" one curve to another
 is to be created. Several methods of metamorphosis are supported according
 to the value of {\bf Method},
# 3 2 0 1
  Simple convex blend.
  Corner/Edge cutting scheme, scaled to same curve length.
  Corner/Edge cutting scheme, scaled to same bounding box.
  Same as 1 but with filtering out of tangencies.
  Same as 2 but with filtering out of tangencies.
  Multiresolution decompsition based metamorphosis. See CMULTRES.
   In {\bf Method} 1, {\bf Blend} is a number between zero ({\bf Crv1})
 and one ({\bf Crv2}) defining the similarity to {\bf Crv1} and {\bf Crv2},
 respectively. A single curve is returned.
   In {\bf Method}s 2 to 5, {\bf Blend} is a step size for the
 metamorphosis operation and a whole list describing the entire
 metamorphosis operation is returned.
 Examples:
@\begin{verbatim}
 crv1 = cbezier( list( ctlpt( E2,  0.3,  0.0 ),
                       ctlpt( E2,  0.0,  0.5 ),
                       ctlpt( E2, -0.2,  0.0 ) ) );
 crv1a = crv1 * trans( vector( -0.4, 0.0, 0.0 ) );
 crv1b = crv1a * scale( vector( -1.0, 1.0, 1.0 ) );
 for ( i = 0, 1, 300,
     c = cmorph( crv1a, crv1b, 0, i / 300.0 ):
     color( c, yellow ):
     viewobj( c )
 crvs = cmorph( crv1a, crv1b, 2, 0.003 );
 snoc( crv1b, crvs );
 for ( i = 1, 1, sizeof( crvs ),
     c = nth( crvs, i ):
     color( c, yellow ):
     viewobj( c )
@\end{verbatim}
 creates two metamorphosis animation sequences, one that is based on
 a convex blend and one that is based on corner/edge cutting scheme.
 See alost SMORPH.
@See Figure~\ref{fig-cmorph}.
@\begin{figure}
@\begin{picture}(0,200)
@    \put(110,  0){\large (a)}
@    \put(320,  0){\large (b)}
@\end{picture}
@\special{psfile=user_man/cmorph.ps hscale=100 vscale=100 hoffset=-50 voffset=-260}
@\caption{A morphing sequence using convex blend (a) and edge cutting (b).}
@\label{fig-cmorph}
@\end{figure}
@\subsubsection{CMULTIRES}
!CMULTIRES
@\begin{verbatim}
 ListType CMULTIRES( CurveType Crv, NumericType Discont )
@\end{verbatim}
   Computes a multiresolution decomposition of curve {\bf Crv} using least
 squares approximation. The resulting list of curves describes an hierarchy
 of curves in linear subspaces of the space {\bf Crv} was in that can be
 sum algebraically to form {\bf Crv}. Each of the curves in the hierarchy
 is a least squares approximation of {\bf Crv} in the subspace it is defined
 in. {\bf Discont} is a boolean flat that controls the way tangent
 discontinuities are computed throughout the decomposition.
 Example:
@\begin{verbatim}
    MRCrv = CMULTIRES( Animal, false );
    sum = nth( MRCrv, 1 );
    MRCrvs = list( sum * tx( 3.0 ) );
    for ( ( i = 2 ), 1, sizeof( MRCrv ),
        sum = symbsum( sum, nth( MRCrv, i ) ):
        snoc( sum * tx( ( 3 - i ) * 1.5 ), MRCrvs )
    );
    All = MRCrvs * sc ( 0.25 );
    view( All, on );
@\end{verbatim}
 Computes a multiresolution decomposition to curve {\bf CrossSec} as
 {\bf MRCrv} and display all the decomposition levels by summing them all
 up. The use of {\bf none} as on object name allows one to display an
 object in the display device without replacing the previous object in the
 display device, carrying the same name.
 creates two metamorphosis animation sequences, one that is based on
 a convex blend and one that is based on corner/edge cutting scheme.
@See Figure~\ref{fig-cmultres}.
@\begin{figure}
@\vspace{1.2in}
@\special{psfile=user_man/cmultres.ps hscale=100 vscale=100 hoffset=-50 voffset=-280}
@\caption{A multiresolution decomposition of a curve of an animal using
@         list squares. Original curve is shown on the left.}
@\label{fig-cmultres}
@\end{figure}
@\subsubsection{CMESH}
!CMESH
@\begin{verbatim}
 CurveType CMESH( SurfaceType Srf, ConstantType Direction, NumericType Index )
@\end{verbatim}
   Returns a single ROW or COLumn as specified by the {\bf Direction} and
 {\bf Index} (base count is 0) of the control mesh of surface {\bf Srf}.
   The returned curve will have the same knot vector as {\bf Srf} in the
 appropriate direction. See also CSURFACE.
   This curve is {\em not} necessarily in the surface {\bf Srf}.
@It is equal to,
@\begin{equation}
@     C(t) = \sum_{i=0}^m P_{ij} B_i(t),
@\end{equation}
@and similar for the other parametric direction.
 Example:
@\begin{verbatim}
    Crv = CMESH( Srf, COL, 0 );
@\end{verbatim}
 extracts the first column of surface {\bf Srf} as a curve. See also
 CSURFACE.
@\subsubsection{COERCE}
!COERCE
@\begin{verbatim}
 AnyType COERCE( AnyType Object, ConstantType NewType )
@\end{verbatim}
   Provides a coercion mechanism between different objects or object types.
 PointType, VectorType, PlaneType, CtlPtType can be all coerced to each
 other by using the {\bf NewType} of POINT\_TYPE, VECTOR\_TYPE, PLANE\_TYPE,
 or one of E1-E5, P1-P5 (CtlPtType). Similarly, CurveType, SurfaceType,
 TrimSrfType, and TrivarType can all be coerced to hold different
 CtlPtType of control points, or even different open end conditions from
 KV\_PERIODIC to KV\_FLOAT to KV\_OPEN.
   If a scalar (E1 or P1) curve is coerced to E2 or P2 curve or
 a scalar (E1 or P1) surface is coerced to E3 or P3 surface, the Y (YZ)
 coordinate(s) is (are) updated to hold the parametric domain of the curve
 (surface).
 Example:
@\begin{verbatim}
    CrvE2 = COERCE( Crv, E2 );
@\end{verbatim}
 coerce {\bf Crv} to a new curve that will have an E2 CtlPtType control
 points. Coerction of a projective curve (P1-P5) to a Euclidean curve
 (E1-E5) does not preseve the shape of the curve.
@\subsubsection{COMPOSE}
!COMPOSE
@\begin{verbatim}
 CurveType COMPOSE( CurveType Crv1, CurveType Crv2 )
 CurveType COMPOSE( SurfaceType Srf, CurveType Crv )
@\end{verbatim}
   Symbolically compute the composition curve {\bf Crv1(Crv2(t))} or
 {\bf Srf(Crv(t))}. In {\bf Crv1(Crv2(t)}, {\bf Crv1} can be any curve
 while {\bf Crv2} must be a one-dimensional curve that is either E1 or
 P1. In {\bf Srf(Crv(t))}, {\bf Srf} can be any surface, while {\bf Crv}
 must be a two-dimensional curve, that is either E2 or P2. Both {\bf Crv2}
 in the curve's composition, and {\bf Crv} is the surface's composition
 must be contained in the curve or surface parametric domain.
 Example:
@\begin{verbatim}
   srf = sbezier( list( list( ctlpt( E3, 0.0, 0.0, 0.0 ),
                              ctlpt( E3, 0.0, 0.5, 1.0 ),
                              ctlpt( E3, 0.0, 1.0, 0.0 ) ),
                        list( ctlpt( E3, 0.5, 0.0, 1.0 ),
                              ctlpt( E3, 0.5, 0.5, 0.0 ),
                              ctlpt( E3, 0.5, 1.0, 1.0 ) ),
                        list( ctlpt( E3, 1.0, 0.0, 1.0 ),
                              ctlpt( E3, 1.0, 0.5, 0.0 ),
                              ctlpt( E3, 1.0, 1.0, 1.0 ) ) ) );
   crv = coerce( circle( vector( 0.0, 0.0, 1.0 ), 0.4 ), p2 ) *
         trans( vector( 0.5, 0.5, 0.0 ) );
   comp_crv = COMPOSE( srf, crv );
@\end{verbatim}
 compose a circle {\bf Crv} to be on the surface {\bf Srf}.
@See Figure~\ref{fig-compose}.
@\begin{figure}
@\vspace{2.5in}
@\special{psfile=user_man/compose.ps hscale=100 vscale=100 hoffset=-10 voffset=-210}
@\caption{A circle in the parametric space of the freefrom surface is composed
@        to create a closed loop curve on the surface using COMPOSE.}
@\label{fig-compose}
@\end{figure}
@\subsubsection{CON2}
!CON2
@\begin{verbatim}
 PolygonType CON2( VectorType Center, VectorType Direction,
                   NumericType Radius1, NumericType Radius2 )
@\end{verbatim}
   Creates a truncated CONE geometric object, defined by {\bf Center} as the
 center of the main base of the CONE, {\bf Direction} as both the CONE's axis
 and the length of CONE, and the two radii {\bf Radius1/2} of the two bases of
 the CONE.
   Unlike the regular cone (CONE) constructor which has inherited
 discontinuities in its generated normals at the apex, CON2 can be used to
 form a (truncated) cone with continuous normals.
   See RESOLUTION for the accuracy of the CON2 approximation as a polygonal
 model.
 Example:
@\begin{verbatim}
    Cone2 = CON2( vector( 0, 0, -1 ), vector( 0, 0, 4 ), 2, 1 );
@\end{verbatim}
 constructs a truncated cone with bases parallel to the $XY$ plane at
 $Z = -1$ and $Z = 3$, and with radii of 2 and 1 respectively.
@See Figure~\ref{fig-cones}.
@\begin{figure}
@\vspace{2.7in}
@\special{psfile=user_man/cones.ps hscale=100 vscale=100 hoffset=0 voffset=-220}
@\caption{A cone (left) can be constructed using the CONE constructor and
@         a truncated cone (right) using the constructor CONE2.}
@\label{fig-cones}
@\end{figure}
@\subsubsection{CONE}
!CONE
@\begin{verbatim}
 PolygonType CONE( VectorType Center, VectorType Direction,
                   NumericType Radius )
@\end{verbatim}
   Creates a CONE geometric object, defined by {\bf Center} as the center of
 the base of the CONE, {\bf Direction} as the CONE's axis and height, and
 {\bf Radius} as the radius of the base of the CONE.
   See RESOLUTION for accuracy of the CONE approximation as a polygonal model.
 Example:
@\begin{verbatim}
    Cone1 = CONE( vector( 0, 0, 0 ), vector( 1, 1, 1 ), 1 );
@\end{verbatim}
 constructs a cone based in an $XY$ parallel plane, centered at the origin
 with radius 1 and with tilted apex at ( 1, 1, 1 ).
   See also CON2.
@See Figure~\ref{fig-cones}.
@\subsubsection{CONVEX}
!CONVEX
@\begin{verbatim}
 PolygonType CONVEX( PolygonType Object )
 ListType CONVEX( ListType Object )
@\end{verbatim}
   Converts non-convex polygons in {\bf Object}, into convex ones. New vertices
 are introduced into the polygonal data during this process. The Boolean
 operations require the input to have convex polygons only (although it may
 return non convex polygons...) and it automatically converts non-convex input
 polygons to convex ones, using this same routine.
   However, some external tools (like irit2ray and poly3d-h) require convex
 polygons. This function must be used on the objects to guarantee that
 only convex polygons are saved into data files for these external tools.
@\begin{verbatim}
    CnvxObj = CONVEX( Obj );
    save( "data", CnvxObj );
@\end{verbatim}
 converts non-convex polygons into convex ones, so that the data file can be
 used by external tools requiring convex polygons.
@\subsubsection{COORD}
!COORD
@\begin{verbatim}
 AnyType COORD( AnyType Object, NumericType Index )
@\end{verbatim}
   Extracts an element from a given {\bf Object}, at index {\bf Index}. From
 a PointType, VectorType, PlaneType, CtlPtType and MatrixType, a NumericType
 is returned with {\bf Index} 0 for the X axis, 1 for the Y axis etc.
 {\bf Index} 0 denotes the weight of CtlPtType. For a PolygonType that
 contains more than one polygon, the {\bf Index}th polygon is returned. For
 a PolygonType that contains a single Polygon, the {\bf Index}th vertex is
 returned. For a CurveType or a SurfaceType, the {\bf Index}th CtlPtType is
 returned. For a ListType, COORD behaves like NTH and returns the {\bf Index}th
 object in the list.
 Example:
@\begin{verbatim}
    a = vector( 1, 2, 3 );
    vector( COORD( a, 0 ), COORD( a, 1 ), COORD( a, 2 ) );
    a = ctlpt( P2, 6, 7, 8, 9 );
    ctlpt( P3, coord( a, 0 ), coord( a, 1 ), coord( a, 2 ), coord( a, 3 ) );
    a = plane( 10, 11, 12, 13 );
    plane( COORD( a, 0 ), COORD( a, 1 ), COORD( a, 2 ), COORD( a, 3 ) );
@\end{verbatim}
 constructs a vector/ctlpt/plane and reconstructs it by extracting the
 constructed scalar components of the objects using COORD.
   See also COERCE.
@\subsubsection{CRAISE}
!CRAISE
@\begin{verbatim}
 CurveType CRAISE( CurveType Curve, NumericType NewOrder )
@\end{verbatim}
   Raise {\bf Curve} to the {\bf NewOrder} Order specified.
 Example:
@\begin{verbatim}
    Crv = cbezier( list( ctlpt( E2, -0.7,  0.3 ),
                         ctlpt( E2,  0.0,  1.0 ),
                         ctlpt( E2,  0.7,  0.0 ) ) );
    Crv2 = CRAISE( Crv, 5 );
@\end{verbatim}
 raises the 90 degrees corner Bezier curve {\bf Crv} to be a quartic.
@See Figure~\ref{fig-craise}.
@\begin{figure}
@\vspace{2.5in}
@\special{psfile=user_man/craise.ps hscale=70 vscale=70 hoffset=30 voffset=-220}
@\caption{Raises a 90 degrees corner quadratic Bezier curve to a quintic
@        using CRAISE. The control polygons are also shown.}
@\label{fig-craise}
@\end{figure}
@\subsubsection{CREFINE}
!CREFINE
@\begin{verbatim}
 CurveType CREFINE( CurveType Curve, NumericType Replace, ListType KnotList )
@\end{verbatim}
   Provides the ability to {\bf Replace} a knot vector of {\bf Curve}, or refine
 it. {\bf KnotList} is a list of knots to refine {\bf Curve} at. All knots
 should be contained in the parametric domain of the {\bf Curve}. If the knot
 vector is replaced, the length of {\bf KnotList} should be identical to the
 length of the original knot vector of the {\bf Curve}. If {\bf Curve} is a
 Bezier curve, it is automatically promoted to be a Bspline curve.
 Example:
@\begin{verbatim}
    Crv2 = CREFINE( Crv, FALSE, list( 0.25, 0.5, 0.75 ) );
@\end{verbatim}
 refines {\bf Crv} and adds three new knots at 0.25, 0.5, and 0.75.
@See Figure~\ref{fig-crefine}.
@\begin{figure}
@\vspace{2.5in}
@\special{psfile=user_man/crefine.ps hscale=70 vscale=70 hoffset=30 voffset=-230}
@\caption{Refines a 90 degrees corner quadratic Bezier curve at three interior
@        knots (result is a Bspline curve) using CREFINE.
@        The control polygons are also shown.}
@\label{fig-crefine}
@\end{figure}
@\subsubsection{CREGION}
!CREGION
@\begin{verbatim}
 CurveType CREGION( CurveType Curve, NumericType MinParam,
                                                       NumericType MaxParam )
@\end{verbatim}
   Extracts a region from {\bf Curve} between {\bf MinParam} and {\bf MaxParam}.
 Both {\bf MinParam} and {\bf MaxParam} should be contained in the
 parametric domain of the {\bf Curve}.
 Example:
@\begin{verbatim}
    SubCrv = CREGION( Crv, 0.3, 0.6 );
@\end{verbatim}
 extracts the region from {\bf Crv} from the parameter value 0.3 to the
 parameter value 0.6.
@See Figure~\ref{fig-cregion}.
@\begin{figure}
@\vspace{2.5in}
@\special{psfile=user_man/cregion.ps hscale=70 vscale=70 hoffset=30 voffset=-230}
@\caption{Extracts a sub region from a curve using CREGION.}
@\label{fig-cregion}
@\end{figure}
@\subsubsection{CREPARAM}
!CREPARAM
@\begin{verbatim}
 CurveType CREPARAM( CurveType Curve, NumericType MinParam,
                                                       NumericType MaxParam )
@\end{verbatim}
   Reparametrize {\bf Curve} over a new domain from {\bf MinParam} to {\bf MaxParam}.
 This operation does not affect the geometry of the curve and only affine
 transforms its knot vector. A Bezier curve will automatically be promoted
 into a Bspline curve by this function.
 Example:
@\begin{verbatim}
    arc1 = arc( vector( 0.0, 0.0, 0.0 ),
                vector( 0.5, 2.0, 0.0 ),
                vector( 1.0, 0.0, 0.0 ) );
    crv1 = arc( vector( 1.0, 0.0, 0.75 ),
                vector( 0.75, 0.0, 0.7 ),
                vector( 0.5,  0.0, 0.85 ) ) +
           arc( vector( 0.5,  0.0, 0.75 ),
                vector( 0.75, 0.0, 0.8 ),
                vector( 1.0,  0.0, 0.65 ) );
    arc1 = CREPARAM( arc1, 0, 10 );
    crv1 = CREPARAM( crv1, 0, 10 );
@\end{verbatim}
 Sets the domain of the given two curves to be from zero to ten. The
 Bezier curve arc1 is promoted to a Bspline curve.
@\subsubsection{CROSSEC}
!CROSSEC
@\begin{verbatim}
 PolygonType CROSSEC( PolygonType Object )
@\end{verbatim}
;   Invoke interactive mode to edit/create a polygon in the plane Z = 0. The
; polygon must be in the domain [0..1] in X,Y. The first polygon of the given
; Object is copied to begin with. If the given {\bf Operand} is NOT a geometric
; object, but FALSE (numeric 0.0), a new polygon is created. Returns an (open)
; object with this one polygon only and inside side of $+Z$. Note that if the
; given polygon (first polygon of Object) is not on the $XY$ plane, it is transformed
; to it before editing, and transformed back after.
   This feature is NOT implemented.
@\subsubsection{CRVLNDST}
!CRVLNDST
@\begin{verbatim}
 NumericType CRVLNDST( CurveType Crv, PointType PtOnLine, VectorType LnDir,
                                 NumericType IsMinDist, NumericType Epsilon )
 ListType CRVLNDST( CurveType Crv, PointType PtOnLine, VectorType LnDir,
                                NumericType IsMinDist, NumericType Epsilon )
@\end{verbatim}
   Computes the closest (if {\bf IsMinDist} is TRUE, farthest if FALSE) point
 on {\bf Curve} to the line specified by {\bf PtOnLine} and {\bf LnDir} as a
 point on the line and a line direction.
   Since this operation is partially numeric, {\bf Epsilon} is used to set
 the needed accuracy. It returns the parameter value of the location on
 {\bf Crv} closest to the line.
   If, however, {\bf Epsilon} is negative, -{\bf Epsilon} is used instead,
 and all local extrema in the distance function are returned as a list
 (both minima and maxima).
   If the line and the curve intersect, the point of intersection is
 returned as the minimum.
 Example:
@\begin{verbatim}
    Param = CRVLNDST( Crv, linePt, lineVec, TRUE, 0.001 );
@\end{verbatim}
 finds the closest point on {\bf Crv} to the line defined by {\bf linePt}
 and {\bf lineVec}.
@See Figure~\ref{fig-crvlndst}.
@\begin{figure}
@\vspace{2.2in}
@\special{psfile=user_man/crvlndst.ps hscale=100 vscale=100 hoffset=-40 voffset=-240}
@\caption{Computes the locations on the freeform curve with local extreme
@        distance to the given line, using CRVLNDST.}
@\label{fig-crvlndst}
@\end{figure}
@\subsubsection{CRVPTDST}
!CRVPTDST
@\begin{verbatim}
 NumericType CRVPTDST( CurveType Crv, PointType Point, NumericType IsMinDist,
                                                         NumericType Epsilon )
 ListType CRVPTDST( CurveType Crv, PointType Point, NumericType IsMinDist,
                                                         NumericType Epsilon )
@\end{verbatim}
   Computes the closest (if {\bf IsMinDist} is TRUE, farthest if FALSE) point
 on {\bf Crv} to {\bf Point}.
   Since this operation is partially numeric, {\bf Epsilon} is used to set
 the needed accuracy. It returns the parameter value of the location on
 {\bf Crv} closest to {\bf Point}.
   If, however, {\bf Epsilon} is negative, -{\bf Epsilon} is used instead,
 and all local extrema in the distance function are returned as a list
 (both minima and maxima).
 Example:
@\begin{verbatim}
    Param = CRVPTDST( Crv, Pt, FALSE, 0.0001 );
@\end{verbatim}
 finds the farthest point on {\bf Crv} from point {\bf Pt}.
@See Figure~\ref{fig-crvptdst}.
@\begin{figure}
@\vspace{2.2in}
@\special{psfile=user_man/crvptdst.ps hscale=100 vscale=100 hoffset=-40 voffset=-240}
@\caption{Computes the locations on the freeform curve with local extreme
@        distance to the given point, using CRVPTDST.}
@\label{fig-crvptdst}
@\end{figure}
@\subsubsection{CSURFACE}
!CSURFACE
@\begin{verbatim}
 CurveType CSURFACE( SurfaceType Srf, ConstantType Direction,
                                                          NumericType Param )
@\end{verbatim}
   Extract an isoparametric curve out of {\bf Srf} in the specified
 {\bf Direction} (ROW or COL) at the specified parameter value {\bf Param}.
 {\bf Param} must be contained in the parametric domain of {\bf Srf} in
 {\bf Direction} direction.
 The returned curve is {\em in} the surface {\bf Srf}.
@It is equal to,
@\begin{equation}
@     C(t) = S(t, v_0) = \sum_{i=0}^m \sum_{j=0}^n P_{ij} B_i(t) B_j(v_0) =
@            \sum_{i=0}^m \left( \sum_{j=0}^n P_{ij} B_j(u_0) \right) B_i(t) =
@            \sum_{i=0}^m Q_i B_i(t),
@     \label{eqn-crv-from-srf}
@\end{equation}
@where $Q_i = \sum_{j=0}^n P_{ij} B_j(u_0)$ are the coefficients of the
@returned curve, and similar for the other parametric direction $S(u_0, t)$.
@{\bf param} is $v_0$ is equation~\eqnref{eqn-crv-from-srf}
 Example:
@\begin{verbatim}
    Crv = CSURFACE( Srf, COL, 0.45 );
@\end{verbatim}
 extracts an isoparametric curve in the COLumn direction at the parameter
 value of 0.15 from surface {\bf Srf}. See also CMESH, COMPOSE.
@See Figure~\ref{fig-csurface}.
@\begin{figure}
@\vspace{2.5in}
@\special{psfile=user_man/csurface.ps hscale=100 vscale=100 hoffset=-40 voffset=-180}
@\caption{Extracts an isoparametric curve from the given surface, using CSURFACE.}
@\label{fig-csurface}
@\end{figure}
@\subsubsection{CTANGENT}
!CTANGENT
@\begin{verbatim}
 VectorType CTANGENT( CurveType Curve, NumericType Param )
@\end{verbatim}
   Computes the tangent vector to {\bf Curve} at the parameter value {\bf Param}.
   The returned vector has a unit length.
 Example:
@\begin{verbatim}
    Tang = CTANGENT( Crv, 0.5 );
@\end{verbatim}
 computes the tangent vector to {\bf Crv} at the parameter value of 0.5.
@\subsubsection{CTLPT}
!CTLPT
@\begin{verbatim}
 CPt = CTLPT( ConstantType PtType, NumericType Coord1, ... )
@\end{verbatim}
   Constructs a single control point to be used in the construction of curves
 and surfaces. Points can have from one to five dimensions, and may be
 either Euclidean or Projective (rational). Points' type is set via the
 constants E1 to E5 and P1 to P5. The coordinates of the point are specified
 in order, weight is first if rational.
 Examples:
@\begin{verbatim}
    CPt1 = CTLPT( E3, 0.0, 0.0, 0.0 );
    CPt2 = CTLPT( P2, 0.707, 0.707, 0.707 );
@\end{verbatim}
 constructs an {\bf E3} point at the origin and a P2 rational point with
 a weight of 0.707. The Projective Pi points are specified as
 CTLPT(Pn, W, W X1, ... , W Xn).
@\subsubsection{CTRIMSRF}
!CTRIMSRF
@\begin{verbatim}
 ListType CTRIMSRF( TrimSrfType TSrf, NumericType Parametric )
@\end{verbatim}
   Extract the trimming curves of a trimmed surface {\bf TSrf}.
 If {\bf Parametric} is not zero, then the trimming curves are extracted
 as parametric space curves of {\bf TSrf}. Otherwise, the trimming curves
 are evaluated into Euclidean space as curves on surface {\bf TSrf}.
 Example:
@\begin{verbatim}
    TrimCrvs = CTRIMSRF( TrimSrf, FALSE );
@\end{verbatim}
 extracts the trimming curves of {\bf TrimSrf} as Euclidean curves on
 {\bf TrimSrf}.
@See Figure~\ref{fig-ctrimsrf}.
@\begin{figure}
@\vspace{3.4in}
@\special{psfile=user_man/ctrimsrf.ps hscale=100 vscale=100 hoffset=-35 voffset=-170}
@\caption{Extracts the trimming curves in Euclidean space (middle) and
@       parametric space (right) of a trimmed surface (left), using CTRIMSRF.}
@\label{fig-ctrimsrf}
@\end{figure}
@\subsubsection{CYLIN}
!CYLIN
@\begin{verbatim}
 PolylineType CYLIN( VectorType Center, VectorType Direction,
                     NumericType Radius )
@\end{verbatim}
   Creates a CYLINder geometric object, defined by {\bf Center} as center of
 the base of the CYLINder, {\bf Direction} as the CYLINder's axis and height,
 and {\bf Radius} as the radius of the base of the CYLINder.
   See RESOLUTION for the accuracy of the CYLINder approximation as a
 polygonal model.
 Example:
@\begin{verbatim}
    Cylinder1 = CYLIN( vector( 0, 0, 0 ), vector( 1, 0, 0 ), 10 );
@\end{verbatim}
 constructs a cylinder along the $X$ axis from the origin to $X = 10$.
@See Figure~\ref{fig-cylinder}.
@\begin{figure}
@\vspace{1.4in}
@\special{psfile=user_man/cylinder.ps hscale=100 vscale=100 hoffset=-40 voffset=-180}
@\caption{A cylinder primitive can be constructor using the CYLIN constructor.}
@\label{fig-cylinder}
@\end{figure}
@\subsubsection{CZEROS}
!CZEROS
@\begin{verbatim}
 ListType CZEROS( CurveType Crv, NumericType Epsilon, NumericType Axis )
@\end{verbatim}
   Computes the zero set of the given {\bf Crv} in the given axis (1 for X,
 2 for Y, 3 for Z). Since this computation is numeric, an {\bf Epsilon} is
 also required to specify the desired tolerance. It returns a list of
 all the parameter values (NumericType) the curve is zero.
 Example:
@\begin{verbatim}
    xzeros = CZEROS( cb, 0.001, 1 );
    pt_xzeros = nil();
    pt = nil();
    for ( i = 1, 1, sizeof( xzeros ),
            pt = ceval( cb, nth( xzeros, i ) ):
            snoc( pt, pt_xzeros )
        );
    interact( list( axes, cb, pt_xzeros ), 0 );
@\end{verbatim}
 Computes the {\bf X} zero set of curve {\bf cb} with error tolerance
 of {\bf 0.001}. This set is then scanned in a loop and evaluated to
 the curve's locations, which are then displayed.
 See also CINFLECT.
@See Figure~\ref{fig-czeros}.
@\begin{figure}
@\vspace{3.6in}
@\special{psfile=user_man/czeros.ps hscale=100 vscale=100 hoffset=-40 voffset=-200}
@\caption{Computes the zero set of a given freeform curve, in the given axis, using
@        CZEROS.}
@\label{fig-czeros}
@\end{figure}
@\subsubsection{EXTRUDE}
!EXTRUDE
@\begin{verbatim}
 PolygonType EXTRUDE( PolygonType Object, VectorType Dir )
 SurfaceType EXTRUDE( CurveType Object, VectorType Dir )
@\end{verbatim}
   Creates an extrusion of the given {\bf Object}. If {\bf Object} is a
 PolygonObject, its first polygon is used as the base for the extrusion in
 {\bf Dir} direction, and a closed PolygonObject is constructed. If {\bf Object}
 is a CurveType, an extrusion surface is constructed instead, which is {\em not}
 a closed object (the two bases of the extrusion are excluded, and the curve
 may be open by itself).
   Direction {\bf Dir} cannot be coplanar with the polygon plane. The curve
 may be nonplanar.
 Example:
@\begin{verbatim}
    Cross = cbspline( 3,
                      list( ctlpt( E2, -0.018, 0.001 ),
                            ctlpt( E2,  0.018, 0.001 ),
                            ctlpt( E2,  0.019, 0.002 ),
                            ctlpt( E2,  0.018, 0.004 ),
                            ctlpt( E2, -0.018, 0.004 ),
                            ctlpt( E2, -0.019, 0.001 ) ),
                      list( KV_OPEN ) );
    Cross = Cross + -Cross * scale( vector( 1, -1, 1 ) );
    Napkin = EXTRUDE( Cross * scale( vector( 1.6, 1.6, 1.6 ) ),
                      vector( 0.02, 0.03, 0.2 ) );
@\end{verbatim}
 constructs a closed cross section {\bf Cross} by duplicating one half of
 it in reverse and merging the two sub-curves. {\bf Cross} is then used as
 the cross-section for the extrusion operation.
@See Figure~\ref{fig-extrude}.
@\begin{figure}
@\vspace{1.5in}
@\special{psfile=user_man/extrude.ps hscale=100 vscale=100 hoffset=-40 voffset=-310}
@\caption{An extrusion of a freeform curve using EXTRUDE to create a freeform
@        surface.}
@\label{fig-extrude}
@\end{figure}
@\subsubsection{FFCOMPAT}
!FFCOMPAT
@\begin{verbatim}
 FFCOMPAT( CurveType Crv1, CurveType Crv2 )
 FFCOMPAT( SurfaceType Srf1, SurfaceType Srf2 )
@\end{verbatim}
 Makes the given two curves or surfaces compatible by making them share the
 same point type, same curve type, same degree, and the same continuity.
 Same point type is gained by promoting a lower dimension into a higher one,
 and non-rational to rational points. Bezier curves are promoted to Bspline
 curves if necessary, for curve type compatibility. Degree compatibility is
 achieved by raising the degree of the lower order curve. Continuity is
 achieve by refining both curves to the space with the same (unioned) knot
 vector. This function returns nothing and compatibility is made
 {\em in place}.
 Example:
@\begin{verbatim}
 FFCOMPAT( Srf1, Srf2 );
@\end{verbatim}
 See also SMORPH.
@\subsubsection{FFEXTREME}
!FFEXTREME
@\begin{verbatim}
 CtlPtType FFEXTREME( CurveType Crv, NumericType Minimum )
 CtlPtType FFEXTREME( SurfaceType Srf, NumericType Minimum )
@\end{verbatim}
 Computes a bound on the extreme values a curves {\bf Crv} or surface
 {\bf Srf} can assume. Returned control points provides a bound on the
 minimum (maximum) values that can be assumed if {\bf Minimum} is TRUE
 (FALSE).
 Example:
@\begin{verbatim}
 Bound = FFEXTREME( Srf, false );
@\end{verbatim}
 Computes a bound on the maximal values Srf can assume.
@\subsubsection{GBOX}
!GBOX
@\begin{verbatim}
 PolygonType GBOX( VectorType Point,
                   VectorType Dx, VectorType Dy, VectorType Dz )
@\end{verbatim}
   Creates a parallelepiped - Generalized BOX polygonal object, defined by
 {\bf Point} as base position, and {\bf Dx, Dy, Dz} as 3 3D vectors to define
 the 6 faces of this generalized BOX. The regular BOX object is a special case
 of GBOX where {\bf Dx} = vector(Dx, 0, 0), {\bf Dy} = vector(0, Dy, 0), and
 {\bf Dz} = vector(0, 0, Dz).
   {\bf Dx}, {\bf Dy}, {\bf Dz} must all be independent in order to create an
 object with positive volume.
 Example:
@\begin{verbatim}
    GB = GBOX(vector(0.0, -0.35, 0.63), vector(0.5, 0.0, 0.5),
                                        vector(-0.5, 0.0, 0.5),
                                        vector(0.0, 0.7, 0.0));
@\end{verbatim}
@See Figure~\ref{fig-gbox}.
@\begin{figure}
@\vspace{2.9in}
@\special{psfile=user_man/gbox.ps hscale=100 vscale=100 hoffset=-40 voffset=-200}
@\caption{A warped box in a general position can be constructed using the GBOX
@        constructor.}
@\label{fig-gbox}
@\end{figure}
@\subsubsection{GETLINE}
!GETLINE
@\begin{verbatim}
 AnyType GETLINE( NumericType RequestedType )
@\end{verbatim}
   Provides a method to get input from keyboard within functions and
 or subroutines. {\bf RequestedType} can be one of NUMERIC\_TYPE,
 POINT\_TYPE, VECTOR\_TYPE, or PLANE\_TYPE in which the entered line
 will be parsed into one, three, or four numeric values (sperated by
 either spaces or commas) and the proper object will be created and
 returned. In any other case, including failure to parse the numeric
 input, a STRING\_TYPE object will be constructed from the entered line.
 Example:
@\begin{verbatim}
    Pt = GETLINE( point_type );
@\end{verbatim}
 to read one point (three numeric values) from stdin.
@\subsubsection{GPOLYGON}
!GPOLYGON
@\begin{verbatim}
 PolygonType GPOLYGON( GeometryTreeType Object, NumericType Normals )
@\end{verbatim}
   Approximates all Surface(s)/Trimmed surface(s)/Trivariate(s) in {\bf Object}
 with polygons using the RESOLUTION and FLAT4PLY variables. The larger the
 RESOLUTION is, the finer (more polygons) the resulting approximation will be.
   FLAT4PLY is a Boolean flag controlling the conversion of an (almost) flat
 patch into four (TRUE) or two (FALSE) polygons. Normals are computed to
 polygon vertices using surface normals, so Gouraud or Phong shading can be
 exploited. It returns a single polygonal object.
   If {\bf Normals} is set, surface normals will be evaluated at the
 vertices. Otherwise flat shading and constant normals across polygons are
 assumed.
 Example:
@\begin{verbatim}
    Polys = GPOLYGON( list( Srf1, Srf2, Srf3 ), off );
@\end{verbatim}
 Converts to polygons the three surfaces {\bf Srf1}, {\bf Srf2}, and {\bf Srf3}
 with no normals.
@\subsubsection{GPOLYLINE}
!GPOLYLINE
@\begin{verbatim}
 PolylineType GPOLYLINE( GeometryTreeType Object, NumericType Optimal )
@\end{verbatim}
   Converts all Curves(s), (Trimmed) Surface(s), and Trivariate(s) {\bf Object}
 into polylines using the RESOLUTION variable. The larger the RESOLUTION is,
 the finer the resulting approximation will be. It returns a single polyline
 object.
   If {\bf Optimal} is false, the points are sampled at equally spaced
 interval in the parametric space. If {\bf Optimal} true, a better, more
 expensive computationally, algorithm is used to derive optimal sampling
 locations as to minimize the maximal distance between the curve and
 piecewise linear approximation (L infinity norm).
 Example:
@\begin{verbatim}
    Polys = GPOLYLINE( list( Srf1, Srf2, Srf3, list( Crv1, Crv2, Crv3 ) ),
                       on );
@\end{verbatim}
 converts to polylines the three surfaces {\bf Srf1}, {\bf Srf2}, and {\bf Srf3}
 and the three curves {\bf Crv1}, {\bf Crv2}, and {\bf Crv3}.
@\subsubsection{LOFFSET}
!LOFFSET
@\begin{verbatim}
 CurveType LOFFSET( CurveType Crv, NumericType OffsetDistance,
                    NumericType NumOfSamples, NumericType NumOfDOF,
                    NumericType Order )
@\end{verbatim}
 Approximate an offset of {\bf OffsetDistance} by sampling {\bf NumOfSamples}
 samples along the offset curve and least square fitting them using a Bspline
 curve of order {\bf Order} and {\bf NumOfDOF} control points.
 Example:
@\begin{verbatim}
    OffCrv1 = LOFFSET( Crv, -0.4, 100, 10, 4 );
@\end{verbatim}
 See also OFFSET and AOFFSET.
@\subsubsection{MERGPOLY}
!MERGEPOLY
@\begin{verbatim}
 PolygonType MERGEPOLY( ListType PolyList )
@\end{verbatim}
 Merges a set of polygonal objects in {\bf PolyList} list to a single polygonal
 object. All elements in {\bf ObjectList} must be of PolygonType type. This
 function performs the same operation as the overloaded {\bf \verb+^+} operator
 would, but might be more convenient to use under some circumstances.
 Example:
@\begin{verbatim}
    Vrtx1 = vector( -3, -2, -1 );
    Vrtx2 = vector( 3, -2, -1 );
    Vrtx3 = vector( 3, 2, -1 );
    Vrtx4 = vector( -3, 2, -1 );
    Poly1 = poly( list( Vrtx1, Vrtx2, Vrtx3, Vrtx4 ), false );
    Vrtx1 = vector( -3, 2, 1 );
    Vrtx2 = vector( 3, 2, 1 );
    Vrtx3 = vector( 3, -2, 1 );
    Vrtx4 = vector( -3, -2, 1 );
    Poly2 = poly( list( Vrtx1, Vrtx2, Vrtx3, Vrtx4 ), false );
    Vrtx1 = vector( -3, -2, 1 );
    Vrtx2 = vector( 3, -2, 1 );
    Vrtx3 = vector( 3, -2, -1 );
    Vrtx4 = vector( -3, -2, -1 );
    Poly3 = poly( list( Vrtx1, Vrtx2, Vrtx3, Vrtx4 ), false );
    PolyObj = MERGEPOLY( list( Poly1, Poly2, Poly3 ) );
@\end{verbatim}
@See Figure~\ref{fig-mergpoly}.
@\begin{figure}
@\vspace{2.6in}
@\special{psfile=user_man/mergpoly.ps hscale=100 vscale=100 hoffset=-40 voffset=-220}
@\caption{Individual polygons can be merged into a complete model using MERGEPOLY.}
@\label{fig-mergpoly}
@\end{figure}
@\subsubsection{MOMENT}
!MOMENT
@\begin{verbatim}
 PointType MOMENT( CurveType Crv, 0 );
 VectorType MOMENT( CurveType Crv, 1 );
@\end{verbatim}
 Approximates the zero and first moment of curve {\bf Crv}.
 Example:
@\begin{verbatim}
    a = circle( vector( 0, 0, 0 ), 1 );
    a = cregion( a, 0, 1 );
    p = moment( a, 0 );
    v = moment( a, 1 );
    view(list(a, p, v), on);
    a = cregion( a, 0, 1 ) * rz( 45 );
    p = moment( a, 0 );
    v = moment( a, 1 );
    view(list(a, p, v), on);
@\end{verbatim}
 computes and displays the zero and first moment of a quarter of a circle
 in two orientations.
@\subsubsection{NIL}
@\begin{verbatim}
 ListType NIL()
@\end{verbatim}
   Creates an empty list so data can be accumulated in it.
 See CINFLECT or CZEROS for examples. See also LIST and SNOC.
@\subsubsection{OFFSET}
!OFFSET
@\begin{verbatim}
 CurveType OFFSET( CurveType Crv, NumericType OffsetDistance,
                   NumericType Tolerance, NumericType BezInterp )
 SurfaceType OFFSET( SurfaceType Srf, NumericType OffsetDistance,
                     NumericType Tolerance )
@\end{verbatim}
 Offsets {\bf Crv} or {\bf Srf}, by translating all the control points in the
 direction of the normal of the curve or surface by an {\bf OffsetDistance}
 amount. Each control point has a {\em node} parameter value associated with
 it, which is used to compute the normal. The returned curve or surface only
 approximates the real offset. If the resulting approximation does not satisfy
 the accuracy required by {\bf Tolerance}, {\bf Crv} or {\bf Srf} is subdivided
 and an offset approximation fit is computed to the two halfs. For curves, one
 can request a Bezier interpolation scheme in the offset approximation by
 setting {\bf BezInter}. Negative {\bf OffsetDistance} denotes offset in
 the reversed direction of the normal.
 Example:
@\begin{verbatim}
    OffCrv = OFFSET( Crv, -0.4, 0.1, off );
@\end{verbatim}
 offsets {\bf Crv} by the amount of $-0.4$ in the reversed normal direction,
 {\bf Tolerance} of 0.1 and no Bezier interpolation.
 See also AOFFSET and LOFFSET.
@See Figure~\ref{fig-coffset}.
@\begin{figure}
@\vspace{2.5in}
@\special{psfile=user_man/coffset.ps hscale=100 vscale=100 hoffset=-40 voffset=-190}
@\caption{Offset approximation (thick) of a Bspline curve (thin) (See also
@        Figure~\protect\ref{fig-caoffset}.)}
@\label{fig-coffset}
@\end{figure}
@\subsubsection{PCIRCLE}
!PCIRCLE
@\begin{verbatim}
 CurveType PCIRCLE( VectorType Center, NumericType Radius )
@\end{verbatim}
 Same as CIRCLE but approximates the circle as a {\em polynomial} curve.
 See CIRCLE.
@\subsubsection{PDOMAIN}
!PDOMAIN
@\begin{verbatim}
 ListType PDOMAIN( CurveType Crv )
 ListType PDOMAIN( SurfaceType Srf )
 ListType PDOMAIN( TrimSrfType TrimSrf )
 ListType PDOMAIN( TrivarType TV )
@\end{verbatim}
   Returns the parametric domain of the curve (TMin, TMax) or of a (trimmed)
 surface (UMin, UMax, VMin, VMax) or of a trivariate function
 (UMin, UMax, VMin, VMax, WMin, WMax) as a list object.
 Example:
@\begin{verbatim}
 circ_domain = PDOMAIN( circle( vector( 0.0, 0.0, 0.0 ), 1.0 ) );
@\end{verbatim}
@\subsubsection{POLY}
!POLY
@\begin{verbatim}
 PolygonType POLY( ListType VrtxList, NumericType IsPolyline )
@\end{verbatim}
   Creates a single polygon/polyline (and therefore open) object, defined by
 the vertices in {\bf VrtxList} (see LIST). All elements in {\bf VrtxList}
 must be of VectorType type. If {\bf IsPolyline}, a polyline is created,
 otherwise a polygon.
 Example:
@\begin{verbatim}
    V1  = vector( 0.0, 0.0, 0.0 );
    V2  = vector( 0.3, 0.0, 0.0 );
    V3  = vector( 0.3, 0.0, 0.1 );
    V4  = vector( 0.2, 0.0, 0.1 );
    V5  = vector( 0.2, 0.0, 0.5 );
    V6  = vector( 0.3, 0.0, 0.5 );
    V7  = vector( 0.3, 0.0, 0.6 );
    V8  = vector( 0.0, 0.0, 0.6 );
    V9  = vector( 0.0, 0.0, 0.5 );
    V10 = vector( 0.1, 0.0, 0.5 );
    V11 = vector( 0.1, 0.0, 0.1 );
    V12 = vector( 0.0, 0.0, 0.1 );
    I = POLY( list( V1, V2, V3, V4, V5, V6, V7, V8, V9, V10, V11, V12 ),
              FALSE );
@\end{verbatim}
 constructs an object with a single polygon in the shape of the letter I.
@See Figure~\ref{fig-poly}.
@\begin{figure}
@\vspace{1.7in}
@\special{psfile=user_man/poly.ps hscale=100 vscale=100 hoffset=-40 voffset=-200}
@\caption{Polygons or polylines can be manually constructed using the
@        POLY constructor.}
@\label{fig-poly}
@\end{figure}
@\subsubsection{PRISA}
!PRISA
@\begin{verbatim}
 ListType PRISA( SurfaceType Srfs, NumericType SamplesPerCurve,
                 NumericType Epsilon, ConstantType Dir, VectorType Space )
@\end{verbatim}
   Computes a layout (prisa) of the given surface(s) {\bf Srfs}, and returns
 a list of surface objects representing the layout.
   The surface is approximated to within {\bf Epsilon} in direction {\bf Dir}
 into a set of ruled surfaces and then developable surfaces that are laid out
 flat onto the $XY$ plane. If {\bf Epsilon} is negative, the piecewise ruled
 surface approximation in 3-space is returned.
   {\bf SamplesPerCurve} controls the piecewise linear approximation of the
 boundary of the ruled/developable surfaces. {\bf Space} is a vector whose
 X component controls the space between the different surfaces' layout, and
 whose Y component controls the space between different layout pieces.
 Example:
@\begin{verbatim}
 cross = cbspline( 3,
                   list( ctlpt( E3, 0.7, 0.0, 0. ),
                         ctlpt( E3, 0.7, 0.0, 0.06 ),
                         ctlpt( E3, 0.1, 0.0, 0.1 ),
                         ctlpt( E3, 0.1, 0.0, 0.6 ),
                         ctlpt( E3, 0.6, 0.0, 0.6 ),
                         ctlpt( E3, 0.8, 0.0, 0.8 ),
                         ctlpt( E3, 0.8, 0.0, 1.4 ),
                         ctlpt( E3, 0.6, 0.0, 1.6 ) ),
                   list( KV_OPEN ) );
 wglass = surfrev( cross );
 wgl_ruled = PRISA( wglass, 6, -0.1, COL, vector( 0, 0.25, 0.0 ) );
 wgl_prisa = PRISA( wglass, 6, 0.1, COL, vector( 0, 0.25, 0.0 ) );
@\end{verbatim}
 Computes a layout of a wine glass in {\bf wgl\_prisa} and a three-dimensional
 ruled surface approximation of wglass in {\bf wgl\_ruled}.
@See Figure~\ref{fig-prisa}.
@\begin{figure}
@\vspace{2.4in}
@\special{psfile=user_man/prisa.ps hscale=100 vscale=100 hoffset=-30 voffset=-210}
@\caption{The layout (prisa in hebrew...) of a freeform surface can be approximated
@        using the PRISA function.}
@\label{fig-prisa}
@\end{figure}
@\subsubsection{RULEDSRF}
!RULEDSRF
@\begin{verbatim}
 SurfaceType RULEDSRF( CurveType Crv1, CurveType Crv2 )
@\end{verbatim}
   Constructs a ruled surface between the two curves {\bf Crv1} and {\bf Crv2}.
   The curves do not have to have the same order or type, and will be promoted
 to their least common denominator.
 Example:
@\begin{verbatim}
    Circ = circle( vector( 0.0, 0.0, 0.0 ), 0.25 );
    Cyl = RULEDSRF( circ, circ * trans( vector( 0.0, 0.0, 1.0 ) ) );
@\end{verbatim}
 Constructs a cylinder of radius 0.25 along the Z axis from 0 to 1.
@See Figure~\ref{fig-ruledsrf}.
@\begin{figure}
@\vspace{2in}
@\special{psfile=user_man/ruledsrf.ps hscale=100 vscale=100 hoffset=-40 voffset=-210}
@\caption{A cylinder can be cunstructed as a RULEDSRF of two different circles.}
@\label{fig-ruledsrf}
@\end{figure}
@\subsubsection{SBEZIER}
!SBEZIER
@\begin{verbatim}
 SurfaceType SBEZIER( ListType CtlMesh )
@\end{verbatim}
   Creates a Bezier surface using the provided control mesh. {\bf CtlMesh} is a
 list of rows, each of which is a list of control points. All control points
 must be of type (E1-E5, P1-P5), or regular PointType defining the surface's
 control polygon. Surface's point type will be of a space which is the union
 of the spaces of all points.
@The created surface is the piecewise polynomial (or rational) surface,
@\begin{equation}
@     S(u, v) = \sum_{i=0}^m \sum_{j=0}^n P_{ij} B_i(u) B_j(v)
@\end{equation}
@where $P_{ij}$ are the control points {\bf CtlMesh}. and $m$ and $n$ are the
@degrees of the surface, which are one less than the number of points in the
@appropriate direction.
 Example:
@\begin{verbatim}
   Srf = SBEZIER( list ( list( ctlpt( E3, 0.0, 0.0, 1.0 ),
                               ctlpt( E3, 0.0, 1.0, 0.0 ),
                               ctlpt( E3, 0.0, 2.0, 1.0 ) ),
                         list( ctlpt( E3, 1.0, 0.0, 0.0 ),
                               ctlpt( E3, 1.0, 1.0, 2.0 ),
                               ctlpt( E3, 1.0, 2.0, 0.0 ) ),
                         list( ctlpt( E3, 2.0, 0.0, 2.0 ),
                               ctlpt( E3, 2.0, 1.0, 0.0 ),
                               ctlpt( E3, 2.0, 2.0, 2.0 ) ),
                         list( ctlpt( E3, 3.0, 0.0, 0.0 ),
                               ctlpt( E3, 3.0, 1.0, 2.0 ),
                               ctlpt( E3, 3.0, 2.0, 0.0 ) ),
                         list( ctlpt( E3, 4.0, 0.0, 1.0 ),
                               ctlpt( E3, 4.0, 1.0, 0.0 ),
                               ctlpt( E3, 4.0, 2.0, 1.0 ) ) ) );
@\end{verbatim}
@See Figure~\ref{fig-surface}.
@\begin{figure}
@\vspace{1.5in}
@\special{psfile=user_man/surface.ps hscale=100 vscale=100 hoffset=-70 voffset=-170}
@\caption{A bezier surface (left) of degree 3 by 5 and a Bspline surface (right)
@        of degree 3 by 3 (bi-quadratic). Both share the same control mesh.}
@\label{fig-surface}
@\end{figure}
@\subsubsection{SBSPLINE}
!SBSPLINE
@\begin{verbatim}
 SurfaceType SBSPLINE( NumericType UOrder, NumericType VOrder,
                       ListType CtlMesh, ListType KnotVectors )
@\end{verbatim}
   Creates a Bspline surface from the provided {\bf UOrder} and {\bf VOrder}
 orders, the control mesh {\bf CtlMesh}, and the two knot vectors {\bf KnotVectors}.
 {\bf CtlMesh} is a list of rows, each of which is a list of control points.
 All control points must be of point type (E1-E5, P1-P5), or regular
 PointType defining the surface's control mesh. Surface's point type will
 be of a space which is the union of the spaces of all points.
   {\bf KnotVectors} is a list of two knot vectors. Each knot vector is a
 list of NumericType knots of length {\bf \#CtlPtList} plus the {\bf Order}.
 If, however, the length of the knot vector is equal to {\bf \#CtlPtList +
 Order + Order - 1} the curve is assumed {\em periodic.}
   The knot vector may also be a list of a single constant KV\_OPEN or
 KV\_FLOAT or KV\_PERIODIC, in which a uniform knot vector with the
 appropriate length and with open, floating or periodic end condition
 will be constructed automatically.
@The created surface is the piecewise polynomial (or rational) surface,
@\begin{equation}
@     S(u, v) = \sum_{i=0}^m \sum_{j=0}^n P_{ij} B_{i,\chi}(u) B_{j,\xi}(v)
@\end{equation}
@where $P_{ij}$ are the control points {\bf CtlMesh}, and $m$ and $n$ are the
@degrees of the surface, which are one less than {\bf UOrder} and {\bf VOrder}.
@$\chi$ and $\xi$ are the two knot vectors of the surface.
 Example:
@\begin{verbatim}
    Mesh = list ( list( ctlpt( E3, 0.0, 0.0, 1.0 ),
                        ctlpt( E3, 0.0, 1.0, 0.0 ),
                        ctlpt( E3, 0.0, 2.0, 1.0 ) ),
                  list( ctlpt( E3, 1.0, 0.0, 0.0 ),
                        ctlpt( E3, 1.0, 1.0, 2.0 ),
                        ctlpt( E3, 1.0, 2.0, 0.0 ) ),
                  list( ctlpt( E3, 2.0, 0.0, 2.0 ),
                        ctlpt( E3, 2.0, 1.0, 0.0 ),
                        ctlpt( E3, 2.0, 2.0, 2.0 ) ),
                  list( ctlpt( E3, 3.0, 0.0, 0.0 ),
                        ctlpt( E3, 3.0, 1.0, 2.0 ),
                        ctlpt( E3, 3.0, 2.0, 0.0 ) ),
                  list( ctlpt( E3, 4.0, 0.0, 1.0 ),
                        ctlpt( E3, 4.0, 1.0, 0.0 ),
                        ctlpt( E3, 4.0, 2.0, 1.0 ) ) );
    Srf = SBSPLINE( 3, 3, Mesh, list( list( KV_OPEN ),
                                      list( 3, 3, 3, 4, 5, 6, 6, 6 ) ) );
@\end{verbatim}
 constructs a bi-quadratic Bspline surface with its first knot vector
 having uniform knot spacing with open end conditions.
@See Figure~\ref{fig-surface}.
@\subsubsection{SCRVTR}
!SCRVTR
@\begin{verbatim}
 SurfaceType SCRVTR( SurfaceType Srf, ConstType PtType, ConstType Dir )
@\end{verbatim}
   Symbolically computes the extreme curvature bound on {\bf Srf}.
   If {\bf Dir} is either ROW or COL, then the normal curvature square
 of {\bf Srf} in {\bf Dir} is computed symbolically and returned.
   Otherwise, a upper bound on the sum of the squares of the two
 principal curvatures is symbolically computed and returned.
   Returned value is a surface that can be evaluated to the curvature
 bound, given a UV location. The returned surface value is a scalar field
 of point type P1 (scalar rational).
   However, if {\bf PtType} is one of E1, P1, E3, P3 the returned surface
 is coerced to this given type. If the types are one of E3, P3, then the
 Y and Z axes are set to be equivalent to the U and V parametric domains.
@   This function computes the square of the normal curvature scalar
@ field for surfaces as (in the U parametric direction, same for V),
@\begin{equation}
@      \kappa_n^u(u, v) = \frac{\inner{n}{\frac{\partial^2 S}{\partial u^2}}}
@                              {\inner{\frac{\partial S}{\partial u}}
@                                     {\frac{\partial S}{\partial u}}}
@\end{equation}
@ and computes $\xi(u, v) = k_1(u, v)^2 + k_2(u, v)^2$ as the scalar field of
@\begin{equation}
@       \xi(u, v) = \frac{(g_{11} l_{22} + l_{11} g_{22} - 2 g_{12}
@                l_{12}) ^ 2 - 2 \left| G \right| \left| L \right|}
@               {\left| G \right|^2 \| n \|^2},
@\end{equation}
@ where $g_{ij}$ and $l_{ij}$ are the coefficients of the first and second
@ fundamental forms G and L.
^   This function computes the square of the normal curvature scalar
^ field for surfaces as (in the U parametric direction, same for V),
^                     2
^                    d S
^              < n , --- >
^                      2
^    u               du
^   k (u, v) = ------------
^    n
^                 dS   ds
^               < -- , -- >
^                 du   du
^ and computes the sum of the squares of the principal curvatures as,
^  2    2  ( g11 l22 + g22 l11 - 2 g12 l12 )^2 - 2 |G| |L|
^ k  + k = -----------------------------------------------
^  1    2                   |G|^2 ||n||^2
 See also CCRVTR.
 Example:
@\begin{verbatim}
 cross = cbspline( 3,
                   list( ctlpt( E2,  0.0,  0.0 ),
                         ctlpt( E2,  0.8,  0.0 ),
                         ctlpt( E2,  0.8,  0.2 ),
                         ctlpt( E2,  0.07, 1.4 ),
                         ctlpt( E2, -0.07, 1.4 ),
                         ctlpt( E2, -0.8,  0.2 ),
                         ctlpt( E2, -0.8,  0.0 ),
                         ctlpt( E2,  0.0,  0.0 ) ),
                   list( KV_OPEN ) );
 cross = coerce( cross, e3 );
 s = sFromCrvs( list( cross,
                      cross * trans( vector( 0.5, 0, 1 ) ),
                      cross * trans( vector( 0, 0, 2 ) ) ), 3 );
 view( list( s, axes ), on );
 UCrvtrZXY = scrvtr( s, E3, row );
 VCrvtrZXY = scrvtr( s, E3, col );
 UCrvtrXYZ = UCrvtrZXY * rotx( -90 ) * roty( -90 ) * scale( vector( 1, 1, 0.001 ) );
 VCrvtrXYZ = VCrvtrZXY * rotx( -90 ) * roty( -90 ) * scale( vector( 1, 1, 10 ) );
 color( UCrvtrXYZ, red );
 color( VCrvtrXYZ, magenta );
 view( list( UCrvtrXYZ, VCrvtrXYZ ), off );
 CrvtrZXY = scrvtr( s, E3, off );
 CrvtrXYZ = CrvtrZXY * rotx( -90 ) * roty( -90 ) * scale( vector( 1, 1, 0.001 ) );
 color( CrvtrXYZ, green );
 view( CrvtrXYZ, off );
@\end{verbatim}
 Computes the sqaure of the normal curvature in the U and V direction, flips
 its scalar value from X to Z using rotations and scale the fields to
 reasonable values and display them.
   Then, display a total bound on the normal curvature as well.
 Due to the large degree of the resulting fields be warned that rational
 surfaces will compute into large degree curvature bound fields. See also
 IRITSTATE("InterpProd", FALSE); for faster symbolic computation.
@See Figure~\ref{fig-scrvtr}.
@\begin{figure}
@\vspace{2in}
@\special{psfile=user_man/scrvtr.ps hscale=100 vscale=100 hoffset=-50 voffset=-170}
@\caption{From left to right: original surface, normal curvature in the U
@         direction, normal curvature in the V direction, sum of square of
@         principle curvatures (different scales).
@         All computed using SCRVTR.}
@\label{fig-scrvtr}
@\end{figure}
@\subsubsection{SDERIVE}
!SDERIVE
@\begin{verbatim}
 SurfaceType SDERIVE( SurfaceType Srf, NumericType Dir )
@\end{verbatim}
   Returns a vector field surface representing the differentiated surface
 in the given direction (ROW or COL). Evaluation of the returned surface at
 a given parameter value will return a vector {\em tangent} to {\bf Srf} in
 {\bf Dir} at that parameter value.
@\begin{verbatim}
 DuSrf = SDERIVE( Srf, ROW );
 DvSrf = SDERIVE( Srf, COL );
 Normal = coerce( seval( DuSrf, 0.5, 0.5 ), VECTOR_TYPE ) ^
          coerce( seval( DvSrf, 0.5, 0.5 ), VECTOR_TYPE );
@\end{verbatim}
 computes the two partial derivatives of the surface {\bf Srf} and computes
 its normal as their cross product, at the parametric location (0.5, 0.5).
@\subsubsection{SDIVIDE}
!SDIVIDE
@\begin{verbatim}
 SurfaceType SDIVIDE( SurfaceType Srf, ConstantType Direction,
                                                          NumericType Param )
@\end{verbatim}
   Subdivides a surface into two at the specified parameter value {\bf Param}
 in the specified {\bf Direction} (ROW or COL). {\bf Srf} can be either a Bspline
 surface in which {\bf Param} must be conatined in the parametric domain of the
 surface, or a Bezier surface in which {\bf Param} must be in the range of zero
 to one.
   It returns a list of the two sub-surfaces. The individual surfaces may be
 extracted from the list using the {\bf NTH} command.
 Example:
@\begin{verbatim}
    SrfLst = SDIVIDE( Srf, ROW, 0.5 );
    Srf1 = nth( SrfLst, 1 );
    Srf2 = nth( SrfLst, 2 );
@\end{verbatim}
 subdivides {\bf Srf} at the parameter value of 0.5 in the ROW direction.
@See Figure~\ref{fig-sdivide}.
@\begin{figure}
@\vspace{2.9in}
@\special{psfile=user_man/sdivide.ps hscale=80 vscale=80 hoffset=-20 voffset=-130}
@\caption{A surface can be subdivided into two distinct regions using SDIVIDE.}
@\label{fig-sdivide}
@\end{figure}
@\subsubsection{SEDITPT}
!SEDITPT
@\begin{verbatim}
 SurfaceType SEDITPT( SurfaceType Srf, CtlPtType CPt, NumericType UIndex,
                                                      NumericType VIndex )
@\end{verbatim}
   Provides a simple mechanism to manually modify a single control point number
 {\bf UIndex} and {\bf VIndex} (base count is 0) in the control mesh of {\bf Srf}
 by substituting {\bf CtlPt} instead. CtlPt must have the same point type as
 the control points of {\bf Srf}. Original surface {\bf Srf} is not modified.
 Example:
@\begin{verbatim}
    CPt = ctlpt( E3, 1, 2, 3 );
    NewSrf = SEDITPT( Srf, CPt, 0, 0 );
@\end{verbatim}
 constructs a {\bf NewSrf} with the first control point of {\bf Srf} being
 {\bf CPt}.
@\subsubsection{SEVAL}
!SEVAL
@\begin{verbatim}
 CtlPtType SEVAL( SurfaceType Srf, NumericType UParam, NumericType VParam )
@\end{verbatim}
   Evaluates the provided surface {\bf Srf} at the given {\bf UParam} and
 {\bf VParam} values. Both {\bf UParam} and {\bf VParam} should be contained
 in the surface parametric domain if {\bf Srf} is a Bspline surface, or
 between zero and one if {\bf Srf} is a Bezier surface. The returned control
 point has the same type as the control points of {\bf Srf}.
 Example:
@\begin{verbatim}
    CPt = SEVAL( Srf, 0.25, 0.22 );
@\end{verbatim}
 evaluates {\bf Srf} at the parameter values of (0.25, 0.22).
@\subsubsection{SFROMCRVS}
!SFROMCRVS
@\begin{verbatim}
 SurfaceType SFROMCRVS( ListType CrvList, NumericType OtherOrder )
@\end{verbatim}
   Constructs a surface by substituting the curves in {\bf CrvList} as rows
 in a control mesh of a surface. Curves in {\bf CrvList} are made compatible
 by promoting Bezier curves to Bsplines if necessary, and raising degree
 and refining as required before substituting the control polygons of the
 curves as rows in the mesh. The other direction order is set by
 {\bf OtherOrder}, which cannot be larger than the number of curves.
   The surface interpolates the first and last curves only.
 Example:
@\begin{verbatim}
    Crv1 = cbspline( 3,
                     list( ctlpt( E3, 0.0, 0.0, 0.0 ),
                           ctlpt( E3, 1.0, 0.0, 0.0 ),
                           ctlpt( E3, 1.0, 1.0, 0.0 ) ),
                     list( KV_OPEN ) );
    Crv2 = Crv1 * trans( vector( 0.0, 0.0, 1.0 ) );
    Crv3 = Crv2 * trans( vector( 0.0, 1.0, 0.0 ) );
    Srf = SFROMCRVS( list( Crv1, Crv2, Crv3 ), 3 );
@\end{verbatim}
@See Figure~\ref{fig-sfromcrvs}.
@\begin{figure}
@\vspace{3.2in}
@\special{psfile=user_man/sfromcrvs.ps hscale=100 vscale=100 hoffset=0 voffset=-85}
@\caption{A surface can be constructed from a list of curves substituted
@         as rows into its mesh using SFROMCRVS. The surface does not
@         necessarily interpolate the curves.}
@\label{fig-sfromcrvs}
@\end{figure}
@\subsubsection{SINTERP}
!SINTERP
@\begin{verbatim}
 SurfaceType SINTERP( ListType PtList, NumericType UOrder, NumericType VOrder,
                      NumericType USize, NumericType VSize,
                      ConstantType Param)
@\end{verbatim}
   Computes a Bspline polynomial surface that interpolates or approximates
 the rectangular grid of points in {\bf PtList}. The Bspline surface will
 have orders {\bf UOrder} and {\bf VOrder} and mesh of size {\bf USize} by
 {\bf VSize} control points. The knots will be spaced according to
 {\bf Param} which can be one of PARAM\_UNIFORM, PARAM\_CHORD or
 PARAM\_CENTRIP. The former prescribed a uniform knot sequence and the
 latters specified a knot spacing accoridng to the chord length and a square
 root of the chord length. Currently only PARAM\_UNIFORM is supported.
   {\bf PtList} is a list of list of points where all lists should carry the
 same amount of points in them, defining a rectangular grid. All points in
 {\bf PtList} must be of type (E1-E5, P1-P5) control point, or regular
 PointType. If {\bf USize} and {\bf VSize} are equal to the number of points
 in the grid {\bf PtList} the resulting curve will {\em interpolate} the
 data set. Otherwise, if {\bf USize} or {\bf VSize} is less than the number
 of points in {\bf PtList} the point data set will be least square
 approximated. In no time can {\bf USize} or {\bf VSize} be larger that the
 number of points in {\bf PtList} or lower than {\bf UOrder} and {\bf VOrder},
 respectively. If {\bf USize} or {\bf VSize} are zero, the grid size
 is used, forcing an interpolation of the data set.
   All interior knots will be distinct preserving maximal continuity.
 The resulting Bspline surface will have open end conditions.
 Example:
@\begin{verbatim}
    pl = nil();
    pll = nil();
    for ( x = -5, 1, 5,
          pl = nil():
          for ( y = -5, 1, 5,
                snoc( point( x, y, sin( x * Pi / 2 ) * cos( y * Pi / 2 ) ),
                      pl )
          ):
          snoc( pl, pll ) );
    s1 = sinterp( pll, 3, 3, 8, 8, PARAM_UNIFORM );
    s2 = sinterp( pll, 3, 3, 11, 11, PARAM_UNIFORM );
@\end{verbatim}
 Samples an explicit surface sin(x) * cos(y) at a grid of 11 by 11 points,
 least square fit with a grid of size of 8 by 8 surface {\bf s1}, and
 interpolate surface {\bf s2} using this data set.
@See Figure~\ref{fig-sinterp}.
@\begin{figure}
@\vspace{1.6in}
@\special{psfile=user_man/sinterp.ps hscale=95 vscale=95 hoffset=-30 voffset=-130}
@\caption{A surface least square fitting a data set with insufficient
@         degrees of freedom (left) and actually interpolating the data
@         set (right), all using SINTERP.}
@\label{fig-sinterp}
@\end{figure}
@\subsubsection{SMERGE}
!SMERGE
@\begin{verbatim}
 SurfaceType SMERGE( SurfaceType Srf1, SurfaceType Srf2,
                     NumericType Dir, NumericType SameEdge )
@\end{verbatim}
 Merges two surfaces along the requested direction (ROW or COL). If
 SameEdge is non-zero (ON or TRUE), then the common edge is assumed to be
 identical and copied only once. Otherwise (OFF or FALSE), a ruled surface
 is constructed between the two surfaces along the (not) common edge.
 Example:
@\begin{verbatim}
 MergedSrf = SMERGE( Srf1, Srf2, ROW, TRUE );
@\end{verbatim}
@\subsubsection{SMORPH}
!SMORPH
@\begin{verbatim}
 SurfaceType SMORPH( SurfaceType Srf1, SurfaceType Srf2, NumericType Blend )
@\end{verbatim}
 Creates a new surface which is a {\em convex blend} of the two given surfaces.
 The two given surfaces must be compatible (see FFCOMPAT) before this blend
 is invoked. Very useful if a sequence that "morphs" one surface to another
 is to be created.
 Example:
@\begin{verbatim}
 for ( i = 0.0, 1.0, 11.0,
        Msrf = SMORPH( Srf1, Srf2, i / 11.0 ):
        color( Msrf, white ):
        attrib( Msrf, "rgb", "255,255,255" ):
        attrib( Msrf, "reflect", "0.7" ):
        save( "morp1-" + i, Msrf )
@\end{verbatim}
 creates a sequence of 12 surfaces, morphed from {\bf Srf1} to {\bf Srf2}
 and saves them in the files "morph-0.dat" to "morph-11.dat".
 See also CMORPH.
@See Figure~\ref{fig-smorph}.
@\begin{figure}
@\vspace{1.2in}
@\special{psfile=user_man/smorph.ps hscale=100 vscale=100 hoffset=-50 voffset=-150}
@\caption{A morphing sequence between a bottle and a glass. Snapshots computed
@        using SMORPH.}
@\label{fig-smorph}
@\end{figure}
@\subsubsection{SNORMAL}
!SNORMAL
@\begin{verbatim}
 VectorType SNORMAL( SurfaceType Srf, NumericType UParam, NumericType VParam )
@\end{verbatim}
   Computes the normal vector to {\bf Srf} at the parameter values {\bf UParam}
 and {\bf VParam}. The returned vector has a unit length.
 Example:
@\begin{verbatim}
    Normal = SNORMAL( Srf, 0.5, 0.5 );
@\end{verbatim}
 computes the normal to {\bf Srf} at the parameter values (0.5, 0.5).
 See also SNRMLSRF.
@\subsubsection{SNRMLSRF}
!SNRMLSRF
@\begin{verbatim}
 SurfaceType SNRMLSRF( SurfaceType Srf )
@\end{verbatim}
 Symbolically computes a vector field surface representing the non-normalized
 normals of the given surface. That is the normal surface, evaluated at
 $(u, v)$, provides a vector in the direction of the normal of the original
 surface at $(u, v)$. The normal surface is computed as the symbolic cross
 product of the two surfaces representing the partial derivatives of the
 original surface.
 Example:
@\begin{verbatim}
 NrmlSrf = SNRMLSRF( Srf );
@\end{verbatim}
@See Figure~\ref{fig-snrmlsrf}.
@\begin{figure}
@\vspace{2.7in}
@\special{psfile=user_man/snrmlsrf.ps hscale=80 vscale=80 hoffset=10 voffset=-140}
@\caption{A vector field normal (right) computed for a unit sphere using SNRMLSRF.
@        The normal field degenerates at the norph and south poles because the
@        surface is not regular there.}
@\label{fig-snrmlsrf}
@\end{figure}
@\subsubsection{SPHERE}
!SPHERE
@\begin{verbatim}
 PolygonType SPHERE( VectorType Center, NumericType Radius )
@\end{verbatim}
   Creates a SPHERE geometric object, defined by {\bf Center} as the center of
 the SPHERE, and with {\bf Radius} as the radius of the SPHERE.
   See RESOLUTION for accuracy of SPHERE approximation as a polygonal model.
@\subsubsection{SRAISE}
!SRAISE
@\begin{verbatim}
 SurfaceType SRAISE( SurfaceType Srf, ConstantType Direction,
                                                      NumericType NewOrder )
@\end{verbatim}
   Raises {\bf Srf} to the specified {\bf NewOrder} in the specified
 {\bf Direction}.
 Example:
@\begin{verbatim}
    Srf = ruledSrf( cbezier( list( ctlpt( E3, -0.5, -0.5, 0.0 ),
                                   ctlpt( E3,  0.5, -0.5, 0.0 ) ) ),
                    cbezier( list( ctlpt( E3, -0.5,  0.5, 0.0 ),
                                   ctlpt( E3,  0.5,  0.5, 0.0 ) ) ) );
    Srf = SRAISE( SRAISE( Srf, ROW, 3 ), COL, 3 );
@\end{verbatim}
 constructs a bilinear flat ruled surface and raises both its directions to be
 a bi-quadratic surface.
@\subsubsection{SREFINE}
!SREFINE
@\begin{verbatim}
 SurfaceType SREFINE( SurfaceType Srf, ConstantType Direction,
                      NumericType Replace, ListType KnotList )
@\end{verbatim}
   Provides the ability to {\bf Replace} a knot vector of {\bf Srf} or refine
 it in the specified direction {\bf Direction} (ROW or COL).
   {\bf KnotList} is a list of knots to refine {\bf Srf} at. All knots should be
 contained in the parametric domain of {\bf Srf} in {\bf Direction}. If the knot
 vector is replaced, the length of {\bf KnotList} should be identical to the
 length of the original knot vector of {\bf Srf} in {\bf Direction}. If {\bf Srf}
 is a Bezier surface, it is automatically promoted to be a Bspline surface.
 Example:
@\begin{verbatim}
    Srf = SREFINE( SREFINE( Srf,
                            ROW, FALSE, list( 0.333, 0.667 ) ),
                   COL, FALSE, list( 0.333, 0.667 ) );
@\end{verbatim}
 refines {\bf Srf} in both directions by adding two more knots at 0.333 and
 0.667.
@\subsubsection{SREGION}
!SREGION
@\begin{verbatim}
 SurfaceType SREGION( SurfaceType Srf, ConstantType Direction,
                                  NumericType MinParam, NumericType MaxParam )
@\end{verbatim}
   Extracts a region of {\bf Srf} between {\bf MinParam} and {\bf MaxParam}
 in the specified {\bf Direction}. Both {\bf MinParam} and {\bf MaxParam}
 should be contained in the parametric domain of {\bf Srf} in {\bf Direction}.
 Example:
@\begin{verbatim}
    Srf = ruledSrf( cbezier( list( ctlpt( E3, -0.5, -0.5, 0.5 ),
                                   ctlpt( E3,  0.0,  0.5, 0.0 ),
                                   ctlpt( E3,  0.5, -0.5, 0.0 ) ) ),
                    cbezier( list( ctlpt( E3, -0.5,  0.5, 0.0 ),
                                   ctlpt( E3,  0.0,  0.0, 0.0 ),
                                   ctlpt( E3,  0.5,  0.5, 0.5 ) ) ) );
    SubSrf = SREGION( Srf, ROW, 0.3, 0.6 );
@\end{verbatim}
 extracts the region of {\bf Srf} from the parameter value 0.3 to the
 parameter value 0.6 along the ROW direction. the COLumn direction is
 extracted as a whole.
@See Figure~\ref{fig-sregion}.
@\begin{figure}
@\vspace{2.2in}
@\special{psfile=user_man/sregion.ps hscale=100 vscale=100 hoffset=-40 voffset=-190}
@\caption{A region can be extracted from a freeform surface using SREGION.}
@\label{fig-sregion}
@\end{figure}
@\subsubsection{SREPARAM}
!SREPARAM
@\begin{verbatim}
 SurfaceType SREPARAM( SurfaceType Srf, ConstantType Direction,
                                  NumericType MinParam, NumericType MaxParam )
@\end{verbatim}
   Reparametrize {\bf Srf} over a new domain from {\bf MinParam} to {\bf MaxParam},
 in the prescribed {\bf Direction}. This operation does not affect the geometry
 of the surface and only affine transforms its knot vectors. A Bezier surface
 will automatically be promoted into a Bspline surface by this function.
 Example:
@\begin{verbatim}
    srf = sbspline( 2, 4,
                     list( list( ctlpt( E3, 0.0, 0.0, 1.0 ),
                                 ctlpt( E2, 0.0, 1.0 ),
                                 ctlpt( E3, 0.0, 2.0, 1.0 ) ),
                           list( ctlpt( E2, 1.0, 0.0 ),
                                 ctlpt( E3, 1.0, 1.0, 2.0 ),
                                 ctlpt( E2, 1.0, 2.0 ) ),
                           list( ctlpt( E3, 2.0, 0.0, 2.0 ),
                                 ctlpt( E2, 2.0, 1.0 ),
                                 ctlpt( E3, 2.0, 2.0, 2.0 ) ),
                           list( ctlpt( E2, 3.0, 0.0 ),
                                 ctlpt( E3, 3.0, 1.0, 2.0 ),
                                 ctlpt( E2, 3.0, 2.0 ) ),
                           list( ctlpt( E3, 4.0, 0.0, 1.0 ),
                                 ctlpt( E2, 4.0, 1.0 ),
                                 ctlpt( E3, 4.0, 2.0, 1.0 ) ) ),
                     list( list( KV_OPEN ),
                           list( KV_OPEN ) ) );
    srf = sreparam( sreparam( srf, ROW, 0, 1 ), COL, 0, 1 );
@\end{verbatim}
 Ensures that the Bspline surface is defined over the unit size parametric
 domain.
@\subsubsection{STANGENT}
!STANGENT
@\begin{verbatim}
 VectorType STANGENT( SurfaceType Srf, ConstantType Direction,
                      NumericType UParam, NumericType VParam )
@\end{verbatim}
   Computes the tangent vector to {\bf Srf} at the parameter values {\bf UParam}
 and {\bf VParam} in {\bf Direction}. The returned vector has a unit length.
 Example:
@\begin{verbatim}
    Tang = STANGENT( Srf, ROW, 0.5, 0.6 );
@\end{verbatim}
 computes the tangent to {\bf Srf} in the ROW direction at the parameter
 values (0.5, 0.6).
@\subsubsection{STRIMSRF}
!STRIMSRF
@\begin{verbatim}
 SurfaceType STRIMSRF( TrimSrfType TSrf )
@\end{verbatim}
   Extracts the surface of a trimmed surface {\bf TSrf}.
 Example:
@\begin{verbatim}
    Srf = STRIMSRF( TrimSrf );
@\end{verbatim}
 extracts the surface of {\bf TrimSrf}.
@\subsubsection{STRIVAR}
!STRIVAR
@\begin{verbatim}
 SurfaceType STRIVAR( TrivarType TV )
@\end{verbatim}
   Extracts an iso surface from a trivariate function {\bf TV}.
 Example:
@\begin{verbatim}
    TV1 = tbezier( list( list( list( ctlpt( E3, 0.1, 0.0, 0.8 ),
                                     ctlpt( E3, 0.2, 0.1, 2.4 ) ),
                               list( ctlpt( E3, 0.3, 2.2, 0.2 ),
                                     ctlpt( E3, 0.4, 2.3, 2.0 ) ) ),
                         list( list( ctlpt( E3, 2.4, 0.8, 0.1 ),
                                     ctlpt( E3, 2.2, 0.7, 2.3 ) ),
                               list( ctlpt( E3, 2.3, 2.6, 0.5 ),
                                     ctlpt( E3, 2.1, 2.5, 2.7) ) ) ) );
    Srf = STRIVAR( TV1, col, 0.4 );
@\end{verbatim}
 extracts an iso surface of {\bf TV1}, in the {\bf col} direction at
 parameter value 0.4.
@See Figure~\ref{fig-strivar}.
@\begin{figure}
@\vspace{2.5in}
@\special{psfile=user_man/strivar.ps hscale=100 vscale=100 hoffset=-35 voffset=-170}
@\caption{Extracts an iso bilinear surface from a trilinear function,
@    using STRIVAR.}
@\label{fig-strivar}
@\end{figure}
@\subsubsection{SURFPREV}
!SURFPREV
@\begin{verbatim}
 SurfaceType SURFPREV( CurveType Object )
@\end{verbatim}
 Same as SURFREV but approximates the surface of revolution as a
 {\em polynomial} surface. Object must be a polynomial curve.
 See SURFREV.
@\subsubsection{SURFREV}
!SURFREV
@\begin{verbatim}
 PolygonType SURFREV( PolygonType Object )
 SurfaceType SURFREV( CurveType Object )
@\end{verbatim}
   Creates a surface of revolution by rotating the first polygon/curve of the
 given {\bf Object}, around the Z axis. Use the linear transformation function
 to position a surface of revolution in a different orientation.
 Example:
@\begin{verbatim}
    VTailAntn = SURFREV( ctlpt( E3, 0.001, 0.0, 1.0 ) +
                         ctlpt( E3, 0.01,  0.0, 1.0 ) +
                         ctlpt( E3, 0.01,  0.0, 0.8 ) +
                         ctlpt( E3, 0.03,  0.0, 0.7 ) +
                         ctlpt( E3, 0.03,  0.0, 0.3 ) +
                         ctlpt( E3, 0.001, 0.0, 0.0 ) );
@\end{verbatim}
 constructs a piecewise linear Bspline curve in the XZ plane and uses it to
 construct a surface of revolution by rotating it around the Z axis.
   See also SURFPREV.
@See Figure~\ref{fig-surfrev}.
@\begin{figure}
@\vspace{2.4in}
@\special{psfile=user_man/surfrev.ps hscale=100 vscale=100 hoffset=-60 voffset=-140}
@\caption{A surface of revolution, VTailAntn in surfrev documentation, can be
@        constructed using SURFREV or SURFPREV.}
@\label{fig-surfrev}
@\end{figure}
@\subsubsection{SWEEPSRF}
!SWEEPSRF
@\begin{verbatim}
 SurfaceType SWEEPSRF( CurveType CrossSection, CurveType Axis,
                     CurveType FrameCrv | VectorType FrameVec | ConstType OFF )
@\end{verbatim}
   Constructs a generalized cylinder surface. This function sweeps a specified
 cross-section {\bf CrossSection} along the provided {\bf Axis}.
   By default, when frame specification is {\bf OFF}, the orientation
 of the cross section is computed using the {\bf Axis} curve tangent and
 normal. However, unlike the Frenet frame, attempt is made to minimize
 the normal change, as can happen along inflection points in {\bf Axis}.
   If a VectorType {\bf FrameVec} is provided as a frame orientation setting,
 it is used to fix the binormal direction to this value. In other words, the
 orientation frame has a fixed binormal. If a CurveType {\bf FrameCrv} is
 specified as a frame orientation setting, this vector field curve is
 evaluated at each placement of the cross-section to yield the needed binormal.
   The resulting sweep is only an approximation of the real sweep. The
 resulting sweep surface will not be exact, in general.
   Refinement of the axis curve at the proper location, where accuracy is
 important, should improve the accuracy of the output. The parametric domains
 of {\bf FrameCrv} do not have to match the parametric domain of {\bf Axis},
 and its parametric domain is automatically made compatible by this function.
 Example:
@\begin{verbatim}
    Cross = arc( vector( 0.2, 0.0, 0.0 ),
                 vector( 0.2, 0.2, 0.0 ),
                 vector( 0.0, 0.2, 0.0 ) ) +
            arc( vector( 0.0, 0.4, 0.0 ),
                 vector( 0.1, 0.4, 0.0 ),
                 vector( 0.1, 0.5, 0.0 ) ) +
            arc( vector( 0.8, 0.5, 0.0 ),
                 vector( 0.8, 0.3, 0.0 ),
                 vector( 1.0, 0.3, 0.0 ) ) +
            arc( vector( 1.0, 0.1, 0.0 ),
                 vector( 0.9, 0.1, 0.0 ),
                 vector( 0.9, 0.0, 0.0 ) ) +
            ctlpt( E2, 0.2, 0.0 );
    Axis = arc( vector( -1.0, 0.0, 0.0 ),
                vector(  0.0, 0.0, 0.1 ),
                vector(  1.0, 0.0, 0.0 ) );
    Axis = crefine( Axis, FALSE, list( 0.25, 0.5, 0.75 ) );
    Srf1 = SWEEPSRF( Cross, Axis, OFF );
    Srf2 = SWEEPSRF( Cross, Axis, vector( 0.0, 1.0, 1.0 ) );
    Srf3 = SWEEPSRF( Cross, Axis,
                     cbezier( list( ctlpt( E3,  1.0, 0.0, 0.0 ),
                                    ctlpt( E3,  0.0, 1.0, 0.0 ),
                                    ctlpt( E3, -1.0, 0.0, 0.0 ) ) ) );
@\end{verbatim}
 constructs a rounded rectangle cross-section and sweeps it along an arc,
 while orienting it several ways. The axis curve {\bf Axis} is manually
 refined to better approximate the requested shape.
 See also SWPSCLSRF for sweep with scale.
@See Figure~\ref{fig-sweepsrf}.
@\begin{figure}
@\vspace{1.4in}
@\special{psfile=user_man/sweepsrf.ps hscale=100 vscale=100 hoffset=-30 voffset=-210}
@\caption{Three examples of the use of SWEEPSRF (Srf1, Srf2, Srf3 from left to right
@        in sweepsrf documentation).}
@\label{fig-sweepsrf}
@\end{figure}
@\subsubsection{SWPSCLSRF}
!SWPSCLSRF
@\begin{verbatim}
 SurfaceType SWPSCLSRF( CurveType CrossSection, CurveType Axis,
                        NumericType Scale | CurveType ScaleCrv,
                        CurveType FrameCrv | VectorType FrameVec
                                                          | ConstType OFF,
                        NumericType ScaleRefine )
@\end{verbatim}
   Constructs a generalized cylinder surface. This function sweeps a specified
 cross-section {\bf CrossSection} along the provided {\bf Axis}.
 The cross-section may be scaled by a constant value {\bf Scale}, or scaled
 along the {\bf Axis} parametric direction via a scaling curve {\bf ScaleCrv}.
   By default, when frame specification is {\bf OFF}, the orientation
 of the cross section is computed using the {\bf Axis} curve tangent and
 normal. However, unlike the Frenet frame, attempt is made to minimize
 the normal change, as can happen along inflection points in {\bf Axis}.
   If a VectorType {\bf FrameVec} is provided as a frame orientation setting,
 it is used to fix the binormal direction to this value. In other words, the
 orientation frame has a fixed binormal. If a CurveType {\bf FrameCrv} is
 specified as a frame orientation setting, this vector field curve is
 evaluated at each placement of the cross-section to yield the needed binormal.
   {\bf ScaleRefine} is an integer value to define possible refinement of the
 {\bf Axis} to reflect the information in {\bf ScalingCrv}. Value of zero will
 force no refinement while value of $n > 0$ will insert $n$ times the
 number of control points in {\bf ScaleCrv} into {\bf Axis}, better emulating
 the scaling requested.
   The resulting sweep is only an approximation of the real sweep. The
 scaling and axis placement will not be exact, in general.
   Manual refinement (in addition to {\bf ScaleRefine}) of the axis curve at
 the proper location, where accuracy is important, should improve the accuracy
 of the output. The parametric domains of {\bf ScaleCrv} and {\bf FrameCrv} do
 not have to match the parametric domain of {\bf Axis}, and their domains are
 made compatible by this function.
 Example:
@\begin{verbatim}
    Cross = arc( vector( -0.11, -0.01, 0.0 ),
                 vector( -0.1,  -0.1,  0.0 ),
                 vector( -0.1,  -0.11, 0.0 ) ) +
            arc( vector(  0.1,  -0.11, 0.0 ),
                 vector(  0.1,  -0.1,  0.0 ),
                 vector(  0.11, -0.1,  0.0 ) ) +
            arc( vector(  0.11,  0.1,  0.0 ),
                 vector(  0.1,   0.1,  0.0 ),
                 vector(  0.1,   0.11, 0.0 ) ) +
            arc( vector( -0.1,   0.11, 0.0 ),
                 vector( -0.1,   0.1,  0.0 ),
                 vector( -0.11,  0.1,  0.0 ) ) +
            ctlpt( E2, -0.11, -0.1 );
    scaleCrv = cbspline( 3,
                         list( ctlpt( E2, 0.05, 1.0 ),
                               ctlpt( E2, 0.1,  0.0 ),
                               ctlpt( E2, 0.2,  2.0 ),
                               ctlpt( E2, 0.3,  0.0 ),
                               ctlpt( E2, 0.4,  2.0 ),
                               ctlpt( E2, 0.5,  0.0 ),
                               ctlpt( E2, 0.6,  2.0 ),
                               ctlpt( E2, 0.7,  0.0 ),
                               ctlpt( E2, 0.8,  2.0 ),
                               ctlpt( E2, 0.85, 1.0 ) ),
                         list( KV_OPEN ) );
    Axis = circle( vector( 0, 0, 0 ), 1 );
    Frame = circle( vector( 0, 0, 0 ), 1 )
            * rotx( 90 ) * trans( vector( 1.5, 0.0, 0.0 ) );
    Srf1 = SWPSCLSRF( Cross, Axis, scaleCrv, off, 0 );
    Srf2 = SWPSCLSRF( Cross, Axis, scaleCrv, off, 2 );
    Srf3 = SWPSCLSRF( Cross, Axis, 1.0, Frame, 0 );
@\end{verbatim}
 constructs a rounded rectangle cross-section and sweeps it along a circle,
 while scaling and orienting in several ways. The axis curve {\bf Axis} is
 automatically refined in {\bf Srf2} to better approximate the requested
 scaling.
 See also SWEEPSRF for sweep with no scale.
@See Figure~\ref{fig-swpsclsrf}.
@\begin{figure}
@\vspace{1.2in}
@\special{psfile=user_man/swpsclsrf.ps hscale=100 vscale=100 hoffset=-35 voffset=-170}
@\caption{Three examples of the use of SWPSCLSRF (Srf1, Srf2, Srf3 from left to right
@        in swpsclsrf documentation).}
@\label{fig-swpsclsrf}
@\end{figure}
@\subsubsection{SYMBPROD}
!SYMBPROD
@\begin{verbatim}
 CurveType SYMBPROD( CurveType Crv1, CurveType Crv2 )
 SurfaceType SYMBPROD( SurfaceType Srf1, SurfaceType Srf2 )
@\end{verbatim}
 Computes the symbolic product of the given two curves or surfaces as
 a curve or surface. The product is computed coordinate-wise.
 Example:
@\begin{verbatim}
 ProdSrf = SYMBPROD( Srf1, Srf2 )
@\end{verbatim}
@\subsubsection{SYMBDPROD}
!SYMBDPROD
@\begin{verbatim}
 CurveType SYMBDPROD( CurveType Crv1, CurveType Crv2 )
 SurfaceType SYMBDPROD( SurfaceType Srf1, SurfaceType Srf2 )
@\end{verbatim}
 Computes the symbolic dot (inner) product of the given two curves or surfaces
 as a {\em scalar} curve or surface.
 Example:
@\begin{verbatim}
 DiffCrv = symbdiff( Crv1, Crv2 )
 DistSqrCrv = SYMBDPROD( DiffCrv, DiffCrv )
@\end{verbatim}
 Computes a scalar curve that at parameter $t$ is equal to the distance
 square between Crv1 at $t$ and Crv2.
@\subsubsection{SYMBCPROD}
!SYMBCPROD
@\begin{verbatim}
 CurveType SYMBCPROD( CurveType Crv1, CurveType Crv2 )
 SurfaceType SYMBCPROD( SurfaceType Srf1, SurfaceType Srf2 )
@\end{verbatim}
 Computes the symbolic cross product of the given two curves or surfaces as
 a curve or surface.
 Example:
@\begin{verbatim}
 NrmlSrf = SYMBCPROD( sderive( Srf, ROW ), sderive( Srf, COL ) )
@\end{verbatim}
 computes a normal surface as the cross product of the surface two partial
 derivatives (see SNRMLSRF).
@\subsubsection{SYMBSUM}
!SYMBSUM
@\begin{verbatim}
 CurveType SYMBSUM( CurveType Crv1, CurveType Crv2 )
 SurfaceType SYMBSUM( SurfaceType Srf1, SurfaceType Srf2 )
@\end{verbatim}
 Computes the symbolic sum of the given two curves or surfaces as
 a curve or surface. The sum is computed coordinate-wise.
 Example:
@\begin{verbatim}
 SumCrv = SYMBSUM( Crv1, Crv2 )
@\end{verbatim}
@\subsubsection{SYMBDIFF}
!SYMBDIFF
@\begin{verbatim}
 CurveType SYMBDIFF( CurveType Crv1, CurveType Crv2 )
 SurfaceType SYMBDIFF( SurfaceType Srf1, SurfaceType Srf2 )
@\end{verbatim}
 Computes the symbolic difference of the given two curves or surfaces as
 a curve or surface. The difference is computed coordinate-wise.
 Example:
@\begin{verbatim}
 DiffCrv = SYMBDIFF( Crv1, Crv2 )
 DistSqrCrv = symbdprod( DiffCrv, DiffCrv )
@\end{verbatim}
@\subsubsection{TBEZIER}
!TBEZIER
@\begin{verbatim}
 TrivarType TBEZIER( ListType CtlMesh )
@\end{verbatim}
   Creates a Bezier trivariate using the provided control mesh. {\bf CtlMesh}
 is a list of planes, each of which is a list of rows, each of which is a list
 of control points. All control points must be of type (E1-E5, P1-P5), or
 regular PointType defining the trivariate's control mesh. Surface's point
 type will be of a space which is the union of the spaces of all points.
@The created trivariate is the piecewise polynomial (or rational) function,
@\begin{equation}
@     T(u, v, w) = \sum_{i=0}^m \sum_{j=0}^n \sum_{k=0}^l
@                        P_{ijk} B_i(u) B_j(v) B_k(w)
@\end{equation}
@where $P_{ijk}$ are the control points {\bf CtlMesh}. and $l$, $m$ and $n$
@are the degrees of the trivariate, which are one less than the number of
@points in the appropriate direction.
 Example:
@\begin{verbatim}
   TV = TBEZIER( list( list( list( ctlpt( E3, 0.1, 0.1, 0.0 ),
                                   ctlpt( E3, 0.2, 0.5, 1.1 ),
                                   ctlpt( E3, 0.3, 0.1, 2.2 ) ),
                             list( ctlpt( E3, 0.4, 1.3, 0.5 ),
                                   ctlpt( E3, 0.5, 1.7, 1.7 ),
                                   ctlpt( E3, 0.6, 1.3, 2.9 ) ),
                             list( ctlpt( E3, 0.7, 2.4, 0.5 ),
                                   ctlpt( E3, 0.8, 2.6, 1.4 ),
                                   ctlpt( E3, 0.9, 2.8, 2.3 ) ) ),
                       list( list( ctlpt( E3, 1.1, 0.1, 0.5 ),
                                   ctlpt( E3, 1.3, 0.2, 1.7 ),
                                   ctlpt( E3, 1.5, 0.3, 2.9 ) ),
                             list( ctlpt( E3, 1.7, 1.2, 0.0 ),
                                   ctlpt( E3, 1.9, 1.4, 1.2 ),
                                   ctlpt( E3, 1.2, 1.6, 2.4 ) ),
                             list( ctlpt( E3, 1.4, 2.3, 0.9 ),
                                   ctlpt( E3, 1.6, 2.5, 1.7 ),
                                   ctlpt( E3, 1.8, 2.7, 2.5 ) ) ) ) );
@\end{verbatim}
 creats a trivariate Bezier which is linear in the first direction, and
 quadratic in the second and third.
@See Figure~\ref{fig-tbezier}.
@\begin{figure}
@\vspace{3.2in}
@\special{psfile=user_man/tbezier.ps hscale=100 vscale=100 hoffset=-60 voffset=-100}
@\caption{A trivariate Bezier of degree 2 by 3 by 3 (left) and a trilinear
@     Bspline (right). Both share the same control mesh.}
@\label{fig-tbezier}
@\end{figure}
@\subsubsection{TBSPLINE}
!TBSPLINE
@\begin{verbatim}
 TrivarType TBSPLINE( NumericType UOrder,
                      NumericType VOrder,
                      NumericType WOrder,
                      ListType CtlMesh,
                      ListType KnotVectors )
@\end{verbatim}
   Creates a Bspline trivariate with the provided {\bf UOrder}, {\bf VOrder}
 and {\bf WOrder} orders, the control mesh {\bf CtlMesh}, and the three knot
 vectors in {\bf KnotVectors}.
   {\bf CtlMesh} is a list of planes, each of which is a list of rows, each
 of which is a list of control points. All control points must be of point
 type (E1-E5, P1-P5), or regular PointType defining the trivariate's control
 mesh. Trivariate's point type will be of a space which is the union of the
 spaces of all points.
   {\bf KnotVectors} is a list of three knot vectors. Each knot vector is a
 list of NumericType knots of length {\bf \#CtlPtList} plus the {\bf Order}.
 If, however, the length of the knot vector is equal to {\bf \#CtlPtList +
 Order + Order - 1} the curve is assumed {\em periodic.}
   The knot vector may also be a list of a single constant KV\_OPEN or
 KV\_FLOAT or KV\_PERIODIC, in which a uniform knot vector with the
 appropriate length and with open, floating or periodic end condition
 will be constructed automatically.
@The created surface is the piecewise polynomial (or rational) surface,
@\begin{equation}
@     T(u, v, w) = \sum_{i=0}^m \sum_{j=0}^n \sum_{k=0}^l P_{ijk}
@                               B_{i,\chi}(u) B_{j,\xi}(v) B_{k,\phi}(w)
@\end{equation}
@where $P_{ijk}$ are the control points {\bf CtlMesh}, and $l$, $m$ and $n$
@are the degrees of the surface, which are one less than {\bf UOrder},
@{\bf VOrder} and {\bf WOrder} and $\chi$, $\xi$ and $\phi$ are the three
@knot vectors of the trivariate.
 Example:
@\begin{verbatim}
   TV = TBSPLINE( 2, 2, 2,
                  list( list( list( ctlpt( E3, 0.1, 0.1, 0.0 ),
                                    ctlpt( E3, 0.2, 0.5, 1.1 ),
                                    ctlpt( E3, 0.3, 0.1, 2.2 ) ),
                              list( ctlpt( E3, 0.4, 1.3, 0.5 ),
                                    ctlpt( E3, 0.5, 1.7, 1.7 ),
                                    ctlpt( E3, 0.6, 1.3, 2.9 ) ),
                              list( ctlpt( E3, 0.7, 2.4, 0.5 ),
                                    ctlpt( E3, 0.8, 2.6, 1.4 ),
                                    ctlpt( E3, 0.9, 2.8, 2.3 ) ) ),
                        list( list( ctlpt( E3, 1.1, 0.1, 0.5 ),
                                    ctlpt( E3, 1.3, 0.2, 1.7 ),
                                    ctlpt( E3, 1.5, 0.3, 2.9 ) ),
                              list( ctlpt( E3, 1.7, 1.2, 0.0 ),
                                    ctlpt( E3, 1.9, 1.4, 1.2 ),
                                    ctlpt( E3, 1.2, 1.6, 2.4 ) ),
                              list( ctlpt( E3, 1.4, 2.3, 0.9 ),
                                    ctlpt( E3, 1.6, 2.5, 1.7 ),
                                    ctlpt( E3, 1.8, 2.7, 2.5 ) ) ) ),
                  list( list( KV_OPEN ),
                        list( KV_OPEN ),
                        list( KV_OPEN ) ) );
@\end{verbatim}
 constructs a trilinear Bspline trivariate with open end conditions.
@See Figure~\ref{fig-tbezier}.
@\subsubsection{TDERIVE}
!TDERIVE
@\begin{verbatim}
 TrivarType TDERIVE( TrivarType TV, NumericType Dir )
@\end{verbatim}
   Returns a vector field trivariate representing the differentiated
 trivariate in the given direction (ROW, COL, or DEPTH). Evaluation of the
 returned trivariate at a given parameter value will return a vector
 representing the partial derivative of {\bf TV} in {\bf Dir} at that
 parameter value.
@\begin{verbatim}
 TV = tbezier( list( list( list( ctlpt( E1, 0.1 ),
                                 ctlpt( E1, 0.2 ) ),
                           list( ctlpt( E1, 0.3 ),
                                 ctlpt( E1, 0.4 ) ) ),
                     list( list( ctlpt( E1, 2.4 ),
                                 ctlpt( E1, 2.2 ) ),
                           list( ctlpt( E1, 2.3 ),
                                 ctlpt( E1, 2.1 ) ) ) ) );
 DuTV = TDERIVE( TV, ROW );
 DvTV = TDERIVE( TV, COL );
 DwTV = TDERIVE( TV, DEPTH );
@\end{verbatim}
 computes the gradiate of a scalar trivariate field, by computing its
 partials with respect to u, v, and w.
@\subsubsection{TDIVIDE}
!TDIVIDE
@\begin{verbatim}
 TrivarType TDIVIDE( TrivarType TV, ConstantType Direction,
                                                          NumericType Param )
@\end{verbatim}
   Subdivides a trivariate into two at the specified parameter value {\bf Param}
 in the specified {\bf Direction} (ROW, COL, or DEPTH). {\bf TV} can be either
 a Bspline trivairate in which {\bf Param} must be conatined in the parametric
 domain of the trivariate, or a Bezier trivariate in which {\bf Param} must be
 in the range of zero to one.
   It returns a list of the two sub-trivariates. The individual trivariates
 may be extracted from the list using the {\bf NTH} command.
 Example:
@\begin{verbatim}
    TvDiv = TDIVIDE( Tv2, depth, 0.3 );
    Tv2a = nth( TvDiv, 1 ) * tx( -2.2 );
    Tv2b = nth( TvDiv, 2 ) * tx( 2.0 );
@\end{verbatim}
 subdivides {\bf Tv2} at the parameter value of 0.3 in the DEPTH direction,
@See Figure~\ref{fig-tdivide}.
@\begin{figure}
@\vspace{2.6in}
@\special{psfile=user_man/tdivide.ps hscale=110 vscale=110 hoffset=-60 voffset=-135}
@\caption{A trivariate can be subdivided into two distinct regions using TDIVIDE.}
@\label{fig-tdivide}
@\end{figure}
@\subsubsection{TEVAL}
!TEVAL
@\begin{verbatim}
 CtlPtType TEVAL( TrivarType TV,
                  NumericType UParam,
                  NumericType VParam,
                  NumericType WParam )
@\end{verbatim}
   Evaluates the provided trivariate {\bf TV} at the given {\bf UParam},
 {\bf VParam}  and {\bf WParam} values. {\bf UParam}, {\bf VParam},
 {\bf WParam} must be contained in the surface parametric domain if {\bf TV}
 is a Bspline surface, or between zero and one if {\bf TV} is a Bezier
 trivariate. The returned control point has the same type as the control
 points of {\bf TV}.
 Example:
@\begin{verbatim}
    CPt = TEVAL( TV1, 0.25, 0.22, 0.7 );
@\end{verbatim}
 evaluates {\bf TV} at the parameter values of (0.25, 0.22, 0.7).
@\subsubsection{TINTERP}
!TINTERP
@\begin{verbatim}
 TrivarType TINTERP( TrivarType TV );
@\end{verbatim}
   Given a trivariate data structure, computes a new trivariate in the
 same function space (i.e. same knot sequences and orders) that interpolates
 the given triavriate, {\bf TV}, at the node parameter values.
 Example:
@\begin{verbatim}
     tv = tbspline( 3, 3, 2,
                    list( list( list( ctlpt( E3, 0.1, 0.1, 0.0 ),
                                      ctlpt( E3, 0.2, 0.5, 1.1 ),
                                      ctlpt( E3, 0.3, 0.1, 2.2 ) ),
                                list( ctlpt( E3, 0.4, 1.3, 0.5 ),
                                      ctlpt( E3, 0.5, 1.7, 1.7 ),
                                      ctlpt( E3, 0.6, 1.3, 2.9 ) ),
                                list( ctlpt( E3, 0.7, 2.4, 0.5 ),
                                      ctlpt( E3, 0.8, 2.6, 1.4 ),
                                      ctlpt( E3, 0.9, 2.8, 2.3 ) ) ),
                          list( list( ctlpt( E3, 1.1, 0.1, 0.5 ),
                                      ctlpt( E3, 1.3, 0.2, 1.7 ),
                                      ctlpt( E3, 1.5, 0.3, 2.9 ) ),
                                list( ctlpt( E3, 1.7, 1.2, 0.0 ),
                                      ctlpt( E3, 1.9, 1.4, 1.2 ),
                                      ctlpt( E3, 1.2, 1.6, 2.4 ) ),
                                list( ctlpt( E3, 1.4, 2.3, 0.9 ),
                                      ctlpt( E3, 1.6, 2.5, 1.7 ),
                                      ctlpt( E3, 1.8, 2.7, 2.5 ) ) ),
                          list( list( ctlpt( E3, 2.8, 0.1, 0.4 ),
                                      ctlpt( E3, 2.6, 0.7, 1.3 ),
                                      ctlpt( E3, 2.4, 0.2, 2.2 ) ),
                                list( ctlpt( E3, 2.2, 1.1, 0.4 ),
                                      ctlpt( E3, 2.9, 1.2, 1.5 ),
                                      ctlpt( E3, 2.7, 1.3, 2.6 ) ),
                                list( ctlpt( E3, 2.5, 2.9, 0.7 ),
                                      ctlpt( E3, 2.3, 2.8, 1.7 ),
                                      ctlpt( E3, 2.1, 2.7, 2.7 ) ) ) ),
                    list( list( KV_OPEN ),
                          list( KV_OPEN ),
                          list( KV_OPEN ) ) );
    tvi = TINTERP( tv );
@\end{verbatim}
 creates a quadratic by quaratic by linear trivairatiate {\bf tvi} that
 interpolates the control points of {\bf tv} at the node parameter values.
@\subsubsection{TORUS}
!TORUS
@\begin{verbatim}
 PolygonType TORUS( VectorType Center, VectorType Normal,
                    NumericType MRadius, NumericType mRadius )
@\end{verbatim}
   Creates a TORUS geometric object, defined by {\bf Center} as the center
 of the TORUS, {\bf Normal} as the normal to the main plane of the TORUS,
 {\bf MRadius} and {\bf mRadius} as the major and minor radii of the TORUS.
   See RESOLUTION for the accuracy of the TORUS approximation as a polygonal
 model.
 Example:
@\begin{verbatim}
    T = TORUS( vector( 0.0, 0.0, 0.0), vector( 0.0, 0.0, 1.0), 0.5, 0.2 );
@\end{verbatim}
 constructs a torus with major plane as the $XY$ plane, major radius of 0.5,
 and minor radius of 0.2.
@See Figure~\ref{fig-torus}.
@\begin{figure}
@\vspace{2.2in}
@\special{psfile=user_man/torus.ps hscale=100 vscale=100 hoffset=-40 voffset=-140}
@\caption{A torus primitive can be constructed using a TORUS constructor...}
@\label{fig-torus}
@\end{figure}
@\subsubsection{TREFINE}
!TREFINE
@\begin{verbatim}
 TrivarType TREFINE( TrivarType TV, ConstantType Direction,
                     NumericType Replace, ListType KnotList )
@\end{verbatim}
   Provides the ability to {\bf Replace} a knot vector of {\bf TV} or refine
 it in the specified direction {\bf Direction} (ROW, COL, or DEPTH).
   {\bf KnotList} is a list of knots to refine {\bf TV} at. All knots should be
 contained in the parametric domain of {\bf TV} in {\bf Direction}. If the knot
 vector is replaced, the length of {\bf KnotList} should be identical to the
 length of the original knot vector of {\bf TV} in {\bf Direction}. If {\bf TV}
 is a Bezier trivariate, it is automatically promoted to be a Bspline
 trivariate.
 Example:
@\begin{verbatim}
    TV = TREFINE( TREFINE( TREFINE( TV,
                                    ROW, FALSE, list( 0.333, 0.667 ) ),
                           COL, FALSE, list( 0.333, 0.667 ) ),
                  DEPTH, FALSE, list( 0.333, 0.667 ) );
@\end{verbatim}
 refines {\bf TV} in all directions by adding two more knots at 0.333 and
 0.667.
@\subsubsection{TREGION}
!TREGION
@\begin{verbatim}
 TrivarType TREGION( TrivarType Srf, ConstantType Direction,
                     NumericType MinParam, NumericType MaxParam )
@\end{verbatim}
   Extracts a region of {\bf TV} between {\bf MinParam} and {\bf MaxParam}
 in the specified {\bf Direction}. Both {\bf MinParam} and {\bf MaxParam}
 should be contained in the parametric domain of {\bf TV} in {\bf Direction}.
 Example:
@\begin{verbatim}
    Tv1 = tbezier( list( list( list( ctlpt( E3, 0.1, 0.0, 0.8 ),
                                     ctlpt( E3, 0.2, 0.1, 2.4 ) ),
                               list( ctlpt( E3, 0.3, 2.2, 0.2 ),
                                     ctlpt( E3, 0.4, 2.3, 2.0 ) ) ),
                         list( list( ctlpt( E3, 2.4, 0.8, 0.1 ),
                                     ctlpt( E3, 2.2, 0.7, 2.3 ) ),
                               list( ctlpt( E3, 2.3, 2.6, 0.5 ),
                                     ctlpt( E3, 2.1, 2.5, 2.7) ) ) ) );
    Tv1r1 = TREGION( Tv1, row, 0.1, 0.2 );
    Tv1r2 = TREGION( Tv1, row, 0.4, 0.6 );
    Tv1r3 = TREGION( Tv1, row, 0.99, 1.0 );
@\end{verbatim}
 extracts three regions of {\bf Tv1} along the ROW direction.
@See Figure~\ref{fig-tregion}.
@\begin{figure}
@\vspace{3.3in}
@\special{psfile=user_man/tregion.ps hscale=100 vscale=100 hoffset=-40 voffset=-110}
@\caption{A region can be extracted from a freeform trivariate using TREGION.}
@\label{fig-tregion}
@\end{figure}
@\subsubsection{TRIMSRF}
!TRIMSRF
@\begin{verbatim}
 TrimSrfType TRIMSRF( SurfaceType Srf,
                      CurveType TrimCrv,
                      NumericType UpperLevel )
 TrimSrfType TRIMSRF( SurfaceType Srf,
                      ListType TrimCrvs,
                      NumericType UpperLevel )
@\end{verbatim}
   Creates a trimmed surface from the provided surface {\bf Srf} and the
 trimming curve {\bf TrimCrv} or curves {\bf TrimCrvs}. If {\bf UpperLevel},
 an additional trimming curve is automatically being added that contains the
 entire parametric domain of {\bf Srf}. No validity test is performed on the
 trimming curves which are assumed two dimensional curves contained in
 the parametric domain of {\bf Srf}.
 Example:
@\begin{verbatim}
    spts = list( list( ctlpt( E3, 0.1, 0.0, 1.0 ),
                       ctlpt( E3, 0.3, 1.0, 0.0 ),
                       ctlpt( E3, 0.0, 2.0, 1.0 ) ),
                 list( ctlpt( E3, 1.1, 0.0, 0.0 ),
                       ctlpt( E3, 1.3, 1.5, 2.0 ),
                       ctlpt( E3, 1.0, 2.1, 0.0 ) ),
                 list( ctlpt( E3, 2.1, 0.0, 2.0 ),
                       ctlpt( E3, 2.3, 1.0, 0.0 ),
                       ctlpt( E3, 2.0, 2.0, 2.0 ) ),
                 list( ctlpt( E3, 3.1, 0.0, 0.0 ),
                       ctlpt( E3, 3.3, 1.5, 2.0 ),
                       ctlpt( E3, 3.0, 2.1, 0.0 ) ),
                 list( ctlpt( E3, 4.1, 0.0, 1.0 ),
                       ctlpt( E3, 4.3, 1.0, 0.0 ),
                       ctlpt( E3, 4.0, 2.0, 1.0 ) ) );
    sb = sbspline( 3, 3, spts, list( list( KV_OPEN ), list( KV_OPEN ) ) );
    TCrv1 = cbspline( 2,
                      list( ctlpt( E2, 0.3, 0.3 ),
                            ctlpt( E2, 0.7, 0.3 ),
                            ctlpt( E2, 0.7, 0.7 ),
                            ctlpt( E2, 0.3, 0.7 ),
                            ctlpt( E2, 0.3, 0.3 ) ),
                      list( KV_OPEN ) );
    TCrv2 = circle( vector( 0.5, 0.5, 0.0 ), 0.25 );
    TCrv3 = cbspline( 3,
                      list( ctlpt( E2, 0.3, 0.3 ),
                            ctlpt( E2, 0.7, 0.3 ),
                            ctlpt( E2, 0.7, 0.7 ),
                            ctlpt( E2, 0.3, 0.7 ) ),
                      list( KV_PERIODIC ) );
    TSrf1 = TRIMSRF( sb, TCrv1, false );
    TSrf2 = TRIMSRF( sb, TCrv1, true );
    TSrf3 = TRIMSRF( sb, list( TCrv1, TcRv2 * ty( 1 ), TCrv3 * ty( 2 ) ),
                      false );
@\end{verbatim}
 constructs three trimmed surfaces. {\bf Tsrf1} contains the out boundary
 and excludes what is inside {\bf TCrv1}, {\bf TSrf2} contains only the
 domain inside {\bf TCrv1}. {\bf TCrv3} has three holes corresponds to the
 three trimming curves.
@See Figure~\ref{fig-trimsrf}.
@\begin{figure}
@\vspace{3.3in}
@\special{psfile=user_man/trimsrf.ps hscale=100 vscale=100 hoffset=-40 voffset=-140}
@\caption{Three trimmed surfaces created from the same Bspline surface. In
@    thin lines is the original surface while in thick lines are the trimmed
@    surfaces.}
@\label{fig-trimsrf}
@\end{figure}
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{Object transformation functions}
&Object transformation functions
 All the routines in this section construct a 4 by 4 homogeneous
 transformation matrix representing the required transform. These matrices
 may be concatenated to achieve more complex transforms using the matrix
 multiplication operator $*$. For example, the expression
@\begin{verbatim}
    m = trans( vector( -1, 0, 0 ) ) * rotx( 45 ) * trans( vector( 1, 0, 0 ) );
@\end{verbatim}
 constructs a transform to rotate an object around the X = 1 line, 45 degrees.
 A matrix representing the inverse transformation can be computed as:
@\begin{verbatim}
    InvM = m ^ -1
@\end{verbatim}
 See also overloading of the - operator.
@\subsubsection{HOMOMAT}
!HOMOMAT
@\begin{verbatim}
 MatrixType HOMOMAT( ListType MatData )
@\end{verbatim}
   Creates an arbitrary homogeneous transformation matrix by manually providing
 its 16 coefficients.
 Example:
@\begin{verbatim}
 for ( a = 1, 1, 720 / step,
       view_mat = save_mat *
                  HOMOMAT( list( list( 1, 0, 0, 0 ),
                                 list( 0, 1, 0, 0 ),
                                 list( 0, 0, 1, -a * step / 500 ),
                                 list( 0, 0, 0, 1 ) ) ):
       view(list(view_mat, b, axes), on)
@\end{verbatim}
 looping and viewing through a sequence of perspective transforms, created
 using the HOMOMAT constructor.
@\subsubsection{ROTX}
!ROTX
@\begin{verbatim}
 MatrixType ROTX( NumericType Angle )
@\end{verbatim}
   Creates a rotation around the X transformation matrix with {\bf Angle} degrees.
@\subsubsection{ROTY}
!ROTY
@\begin{verbatim}
 MatrixType ROTY( NumericType Angle )
@\end{verbatim}
   Creates a rotation around te Y transformation matrix with {\bf Angle} degrees.
@\subsubsection{ROTZ}
!ROTZ
@\begin{verbatim}
 MatrixType ROTZ( NumericType Angle )
@\end{verbatim}
   Creates a rotation around the Z transformation matrix with {\bf Angle} degrees.
@\subsubsection{SCALE}
!SCALE
@\begin{verbatim}
 MatrixType SCALE( VectorType ScaleFactors )
@\end{verbatim}
   Creates a scaling by the {\bf ScaleFactors} transformation matrix.
@\subsubsection{TRANS}
!TRANS
@\begin{verbatim}
 MatrixType TRANS( VectorType TransFactors )
@\end{verbatim}
   Creates a translation by the {\bf TransFactors} transformation matrix.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{General purpose functions}
&General purpose functions
@\subsubsection{ATTRIB}
!ATTRIB
@\begin{verbatim}
 ATTRIB( AnyType Object, StringType Name, AnyType Value )
@\end{verbatim}
   Provides a mechanism to add an attribute of any type to an {\bf Object},
 with name {\bf Name} and value {\bf Value}. This ATTRIB function is tuned
 and optimized toward numeric values or strings as {\bf Value} although any
 other object type can be saved as attribue.
   These attributes may be used to pass information to other programs about
 this object, and are saved with the objects in data files. For example,
@\begin{verbatim}
    ATTRIB(Glass, "rgb", "255,0,0");
    ATTRIB(Glass, "refract", 1.4);
        .
        .
        .
    RMATTR(Glass, "rgb");   # Removes "rgb" attribute.
@\end{verbatim}
 sets the RGB color and refraction index of the {\bf Glass} object and
 later removes the RGB attribute.
   Attribute names are case insensitive. Spaces are allowed in the {\bf Value}
 string, as well as the double quote itself, although the latter must be
 escaped:
@\begin{verbatim}
    ATTRIB(Glass, "text", "Say \"this is me\"");
@\end{verbatim}
   See also RMATTR for removal of attributes.
@\subsubsection{CHDIR}
!CHDIR
@\begin{verbatim}
 CHDIR( StringType NewDir )
@\end{verbatim}
   Sets the current working directory to be {\bf NewDir}.
@\subsubsection{CLNTCLOSE}
!CLNTCLOSE
@\begin{verbatim}
 CLNTCLOSE( NumericType Handler, NumericType Kill )
@\end{verbatim}
   Closes a communication channel to a client. {\bf Handler} contains the
 index of the communication channel opened via CLNTEXEC. If {\bf Kill}, the
 client is send an  exit request for it to die. Otherwise, the communication
 is closed and the client is running stand alone.  See also CLNTREAD,
 CLNTWRITE, and CLNTEXEC.
 Example:
@\begin{verbatim}
   h2 = clntexec( "nuldrvs -s-" );
       .
       .
       .
   CLNTCLOSE( h2,TRUE );
@\end{verbatim}
 closes the connection to the nuldrvs client, opened via CLNTEXEC.
@\subsubsection{CLNTWRITE}
!CLNTWRITE
@\begin{verbatim}
 CLNTWRITE( NumericType Handler, AnyType Object )
@\end{verbatim}
   Writes one object {\bf Object} to a communication channel of a client.
 {\bf Handler} contains the index of the communication channel opened via
 CLNTEXEC.  See also CLNTREAD, CLNTCLOSE, and CLNTEXEC.
 Example:
@\begin{verbatim}
   h2 = clntexec( "nuldrvs -s-" );
       .
       .
   CLNTWRITE( h2, Model );
       .
       .
   clntclose( h2,TRUE );
@\end{verbatim}
 writes the object named Model to client through communication channel h2.
@\subsubsection{COLOR}
!COLOR
@\begin{verbatim}
 COLOR( GeometricType Object, NumericType Color )
@\end{verbatim}
   Sets the color of the object to one of those specified below. Note that an
 object has a default color (see IRIT.CFG file) according to its origin -
 loaded with the LOAD command, PRIMITIVE, or BOOLEAN operation result.
   The system internally supports colors (although you may have a B\&W system)
 and the colors recognized are:
 {\bf BLACK, BLUE, GREEN, CYAN, RED, MAGENTA, YELLOW, and WHITE}.
   See the ATTRIB command for more fine control of colors using the RGB
 attribute.
@\subsubsection{COMMENT}
!COMMENT
@\begin{verbatim}
 COMMENT
@\end{verbatim}
 Two types of comments are allowed:
 1. One-line comment: starts anywhere in a line at the '\#' character, up to
    the end of the line.
 2. Block comment: starts at the COMMENT keyword followed by a unique
    character (anything but white space), up to the second occurrence of that
    character. This is a fast way to comment out large blocks.
 Example:
@\begin{verbatim}
    COMMENT $
      This is a comment
    $
@\end{verbatim}
@\subsubsection{ERROR}
!ERROR
@\begin{verbatim}
 ERROR( StringType Message);
@\end{verbatim}
 Breaks the execution and returns to IRIT main loop, after printing
 {\bf Message} to the screen. May be useful in user defined function to
 break execution in cases of fatal errors.
@\subsubsection{EXIT}
!EXIT
@\begin{verbatim}
 EXIT();
@\end{verbatim}
   Exits from the solid modeler. NO warning is given!
@\subsubsection{FOR}
@\begin{verbatim}
 FOR( NumericType Start, NumericType Increment, NumericType End, AnyType Body )
@\end{verbatim}
   Executes the {\bf Body} (see below), while the FOR loop conditions hold.
   {\bf Start, Increment, End} are evaluated first, and the loop is executed
 while {\bf $<=$ End} if {\bf Increment $>$ 0}, or while {\bf $>=$ End} if {\bf Increment $<$ 0}.
   If {\bf Start} is of the form "Variable = Expression", then that variable is
 updated on each iteration, and can be used within the body.
   The body may consist of any number of regular commands, separated by
 COLONs, including nesting FOR loops to an arbitrary level.
 Example:
@\begin{verbatim}
 step = 10;
 rotstepx = rotx(step);
 FOR ( a = 1, 1, 360 / step,
     view_mat = rotstepx * view_mat:
     view( list( view_mat, b, axes ), ON )
@\end{verbatim}
 Displays b and axes with a view direction that is rotated 10 degrees at a
 time around the X axis.
@\subsubsection{HELP}
!HELP
@\begin{verbatim}
 HELP( StringType Subject )
@\end{verbatim}
   Provides help on the specified Subject.
 Example:
@\begin{verbatim}
    HELP("");
@\end{verbatim}
 will list all {\em IRIT} help subjects.
@\subsubsection{FREE}
!FREE
@\begin{verbatim}
 FREE( GeometricType Object )
@\end{verbatim}
   Because of the usually huge size of geometric objects, this procedure
 may be used to free them. Reassigning a value (even of different type)
 to a variable automatically releases the old variable's allocated space
 as well.
@\subsubsection{FUNCTION}
!FUNCTION
@\begin{verbatim}
 FuncName = FUNCTION(Prm1, Prm2, ... , PrmN):LclVal1:LclVar2: ... :LclVarM:
     FuncBody;
@\end{verbatim}
 Defines a function named FuncName with N parameters and M local variables
 $(N, M >= 0)$. Here is a (simple) example of a function with no local variables
 and a single parameter that computes the square of a number:
@\begin{verbatim}
 sqr = FUNCTION(x):
    return = x * x;
@\end{verbatim}
   Functions can be defined with optional parameters and optional local
 variables. A function's body may contain an arbitrary set of expressions
 including for loops, (user) function calls, or even recursive function calls,
 all separated by colons.
   The returned value of the function is the value of an automatically defined
 local variable named return. The return variable is a regular local variable
 within the scope of the function and can be used as any other variable.
   If a variable's name is found in neither the local variable list nor
 the parameter list, it is searched in the global variable list (outside
 the scope of the function). Binding of names of variables is static as in the
 C programming language.
   Because binding of variables is performed in execution time, there is a
 somewhat less restrictive type checking of parameters of functions that are
 invoked within a user's defined function.
   A function can invoke itself, i.e., it can be recursive. However, since a
 function should be defined when it is called, a dummy function should be
 defined before the recursive one is defined:
@\begin{verbatim}
 factorial = function(x):return = x; # Dummy function.
 factorial = function(x):
     if (x <= 1, return = 1, return = x * factorial(x - 1));
@\end{verbatim}
   Overloading is valid inside a function as it is outside. For example, for
@\begin{verbatim}
 add = FUNCTION(x, y):
    return = x + y;
@\end{verbatim}
 the following function calls are all valid:
@\begin{verbatim}
 add(1, 2);
 add(vector(1,2,3), point(1,2,3));
 add(box(vector(-3, -2, -1), 6, 4, 2), box(vector(-4, -3, -2), 2, 2, 4));
@\end{verbatim}
 Finally, here is a more interesting example that computes an approximation
 of the length of a curve, using the sqr function defined above:
@\begin{verbatim}
 distptpt = FUNCTION(pt1, pt2):
     return = sqrt(sqr(coord(pt1, 1) - coord(pt2, 1)) +
                   sqr(coord(pt1, 2) - coord(pt2, 2)) +
                   sqr(coord(pt1, 3) - coord(pt2, 3)));
 crvlength = FUNCTION(crv, n):pd:t:t1:t2:dt:pt1:pt2:i:
     return = 0.0:
     pd = pdomain(crv):
     t1 = nth(pd, 1):
     t2 = nth(pd, 2):
     dt = (t2 - t1) / n:
     pt1 = coerce(ceval(crv, t1), e3):
     for (i = 1, 1, n,
          pt2 = coerce(ceval(crv, t1 + dt * i), e3):
          return = return + distptpt(pt1, pt2):
          pt1 = pt2);
@\end{verbatim}
 Try, for example:
@\begin{verbatim}
 crvlength(circle(vector(0.0, 0.0, 0.0), 1.0), 30) / 2;
 crvlength(circle(vector(0.0, 0.0, 0.0), 1.0), 100) / 2;
 crvlength(circle(vector(0.0, 0.0, 0.0), 1.0), 300) / 2;
@\end{verbatim}
 See PROCEDURE and IRITSTATE's "DebugFunc" for more.
@\subsubsection{IF}
@\begin{verbatim}
 IF( NumericType Cond, AnyType TrueBody { , AnyType FalseBody } )
@\end{verbatim}
   Executes {\bf TrueBody} (group of regular commands, separated by COLONs -
 see FOR loop) if the {\bf Cond} holds, i.e., it is a numeric value other than
 zero, or optionally, if it exists, executes {\bf FalseBody} if the {\bf Cond}
 does not hold, i.e., it evaluates to a numeric value equal to zero.
 Examples:
@\begin{verbatim}
    IF ( machine == IBMOS2, resolution = 5, resolution = 10 );
    IF ( a > b, max = a, max = b );
@\end{verbatim}
 sets the resolution to be 10, unless running on an IBMOS2 system, in which
 case the resolution variable will be set to 5 in the first statement, and
 set max to the maximum of a and b in the second statement.
@\subsubsection{INCLUDE}
!INCLUDE
@\begin{verbatim}
 INCLUDE( StringType FileName )
@\end{verbatim}
   Executes the script file {\bf FileName}. Nesting of include file is allowed up
 to 10 levels deep. If an error occurs, all open files in all nested files
 are closed and data are waited for at the top level (standard input).
   A script file can contain any command the solid modeler supports.
 Example:
@\begin{verbatim}
    INCLUDE( "general.irt" );
@\end{verbatim}
 includes the file "general.irt".
@\subsubsection{IRITSTATE}
!IRITSTATE
@\begin{verbatim}
 IRITSTATE( StringType State, AnyType Data )
@\end{verbatim}
   Sets a state variable in the {\em IRIT} solid modeller. Current supported
 state variables are,
# 13 3 1 1
 State Name
 Data Type
 Comments
 InterpProd
 ConstantType
 TRUE for Bspline sym. products via interpolation
 FALSE for Bspline sym. products via bezier
 DebugFunc
 NumericType
 $>0$ user func. debug information. $>2$ print params
 on entry, ret. val. on exit. $>4$ global var. list
 FloatFrmt
 StringType
 Specifies a new printf floating point format.
 InterCrv
 NumericType
 If TRUE Boolean operations creates only
 intersection curves. If FALSE, full Boolean
 operation results.
 Coplanar
 NumericType
 If TRUE, Coplanar polygons are handled by Boolean
 operations.
 PolySort
 NumericType
 Axis of Polygon Intersection sweep in Boolean
 operations: 0 for X axis, 1 for Y axis, 2 for
 Z axis.
 EchoSource
 NumericType
 If TRUE, irit scripts are echoed to stdout.
 DumpLevel
 NumericType
 Controls the way variables/expressions ar dumped.
 Only object names/types if $>=$ 0, Scalars and
 vectors are dumped if $>=$ 1, Curves and Surfaces
 are dumped if DumpLvl $>=$ 2, Polygons/lines are
 dumped if DumpLvl $>=$ 3, and List objects are
 traversed recursively if DumpLvl $>=$ 4.
 TrimCrvs
 NumericType
 Number of samples the higher order trimmed curves
 are sampled, in piecewise linear approximation.
 If zero, computed symbolically as composition.
 Example:
@\begin{verbatim}
    IRITSTATE( "DebugFunc", 3 );
    IRITSTATE( "FloatFrmt", "%8.5lg" );
@\end{verbatim}
 To print parameters of user defined functions on entry, and return value on
 exit. Also selects a floating point printf format of "%8.5lg".
@\subsubsection{INTERACT}
!INTERACT
@\begin{verbatim}
 INTERACT( GeometryTreeType Object )
@\end{verbatim}
   A user-defined function (see iritinit.irt) that does the following,
 in order:
@\begin{enumerate}
@\item
 Clear the display device.
@\item
 Display the given {\bf Object}.
@\item
 Pause for a keystroke.
@\end{enumerate}
   This user-defined function in version 4.0 of {\em IRIT} is an
 emulation of the INTERACT function that used to exist in previous versions.
 Example:
@\begin{verbatim}
 INTERACT( list( view_mat, Axes, Obj ) );
@\end{verbatim}
 displays and interacts with the object {\bf Obj} and the predefined object
 {\bf Axes}. VIEW\_MAT will be used to set the starting transformation.
   See VIEW and VIEWOBJ for more.
@\subsubsection{LIST}
!LIST
@\begin{verbatim}
 ListType LIST( AnyType Elem1, AnyType Elem2, ... )
@\end{verbatim}
   Constructs an object as a list of several other objects. Only a reference
 is made to the Elements, so modifying Elem1 after being included in the list
 will affect Elem1 in that list next time list is used!
   Each inclusion of an object in a list increases its internal {\bf used}
 reference. The object is freed iff in {\bf used} reference is zero.
   As a result, attempt to delete a variable (using FREE) which is referenced
 in a list removes the variable, but the object itself is freed only when the
 list is freed.
@\subsubsection{LOAD}
!LOAD
@\begin{verbatim}
 AnyType LOAD( StringType FileName )
@\end{verbatim}
   Loads an object from the given {\bf FileName}. The object may be any object
 defined in the system, including lists, in which the structure is recovered
 and reconstructed as well (internal objects are inserted into the global
 system object list if they have names). If no file type is provided, ".dat"
 is assumed.
   This command can also be used to load binary files. Ascii regular data
 files are usually loaded in much more time then binary files due the
 the parsing required. Binary data files can be loaded directly like ascii
 files in {\em IRIT}, but can only be inspected through {\bf IRIT} tools such
 as dat2irit. A binary data file must have a ".bdt" (Binary DaTa) type in
 its name.
   Under unix, compressed files can be loaded if the given file name has
 a postfix of ".Z". The unix system's "zcat" will be invoked via a pipe
 for that purpose.
@\subsubsection{LOGFILE}
!LOGFILE
@\begin{verbatim}
 LOGFILE( NumericType Set )
 LOGFILE( StringType FileName )
@\end{verbatim}
   If {\bf Set} is non zero (see TRUE/FALSE and ON/OFF), then everything
 printed in the input window, will go to the log file specified in the
 IRIT.CFG configuration file. This file will be created the first time
 logfile is turned ON. If a string {\bf FileName} is provided, it will
 be used as a log file name from now on. It also closes the current log
 file. A "LOGFILE( on );" must be issued after a log file name change.
 Example:
@\begin{verbatim}
    LOGFILE( "Data1" );
    LOGFILE( on );
    printf( "Resolution = %lf\\n", list( resolution ) );
    LOGFILE( off );
@\end{verbatim}
 to print the current resolution level into file Data1.
@\subsubsection{MSLEEP}
!MSLEEP
@\begin{verbatim}
 MSLEEP( NumericType MilliSeconds )
@\end{verbatim}
 Causes the solid modeller to sleep for the prescribed time in milliseconds.
 Example:
@\begin{verbatim}
 for ( i = 1, 1, sizeof( crvs ),
     c = nth( crvs, i ):
     color( c, yellow ):
     msleep(20):
     viewobj( c )
@\end{verbatim}
 Displays an animation sequence and sleeps for 20 milliseconds between
 iterations.
@\subsubsection{NTH}
@\begin{verbatim}
 AnyType NTH( ListType ListObject, NumericType Index )
@\end{verbatim}
 Returns the {\bf Index} (base count 1) element of the list {\bf ListObject}.
 Example:
@\begin{verbatim}
    Lst = list( a, list( b, c ), d );
    Lst2 = NTH( Lst, 2 );
@\end{verbatim}
 and now {\bf Lst2} is equal to 'list( b, c )'.
@\subsubsection{PAUSE}
!PAUSE
@\begin{verbatim}
 PAUSE( NumericType Flush )
@\end{verbatim}
   Waits for a keystroke. Nice to have if a temporary stop in a middle of an
 included file (see INCLUDE) is required. If {\bf Flush} is TRUE, then the input
 is first flushed to guarantee that the actual stop will occur.
@\subsubsection{PRINTF}
!PRINTF
@\begin{verbatim}
 PRINTF( StringType CtrlStr, ListType Data )
@\end{verbatim}
 A formatted printing routine, following the concepts of the C programming
 language's {\em printf} routine. {\bf CtrlStr} is a string object for which
 the following special '\%' commands are supported:
#15 2 0 1
 \%d, \%i, %u
  Prints the numeric object as an integer or unsigned integer.
 \%o, \%x, \%X
  Prints the numeric object as an octal or hexadecimal integer.
 \%e, \%f, \%g,
  Prints the numeric object in several formats of
 \%E, \%F
  floating point numbers.
  Prints the string object as a string.
 \%pe, \%pf, \%pg
  Prints the three coordinates of the point object.
 \%ve, \%vf, \%vg
  Prints the three coordinates of the vector object.
 \%Pe, \%Pf, \%Pg,
  Prints the four coordinates of the plane object.
 \%De, \%Df, \%Dg,
  Prints the given object in IRIT's data file format.
 All the '\%' commands can include any modifier that is valid in the C
 programming language printf routine, including l (long), prefix
 character(s), size, etc. The point, vector, plane, and object commands
 can also be modified in a similar way, to set the format of the
 numeric data printed.
 Also supported are the newline and tab using the backslash escape
 character:
@\begin{verbatim}
* PRINTF("\\tThis is the char \"\\%\"\\n", nil());
@\end{verbatim}
 Backslashes should be escaped themselves as can be seen in the above example.
 Here are few more examples:
@\begin{verbatim}
* PRINTF("this is a string \"%s\" and this is an integer %8d.\\n",
*       list("STRING", 1987));
* PRINTF("this is a vector [%8.5lvf]\\n", list(vector(1,2,3)));
* IritState("DumpLevel", 9);
* PRINTF("this is a object %8.6lDf...\\n", list(axes));
* PRINTF("this is a object %10.8lDg...\\n", list(axes));
@\end{verbatim}
 This implementation of PRINTF is somewhat different than the C programming
 language's version, because the backslash {\em always} escapes the next
 character during the processing stage of IRIT's parser. That is, the string
@\begin{verbatim}
*        '\\tThis is the char \"\\%\"\\n'
@\end{verbatim}
 is actually parsed by the IRIT's parser into
@\begin{verbatim}
*        '\tThis is the char "\%"\n'
@\end{verbatim}
 because this is the way the IRIT parser processes strings. The latter
 string is the one that PRINTF actually see.
@\subsubsection{PROCEDURE}
!PROCEDURE
@\begin{verbatim}
 ProcName = PROCEDURE(Prm1, Prm2, ... , PrmN):LclVal1:LclVar2: ... :LclVarM:
     ProcBody;
@\end{verbatim}
 A procedure is a function that does not return a value, and therefore the
 return variable (see FUNCTION) should not be used. A procedure is
 identical to a function in every other way. See FUNCTION for more.
@\subsubsection{RMATTR}
!RMATTR
@\begin{verbatim}
 RMATTR( AnyType Object, StringType Name )
@\end{verbatim}
   Removes attribute named {\bf Name} from object {\bf Object}. This function
 will have no affect on {\bf Object} if {\bf Object} have no attribute named
 {\bf Name}.
 See also ATTRIB.
@\subsubsection{SAVE}
!SAVE
@\begin{verbatim}
 SAVE( StringType FileName, AnyType Object )
@\end{verbatim}
   Saves the provided {\bf Object} in the specified file name {\bf FileName}.
 No extension type is needed (ignored if specified), and ".dat" is supplied
 by default. {\bf Object} can be any object type, including list, in which
 structure is saved recursively. See also LOAD. If a display device is
 actively running at the time SAVE is invoked, its transformation matrix
 will be saved with the same name but with extension type of ".mat" instead
 of ".dat".
   This command can also be used to save binary files. Ascii regular data
 files are usually loaded in much more time then binary files due the
 the parsing required. Binary data files can be loaded directly like ascii
 files in {\em IRIT}, but must be inspected through {\bf IRIT} tools such
 as dat2irit. A binary data file must have a ".bdt" (Binary DaTa) type in
 its name.
   Under unix, files will be saved compressed if the given file name has
 a postfix of ".Z". The unix system's "compress" will be invoked via a pipe
 for that purpose.
   Example:
@\begin{verbatim}
 SAVE( "Obj1.bdt.Z", Obj1 );
@\end{verbatim}
 Saves Obj1 in the file Obj1.bdt.Z as compressed binary file.
@\subsubsection{SNOC}
!SNOC
@\begin{verbatim}
 SNOC( AnyType Object, ListType ListObject )
@\end{verbatim}
   Similar to the lisp cons operator but puts the new {\bf Object} in the
 {\em end} of the list {\bf ListObject} instead of the beginning, in place.
 Example:
@\begin{verbatim}
    Lst = list( axes );
    SNOC( Srf, Lst );
@\end{verbatim}
 and now {\bf Lst} is equal to the list 'list( axes, Srf )'.
@\subsubsection{SYSTEM}
!SYSTEM
@\begin{verbatim}
 SYSTEM( StringType Command )
@\end{verbatim}
   Executes a system command {\bf Command}. For example,
@\begin{verbatim}
    SYSTEM( "ls -l" );
@\end{verbatim}
@\subsubsection{TIME}
!TIME
@\begin{verbatim}
 TIME( NumericType Reset )
@\end{verbatim}
   Returns the time in seconds from the last time TIME was called with
 {\bf Reset} TRUE. This time is CPU time if such support is available
 from the system (times function), and is real time otherwise (time
 function).
   The time is automatically reset at the beginning of the execution of this
 program.
 Example:
@\begin{verbatim}
    Dummy = TIME( TRUE );
      .
      .
      .
    TIME( FALSE );
@\end{verbatim}
 prints the time in seconds between the above two time function calls.
@\subsubsection{VARLIST}
!VARLIST
@\begin{verbatim}
 VARLIST()
@\end{verbatim}
   List all the currently defined objects in the system.
@\subsubsection{VECTOR}
!VECTOR
@\begin{verbatim}
 VectorType VECTOR( NumericType X, NumericType Y, NumericType Z )
@\end{verbatim}
   Creates a vector type object, using the three provided NumericType scalars.
@\subsubsection{VIEW}
!VIEW
@\begin{verbatim}
 VIEW( GeometricTreeType Object, NumericType ClearWindow )
@\end{verbatim}
   Displays the (geometric) object(s) as given in {\bf Object}.
   If {\bf ClearWindow} is non-zero (see TRUE/FALSE and ON/OFF) the window is
 first cleared (before drawing the objects).
 Example:
@\begin{verbatim}
    VIEW( Axes, FALSE );
@\end{verbatim}
 displays the predefined object {\bf Axes} in the viewing window on top of
 what is drawn already.
 In version 4.0, this function is emulated (see iritinit.irt) using the
 VIEWOBJ function. In order to use the current viewing matrix, VIEW\_MAT
 should be provided as an additional parameter. For example,
@\begin{verbatim}
    VIEW( list( view_mat, Obj ), TRUE );
@\end{verbatim}
 However, since VIEW is a user defined function, the following will not
 use VIEW\_MAT as one would expect:
@\begin{verbatim}
    VIEW( view_mat, TRUE );
@\end{verbatim}
 because VIEW\_MAT will be renamed inside the VIEW user defined function to
 a local (to the user defined function) variable.
 In iritinit.irt one can find several other useful VIEW related functions:
# 15 2 0 1
 VIEWCLEAR
  Clears all data displayed on the display device.
 VIEWREMOVE
  Removes the object specified by name from display.
 VIEWDISC
  Disconnects from display device (which is still running)
  while allowing IRIT to connect to a new device.
 VIEWEXIT
  Forces the display device to exit.
 VIEWSAVE
  Request sdisplay device to save transformation matrix.
 BEEP
  An emulation of the BEEP command of versions prior to 4.0.
 VIEWSTATE
  Allows to change the state of the display device.
   For the above VIEW related functions, only VIEWREMOVE, VIEWSAVE, and
 VIEWSTATE require a parameter, which is the file name and view state
 respectively. The view state can be one of several commands. See the
 display device section for more.
 Examples:
@\begin{verbatim}
    VIEWCLEAR();
    VIEW( axes, off );
    VIEWSTATE( "LngrVecs" );
    VIEWSTATE( "DrawSolid" );
    VIEWSAVE( "matrix1" );
    VIEWREMOVE( "axes" );
    VIEWDISC();
@\end{verbatim}
@\subsubsection{VIEWOBJ}
!VIEWOBJ
@\begin{verbatim}
 VIEWOBJ( GeometricTreeType Object )
@\end{verbatim}
   Displays the (geometric) object(s) as given in {\bf Object}.
 {\bf Object} may be any GeometricType or a list of other
 GeometricTypes nested to an arbitrary level.
   Unlike {\em IRIT} versions prior to 4.0, VIEW\_MAT is not explicitly used
 as the transformation matrix. In order to display with a VIEW\_MAT view,
 VIEW\_MAT should be listed as an argument (in that exact name) to
 VIEWOBJ. Same is true for the perspective matrix PRSP\_MAT.
 Example:
@\begin{verbatim}
    VIEWOBJ( list( view_mat, Axes ) );
@\end{verbatim}
 displays the predefined object {\bf Axes} in the viewing window using the
 viewing matrix VIEW\_MAT.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{System variables}
&System variables
 System variables are predefined objects in the system. Any time {\em IRIT} is
 executed, these variable are automatically defined and set to values which
 are sometimes machine dependent. These are {\em regular} objects in any other
 sense, including the ability to delete or overwrite them. One can modify,
 delete, or introduce other objects using the IRITINIT.IRT file.
@\subsubsection{AXES}
!AXES
   Predefined polyline object (PolylineType) that describes the $XYZ$ axes.
@\subsubsection{DRAWCTLPT}
!DRAWCTLPT
   Predefined Boolean variable (NumericType) that controls whether curves'
 control polygons and surfaces' control meshes are drawn (TRUE) or not
 (FALSE). Default is FALSE.
@\subsubsection{FLAT4PLY}
!FLAT4PLY
   Predefined Boolean object (NumericType) that controls the way almost flat
 surface patches are converted to polygons: four polygons (TRUE) or only
 two polygons (FALSE). Default value is FALSE.
@\subsubsection{MACHINE}
!MACHINE
   Predefined numeric object (NumericType) holding the machine type as one of
 the following constants: MSDOS, SGI, HP, SUN, APOLLO, UNIX, IBMOS2, IBMNT,
 and AMIGA.
@\subsubsection{ POLY\_APPROX\_OPT}
!POLY_APPROX_OPT
   A variable controlling the algorithm to convert surfaces to polygons.
   This two digit number control the method that is used to subdivide a surface
 into polygons.
   The first digit (units) can be one of:
# 4 2 0 1
  An alternate U and V subdivision direction. Once U is
  subdivided and then V is subdivided.
  A min max subdivision direction. In other words, the
  direction that minimizes the maximal error is selected.
   The second digit (tenths) can be one of:
# 4 2 0 1
  A fixed sized regular grid. The side of the grid is set
  via the RESOLUTION variable.
  This mode is {\em not} for general use.
  Maximal distance between the surface and its polygonal
  approximation is bounded by bilinear surface fit.
  Maximal distance allowed is set via POLY\_APPROX\_TOL.
  {\em Recommended} choice for optimal polygonization.
  This mode is {\em not} for general use.
@\subsubsection{POLY\_APPROX\_UV}
!POLY_APPROX_UV
   A Boolean predefined variable. If TRUE, UV values of surface polygonal
 approximation are placed on attribute lists of vertices.
@\subsubsection{POLY\_APPROX\_TOL}
!POLY_APPROX_TOL
   A numeric predefined tolerance control on the distance between the surface
 and its polygonal approximation in POLY\_APPROX\_OPT settings.
@\subsubsection{PRSP\_MAT}
!PRSP_MAT
   Predefined matrix object (MatrixType) to hold the perspective matrix
 used/set by VIEW and/or INTERACT commands. See also VIEW\_MAT.
@\subsubsection{RESOLUTION}
!RESOLUTION
   Predefined numeric object (NumericType) that sets the accuracy of the
 polygonal primitive geometric objects and the approximation of curves and
 surfaces. Holds the number of divisions a circle is divided into (with
 minimum value of 4). If, for example, RESOLUTION is set to 6, then a
 generated CONE will effectively be a six-sided pyramid.
   Also controls the fineness of freeform curves and surfaces when they are
 approximated as piecewise linear polylines, and the fineness of freeform
 surfaces when they are approximated as polygons.
@\subsubsection{VIEW\_MAT}
!VIEW_MAT
   Predefined matrix object (MatrixType) to hold the viewing matrix used/set
 by VIEW and/or INTERACT commands. See also PRSP\_MAT.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{System constants}
&System constants
 The following constants are used by the various functions of the system to
 signal certain conditions. Internally, they are represented numerically,
 although, in general, their exact value is unimportant and may be changed
 in future versions. In the rare circumstance that  you need to know their
 values, simply type the constant as an expression.
 Example:
@\begin{verbatim}
    MAGENTA;
@\end{verbatim}
@\subsection{AMIGA}
!AMIGA
 A constant designating an AMIGA system, in the MACHINE variable.
@\subsubsection{APOLLO}
!APOLLO
 A constant designating an APOLLO system, in the MACHINE variable.
@\subsubsection{BLACK}
!BLACK
 A constant defining a BLACK color.
@\subsubsection{BLUE}
!BLUE
 A constant defining a BLUE color.
@\subsubsection{COL}
 A constant defining the COLumn direction of a surface or a trivariate mesh.
@\subsubsection{CTLPT\_TYPE}
!CTLPT_TYPE
 A constant defining an object of type control point.
@\subsubsection{CURVE\_TYPE}
!CURVE_TYPE
 A constant defining an object of type curve.
@\subsubsection{CYAN}
!CYAN
 A constant defining a CYAN color.
@\subsubsection{DEPTH}
!DEPTH
  A constant defining the DEPTH direction of a trivariate mesh.
 See TBEZIER, TBSPLINE.
@\subsubsection{E1}
 A constant defining an E1 (X only coordinate) control point type.
@\subsubsection{E2}
 A constant defining an E2 (X and Y coordinates) control point type.
@\subsubsection{E3}
 A constant defining an E3 (X, Y and Z coordinates) control point type.
@\subsubsection{E4}
 A constant defining an E4 control point type.
@\subsubsection{E5}
 A constant defining an E5 control point type.
@\subsubsection{FALSE}
!FALSE
 A zero constant. May be used as Boolean operand.
@\subsubsection{GREEN}
!GREEN
 A constant defining a GREEN color.
@\subsubsection{HP}
 A constant designating an HP system, in the MACHINE variable.
@\subsubsection{IBMOS2}
!IBMOS
 A constant designating an IBM system running under OS2, in the MACHINE
 variable.
@\subsubsection{IBMNT}
!IBMNT
 A constant designating an IBM system running under Windows NT, in the MACHINE
 variable.
@\subsubsection{KV\_FLOAT}
!KV_FLOAT
 A constant defining a floating end condition uniformly spaced knot vector.
@\subsubsection{KV\_OPEN}
!KV_OPEN
 A constant defining an open end condition uniformly spaced knot vector.
@\subsubsection{KV\_PERIODIC}
!KV_PERIODIC
 A constant defining a periodic end condition with uniformly spaced knot
 vector.
@\subsubsection{LIST\_TYPE}
!LIST_TYPE
 A constant defining an object of type list.
@\subsubsection{MAGENTA}
!MAGENTA
 A constant defining a MAGENTA color.
@\subsubsection{MATRIX\_TYPE}
!MATRIX_TYPE
 A constant defining an object of type matrix.
@\subsubsection{MSDOS}
!MSDOS
 A constant designating an MSDOS system, in the MACHINE variable.
@\subsubsection{NUMERIC\_TYPE}
!NUMERIC_TYPE
 A constant defining an object of type numeric.
@\subsubsection{OFF}
 Synonym of FALSE.
@\subsubsection{ON}
 Synonym for TRUE.
@\subsubsection{P1}
 A constant defining a P1 (W and WX coordinates, in that order) rational
 control point type.
@\subsubsection{P2}
 A constant defining a P2 (W, WX, and WY coordinates, in that order) rational
 control point type.
@\subsubsection{P3}
 A constant defining a P3 (W, WX, WY, and WZ coordinates, in that order)
 rational control point type.
@\subsubsection{P4}
 A constant defining a P4 rational control
 point type.
@\subsubsection{P5}
 A constant defining a P5 rational control
 point type.
@\subsubsection{PARAM\_CENTRIP}
!PARAM_CENTRIP
 A constant defining a centripetal length parametrization.
@\subsubsection{PARAM\_CHORD}
!PARAM_CHORD
 A constant defining a chord length parametrization.
@\subsubsection{PARAM\_UNIFORM}
!PARAM_UNIFORM
 A constant defining an uniform parametrization.
@\subsubsection{PI}
 The constant of 3.141592...
@\subsubsection{PLANE\_TYPE}
!PLANE_TYPE
 A constant defining an object of type plane.
@\subsubsection{POINT\_TYPE}
!POINT_TYPE
 A constant defining an object of type point.
@\subsubsection{POLY\_TYPE}
!POLY_TYPE
 A constant defining an object of type poly.
@\subsubsection{RED}
 A constant defining a RED color.
@\subsubsection{ROW}
  A constant defining the ROW direction of a surface or a trivariate mesh.
@\subsubsection{SGI}
 A constant designating an SGI system, in the MACHINE variable.
@\subsubsection{STRING\_TYPE}
!STRING_TYPE
 A constant defining an object of type string.
@\subsubsection{SURFACE\_TYPE}
!SURFACE_TYPE
 A constant defining an object of type surface.
@\subsubsection{SUN}
 A constant designating a SUN system, in the MACHINE variable.
@\subsubsection{TRIMSRF\_TYPE}
!TRIMSRF_TYPE
 A constant defining an object of type trimmed surface.
@\subsubsection{TRIVAR\_TYPE}
!TRIVAR_TYPE
 A constant defining an object of type trivariate function.
@\subsubsection{TRUE}
!TRUE
 A non zero constant. May be used as Boolean operand.
@\subsubsection{UNDEF\_TYPE}
!UNDEF_TYPE
 A constant defining an object of no type (yet).
@\subsubsection{UNIX}
!UNIX
 A constant designating a generic UNIX system, in the MACHINE variable.
@\subsubsection{VECTOR\_TYPE}
!VECTOR_TYPE
 A constant defining an object of type vector.
@\subsubsection{WHITE}
!WHITE
 A constant defining a WHITE color.
@\subsubsection{YELLOW}
!YELLOW
 A constant defining a YELLOW color.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\section{Animation}
@\label{sec-animation}
!Animation
 The animation tool adds the capability of animating objects using
 forward kinematics, exploiting animation curves.  Each object has
 different attributes, that prescribe its motion, scale, and visibility
 as a function of time. Every attribute has a name, which designates
 it's role. For instance an attribute animation curve named MOV\_X
 describes a translation motion along the X axis.
@\subsection{How to create animation curves in IRIT}
!How to create animation curves in IRIT
 Let OBJ be an object in IRIT to animate.
 Animation curves are either scalar (E1/P1) curves or three dimensional
 (E3/P3) curves with one of the following names:
# 30 2 1 1
  MOV\_X, MOV\_Y, MOV\_Z
   Translation along one axis
  MOV\_XYZ
   Arbitrary translation along all three axes
  ROT\_X, ROT\_Y, ROT\_Z
   Rotating around a single axis (degrees)
  SCL\_X, SCL\_Y, SCL\_Z
   Scale along a single axis
  SCL
   Global scale
  VISIBLE
   Visibility
 The visibility curve is a scalar curve that enables the display of
 the object if the visibility curve is positive at time t and disables
 the display (hide) the object if the visibility curve is negative at
 time t.
 The animation curves are all attached as an attribute named "animation"
 to the object OBJ.
 Example:
@\begin{verbatim}
    mov_x = cbezier( ctlpt( E1, 0.0 ),
                     ctlpt( E1, 1.0 ) );
    scl   = cbezier( ctlpt( E1, 1.0 ),
                     ctlpt( E1, 0.1 ) );
    rot_y = cbezier( ctlpt( E1, 0.0 ),
                     ctlpt( E1, 0.0 ) );
                     ctlpt( E1, 360.0 ) );
    attrib(OBJ, "animation", list( mov_x, scl, rot_y ) );
@\end{verbatim}
 To animate OBJ between time zero and one (Bezier curves are always
 between zero and one), by moving it a unit size in the X direction,
 scaling it to %10 of its original size and rotating it at increasing
 angular speed from zero to 360 degrees.
 OBJ can now be save into a file or displayed via one of the regular
 viewing commands in IRIT (i.e. VIEWOBJ).
 Animation is not always between zero and one. To that end one can
 apply the CREPARAM function to modify the parametric domain of the
 animation curve. The convention is that if the time is below the
 starting value of the parametric domain, the starting value of the
 curve is used.  Similarly if the time is beyond the end of the
 parameter domain of the animation curve, the end value of the
 animation curve is used.
 Example:
@\begin{verbatim}
    CREPARAM( mov_x, 3.0, 5.0 );
@\end{verbatim}
 to set the time of the motion in the x axis to be from $t = 3$ to
 $t = 5$.  for $t < 3$, mov\_x(3) is used, and for $t > 5$, mov\_x(5) is
 employed.
 the animation curves are regular objects in the IRIT system. Hence,
 only one object named mov\_x or scl can exist at one time. If you
 create a new object named mov\_x, the old one is overwritten! To
 preserve old animation curves you can detach the old ones by executing
 'free(mov\_x)' that removes the object named mov\_x from IRIT's object
 list but not from its previous used locations within other list
 objects, if any. For example:
@\begin{verbatim}
    mov_x = cbezier( ctlpt( E1, 0.0 ),
                     ctlpt( E1, 1.0 ) );
    attrib(obj1, "animation", list( mov_x ) );
    free(mov_x);
    mov_x = cbezier( ctlpt( E1, 2.0 ),
                     ctlpt( E1, 3.0 ) );
    attrib(obj2, "animation", list( mov_x ) );
    free(mov_x);
@\end{verbatim}
@\subsection{A more complete animation example}
!A more complete animation example
@\begin{verbatim}
  a = box( vector( 0, 0, 0 ), 1, 1, 1 );
  b = box( vector( 0, 0, 0 ), 1, 1, 1 );
  c = box( vector( 0, 0, 0 ), 1, 1, 1 );
  d = sphere( vector( 0, 0, 0), 0.7 );
  pt0   =  ctlpt( e1,  0.0 );
  pt1   =  ctlpt( e1,  1.0 );
  pt2   =  ctlpt( e1,  2.0 );
  pt6   =  ctlpt( e1,  6.0 );
  pt360 =  ctlpt( e1,  360.0 );
  pt10 = ctlpt( e1, -4.0 );
  pt11 = ctlpt( e1,  1.0 );
  pt12 = ctlpt( e1,  4.0 );
  pt13 = ctlpt( e1, -1.0 );
  visible = creparam( cbezier( list( pt10,  pt11 ) ), 0.0, 5.0 );
  mov_x   = creparam( cbezier( list( pt0, pt6, pt2 ) ), 0.0, 1.2 );
  mov_y   = mov_x;
  mov_z   = mov_x;
  rot_x   = creparam( cbspline( 2,
                                list( pt0, pt360, pt0 ),
                                list( KV_OPEN ) ),
                      1.2, 2.5 );
  rot_y   = rot_x;
  rot_z   = rot_x;
  scl     = creparam( cbezier( list( pt1, pt2, pt1, pt2, pt1 ) ),
                      2.5, 4.0 );
  scl_x   = scl;
  scl_y   = scl;
  scl_z   = scl;
  mov_xyz = creparam( circle( vector( 0, 0, 0 ), 2.0 ), 4.0, 5.0 );
  attrib( d, "animation", list( mov_xyz, visible ) );
  free( visible );
  visible = creparam( cbezier( list( pt12,  pt13 ) ), 0.0, 5.0 );
  attrib( a, "animation", list( rot_x, mov_x, scl, scl_x, visible ) );
  attrib( b, "animation", list( rot_y, mov_y, scl, scl_y, visible ) );
  attrib( c, "animation", list( rot_z, mov_z, scl, scl_z, visible ) );
  color( a, red );
  color( b, green );
  color( c, blue );
  color( d, cyan );
  demo = list( a, b, c, d );
  interact( demo );
  viewanim( 0, 5, 0.01 );
@\end{verbatim}
 In this example, we create four objects, three cubes and one sphere.
 Animation curves to translate the three cubes along the three axes for
 the time period of t = 0 to t = 1.2 are created. Rotation curves to
 rotate the three cubes along the three axes are then created for time
 period of t = 1.2 to t = 2.5. Finally, for the time period of t = 2.5
 to t = 4.0. the cubes are (not only) unifomly scaled. For the time
 period of t = 4 to t = 5, the cubes become invisible and the sphere,
 that becomes visible, is rotated along a circle of radius 2.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\section{Display devices}
!Display devices
 The following display device drivers are available,
# 22 3 0 1
 Device Name
  Invocation
   Environment
 xgldrvs
  xgldrvs -s-
   SGI 4D GL regular driver.
 xogldrvs
  xogldrvs -s-
   SGI 4D Open GL/Motif driver.
 xgladap
  xgladap -s-
   SGI 4D GL adaptive isocurve
   experimental driver.
 x11drvs
  x11drvs -s-
   X11 driver.
 xmtdrvs
  xmtdrvs -s-
   X11 Motif driver.
 xglmdrvs
  xglmdrvs -s-
   SGI 4D GL and X11/Motif driver.
 wntdrvs
  wntdrvs -s-
   IBM PC Windows NT driver.
 wntgdrvs
  wntgdrvs -s-
   IBM PC Windows NT Open GL driver.
 os2drvs
  os2drvs -s-
   IBM PC OS2 2.x driver.
 amidrvs
  amidrvs -s-
   AmigaDOS 2.04+ driver.
 nuldrvs
  nuldrvs -s- [-d] [-D]
   A device to print the
   object stream to stdout.
 All display devices are clients communicating with the server ({\em IRIT})
 using IPC (inter process communication). On Unix and Window NT sockets are
 used. A Windows NT client can talk to a server ({\em IRIT}) on a unix host if
 hooked to the same netwrok. On OS2 pipes are used, and both the client and
 server must run on the same machine. On AmigaDOS exec messages are used,
 and both the client and server must run on the same machine.
   The server ({\em IRIT}) will automatically start a client display device
 if the IRIT\_DISPLAY environment variable is set to the name and options of
 the display device to run. For example:
@\begin{verbatim}
    setenv IRIT_DISPLAY xgldrvs -s-
@\end{verbatim}
   The display device must be in a directory that is in the {\bf path}
 environment variable. Most display devices require the '-s-' flags to run
 in a non-standalone mode, or a client-server mode. Most drivers can also
 be used to display data in a standalone mode (i.e., no server). For
 example:
@\begin{verbatim}
    xgldrvs -s solid1.dat irit.mat
@\end{verbatim}
    Effectively, all the display devices are also data display programs
 (poly3d, which was the display program prior to version 4.0, is retired
 in 4.0). Therefore some functionality is not always as expected. For
 example, the quit button will always force the display device to quit,
 even if poped up from {\em IRIT}, but will not cause {\em IRIT} to
 quit as might logically expected. In fact, the next time {\em IRIT} will
 try to communicate with the display device, it will find the broken
 connection and will start up a new display device.
    Most display devices recognize attributes found on objects. The following
 attributes are usually recognized (depending on the device capability.):
@\begin{itemize}
@\item
  {\bf COLOR}: Selects the drawn color of the object to be one of the 8/16
        predefined colors in the {\em IRIT} system: white, red, green, blue,
        yellow, cyan, magenta, black.
  {\bf RGB}: Overwrites (if supported) the COLOR attribute (if given) and
        sets the color of the object to the exact prescribed RGB set.
  {\bf DWIDTH}: Sets the width in pixels of the drawn object, when drawn as
        a wireframe.
@\end{itemize}
    All display devices recognize all the command line flags and all the
 configuration options in a configuration file, as described below. The display
 devices will make attemps to honor the requests, to the best of their ability.
    For example, only xgldrvs can render shaded models, and so only it will
 honor a {\bf DrawSolid} configuration options.
@\subsection{Command Line Options}
!Command Line Options
@\begin{verbatim}
 ???drvs [-s] [-u] [-n] [-N] [-i] [-c] [-C] [-m] [-a] [-g x1,x2,y1,y2]
         [-G x1,x2,y1,y2] [-I #IsoLines] [-F PolygonOpti FineNess]
         [-f PolylineOpti SampPerCrv] [-l LineWidth] [-r] [-B] [-2]
         [-d] [-D] [-L NormalLen] [-4] [-b BackGround] [-S LgtSrcPos]
         [-Z ZMin ZMax] [-M] [-P] [-x ExecAnim] [-z] DFiles
@\end{verbatim}
@\begin{itemize}
@\item
  {\bf -s}: Runs the driver in a Standalone mode. Otherwise, the driver will
        attempt to communicate with the {\em IRIT} server.
@\item
  {\bf -u}: Forces a Unit matrix. That is, input data are {\em not}
        transformed at all.
@\item
  {\bf -n}: Draws normals of vertices.
@\item
  {\bf -N}: Draws normals of polygons.
@\item
  {\bf -i}: Draws internal edges (created by {\em IRIT}) - default is not to
        display them, and this option will force displaying them as well.
@\item
  {\bf -c}: Sets depth cueing on. Drawings that are closer to the viewer will
        be drawn in more intense color.
@\item
  {\bf -C}: Cache the piecewise linear geometry so curves and surface can
        be redisplay faster. Purging it will free memory, on the other hand.
@\item
  {\bf -m}: Provides some more information on the data file(s) parsed.
@\item
  {\bf -a}: Sets the support of antialiased lines.
@\item
  {\bf -g x1,x2,y1,y2}: Prescribes the position and location of the
        transformation window by prescribing the domain of the window in
        screen space pixels.
@\item
  {\bf -G x1,x2,y1,y2}: Prescribes the position and location of the
        viewing window by prescribing the domain of the window in
        screen space pixels.
@\item
  {\bf -I \#IsoLines}: Specifies number of isolines per surface, per direction.
        A specification of zero isolines is possible only on the command line
        and it denotes the obvious.
@\item
  {\bf -F PolyOpti FineNess}: Controls the method used to approximate surfaces
        into polygons. See the variable POLY\_APPROX\_OPT for the meaning of
        FineNess. See also -4.
@\item
  {\bf -f PolyOpti SampPerCrv}: Controls the method used to approximate curves
        into polylines. If PolyOpti == 0, equally spaced intervals are used.
        Otherwise, an adaptive subdivision that optimizes the samples is
        employed.
@\item
  {\bf -l LineWidth}: Sets the linewidth, in pixels. Default is one pixel wide.
@\item
  {\bf -r}: Rendered mode. Draws object as solid.
@\item
  {\bf -B}: Back face culling of polygons.
@\item
  {\bf -2}: Double buffering. Prevents screen flicker on the expense of
        possibly less colors.
@\item
  {\bf -d}: Debug objects. Prints to stderr all objects read from communcation
        port with the server {\em IRIT}.
@\item
  {\bf -D}: Debug input. Prints to stderr all characters read from communcation
        port with the server {\em IRIT}. Lowest level of communication.
@\item
  {\bf -L NormalLen}: Sets the length of the drawn normals in thousandths of
        a unit.
@\item
  {\bf -4}: Forces four polygons per almost flat region in the surface to
        polygon conversion. Otherwise two polygons only.
@\item
  {\bf -b BackGround}: Sets the background color as three RGB integers in the
        range of 0 to 255.
@\item
  {\bf -S LgtSrcPos}: Sets the lighting via the light source position.
@\item
  {\bf -Z ZMin ZMax}: Sets the near and far Z clipping planes.
@\item
  {\bf -M}: Draw control mesh/polygon of curves and surfaces, as well.
@\item
  {\bf -x ExecAnim}: Command to execute as a subprocess every iteration of
        display of an animation sequence. This command can for example save
        the display into an image file, saving the animation sequence.
        One parameter is passed, which is an running index starting from one.
@\item
  {\bf -P}: Draws curves and surfaces (surfaces are drawn using a set of
        isocurves, see -I, or polygons, see -f).
@\item
  {\bf -z}: Prints version number and current defaults.
@\end{itemize}
@\subsection{Configuration Options}
!Configuration Options
 The configuration file is read {\em before} the command line options are
 processed. Therefore, all options in this section can be overriden
 by the appropriate command line option, if any.
@\begin{itemize}
@\item
  {\bf TransPrefPos:} Preferred location (Xmin, YMin, Xmax, Ymax) of the
        transformation window.
@\item
  {\bf ViewPrefPos:} Preferred location (Xmin, YMin, Xmax, Ymax) of the
        viewing window.
@\item
  {\bf BackGround:} Background color. Same as '-b'.
@\item
  {\bf Internal:} Draws internal edges. Same as '-i'.
@\item
  {\bf DrawVNormal:} Draws normals of vertices. Same as '-n'.
@\item
  {\bf DrawPNormal:} Draws normals of polygons. Same as '-n'.
@\item
  {\bf MoreVerbose:} Provides some more information on the data file(s)
        parsed. Same as '-m'.
@\item
  {\bf UnitMatrix:} Forces a Unit matrix. That is, input data are {\em not}
        transformed at all. Same as '-u'.
@\item
  {\bf DrawSolid:} Requests a shaded surface rendering, as opposed to isocurve
        surface representation.
@\item
  {\bf BFaceCull:} Requests the removal of back facing polygons, for better
        visibility.
@\item
  {\bf DoubleBuffer:} Requests drawing using a double buffer, if any.
@\item
  {\bf NumOfIsolines:}  Specifies number of isolines per surface, per
        direction. Same as '-I'.
@\item
  {\bf SamplesPerCurve:} Specifies the samples per (iso)curve. See '-f'.
@\item
  {\bf PolylineOpti:} Controls the method used to subdivide a curve into
        polylines that approximate it. See '-f'.
@\item
  {\bf LineWidth:} Sets the linewidth, in pixels. Default is one pixel
       wide. Same as '-l'
@\item
  {\bf AdapIsoDir:} Selects the direction of the adaptive isoline
        rendering.
@\item
  {\bf FineNess:} Controls the fineness of the surface to polygon subdivision.
        See '-F'.
@\item
  {\bf PolygonOpti:} Controls the method used to subdivide a surface into
        polygons that approximate it. See '-F'.
@\item
  {\bf DepthCue:} Set depth cueing on. Drawings that are closer to the
        viewer will be drawn in more intense color. Same as '-c'.
@\item
  {\bf FourPerFlat:} Forces four polygons per almost flat region in the
        surface to polygon conversion. Otherwise two polygons only. Same as
        '-4'.
@\item
  {\bf AntiAlias:} Request the drawing of anti aliased lines.
@\item
  {\bf DrawSurfaceMesh:} Draws control mesh/polygon of curves and surfaces,
        as well. Same as '-M'.
@\item
  {\bf DrawSurfacePoly:} Draws curves and surfaces (surfaces are drawn using
        a set of isocurves, see -I, or polygons, see -f). Same as '-P'.
@\item
  {\bf StandAlone:} Runs the driver in a Stand alone mode. Otherwise, the
        driver will attempt to communicate with the {\em IRIT} server. Same
        as '-s'.
@\item
  {\bf TransMode:} Selects between object space transformations and screen
        space transformation.
@\item
  {\bf ViewMode:} Selects between perspective and orthographic views.
@\item
  {\bf NormalLength:} Sets the length of the drawn normals in thousandths of
        a unit. Same as '-L'.
@\item
  {\bf DebugObjects:} Debug objects. Prints to stderr all objects read
        from the communcation port with the server {\em IRIT}. Same as '-d'.
@\item
  {\bf DebugEchoInput:} Debug input. Prints to stderr all characters read
        from the communcation port with the server {\em IRIT}. Lowest level of
        communications.
@\item
  {\bf LightSrcPos:} Sets the location of the (first) light source as a rational
        four coefficient location. W of zero sets the light source at infinity.
@\end{itemize}
@\subsection{Interactive mode setup}
!Interactive mode setup
   Commands that affect the status of the display device can also be sent
 via the communication port with the {\em IRIT} server. The following commands
 are recognized as string objects with object name of "COMMAND\_":
# 20 2 0 1
 {\bf BEEP}
  Makes some sound.
 {\bf CLEAR}
  Clears the display area. All objects are deleted.
 {\bf DCLEAR}
  Delayed clear. Same as CLEAR but delayed until next
  object is sent from the server. Useful for animation.
 {\bf DISCONNECT}
  Closes connection with the server, but does not quit.
 {\bf EXIT}
  Closes connection with the server and quits.
 {\bf GETOBJ NAME}
  Requests the object named NAME that is returned in the
  output channel to the server.
 {\bf MSAVE NAME}
  Saves the transformation matrix file by the name NAME.
 {\bf REMOVE NAME}
  Request the removal of object named NAME from display.
 {\bf ANIMATE TMin TMax Dt}
  Animates current scene from TMin to TMax in Dt steps.
 {\bf STATE COMMAND}
  Changes the state of the display device. See below.
   The following commands are valid for the STATE COMMAND above,
# 16 2 0 1
 {\bf MoreSense:}
   More sensitive mouse control.
 {\bf LessSense:}
   Less sensitive mouse control.
 {\bf ScrnObject:}
   Toggle screen/object transformation mode.
 {\bf PerspOrtho:}
   Toggles perspective/orthographic trans. mode.
 {\bf DepthCue:}
   Toggles depth cueing drawing.
 {\bf DrawSolid:}
   Toggles isocurve/shaded solid drawing.
 {\bf BFaceCull:}
   Cull back facing polygons.
 {\bf DblBuffer:}
   Toggles single/double buffer mode.
 {\bf AntiAlias:}
   Toggles anti aliased lines.
 {\bf DrawIntrnl:}
   Toggles drawing of internal lines.
 {\bf DrawVNrml:}
   Toggles drawing of normals of vertices.
 {\bf DrawPNrml:}
   Toggles drawing of normals of polygons.
 {\bf DSrfMesh:}
   Toggles drawing of control meshes/polygons.
 {\bf DSrfPoly:}
   Toggles drawing of curves/surfaces.
 {\bf 4PerFlat:}
   Toggles 2/4 polygons per flat surface regions.
 {\bf MoreIso:}
   Doubles the number of isolines in a surface.
 {\bf LessIso:}
   Halves the number of isolines in a surface.
 {\bf FinrAprx:}
   Doubles the number of samples per curve.
 {\bf CrsrAprx:}
   Halves the number of samples per curve.
 {\bf LngrVecs:}
   Doubles the length of displayed normal vectors.
 {\bf ShrtrVecs:}
   Halves the length of displayed normal vectors.
 {\bf WiderLns:}
   Doubles the width of the drawn lines.
 {\bf NarrwLns:}
   Halves the width of the drawn lines.
 {\bf FinrAdapIso:}
   Doubles the number of adaptive isocurves.
 {\bf CrsrAdapIso:}
   Halves the number of adaptive isocurves.
 {\bf FinerRld:}
   Doubles number of ruled surfaces in adaptive isocurves.
 {\bf CrsrRld:}
   Halves number of ruled surfaces in adaptive isocurves.
 {\bf RuledSrfApx:}
   Toggles ruled surface approx. in adaptive isocurves.
 {\bf AdapIsoDir:}
   Toggles the row/col direction of adaptive isocurves.
 {\bf Front:}
   Selects a front view.
 {\bf Side:}
   Selects a side view.
 {\bf Top:}
   Selects a top view.
 {\bf Isometry:}
   Selects an isometric view.
 {\bf Clear:}
   Clears the viewing area.
 Obviously not all state options are valid for all drivers.
   The {\em IRIT} server defines in iritinit.irt several user-defined
 functions that exercise some of the above state commands, such as
 VIEWSTATE and VIEWSAVE.
   In addition to state modification via communication with the {\em IRIT}
 server, modes can be interactively modified on most of the display devices
 using a pop-up menu that is activated using the {\em right button in the
 transformation window}.
   This pop up menu is somewhat different in different drivers, but its
 entries closely follow the entries of the above state command table.
@\subsection{Animation Mode}
!Animation Mode
   All the display drivers are now able to animate objects with animation
 curves' attributes on them. For more on the way animation curves can be
 created see the Animation Section of this manual
@(Section~\ref{sec-animation}).
   Once a scene with animation curves' attributes is being loaded into
 a display device, one can enter "animation" mode using the "Animation"
 button available in all display devices. The user is then prompt (either
 graphically or in a textual based interface) for the starting time,
 termination time and step size of the animation. The parameter space of
 the animation curve is serving as the time domain. The default staring
 and terminating times are set as the minimal and maximal parametric
 domain values of all animation curves. An object at time t below the
 minimal parametric value will be placed at the starting value of the
 animation curve. Similarly, an object at time t above the
 maximal parametric value will be placed at the termination value of the
 animation curve. The user can also set a bouncing back and forth mode,
 the number of repetitions, and if desired, request the saving of all
 the different scenes in the animation as seperate files so a high quality
 animation can be created.
@\subsection{Specific Comments}
!Specific Comments
@\begin{itemize}
@\item
   The x11drvs supports the following X Defaults (searched at ~/.Xdefaults):
@\begin{verbatim}
        #ifndef COLOR
        irit*MaxColors:                    1
        irit*Trans*BackGround:             Black
        irit*Trans*BorderColor:            White
        irit*Trans*TextColor:              White
        irit*Trans*SubWin*BackGround:      Black
        irit*Trans*SubWin*BorderColor:     White
        irit*Trans*CursorColor:            White
        irit*View*BackGround:              Black
        irit*View*BorderColor:             White
        irit*View*CursorColor:             White
        #else
        irit*MaxColors:                    15
        irit*Trans*BackGround:             NavyBlue
        irit*Trans*BorderColor:            Red
        irit*Trans*TextColor:              Yellow
        irit*Trans*SubWin*BackGround:      DarkGreen
        irit*Trans*SubWin*BorderColor:     Magenta
        irit*Trans*CursorColor:            Green
        irit*View*BackGround:              NavyBlue
        irit*View*BorderColor:             Red
        irit*View*CursorColor:             Red
        #endif
        irit*Trans*BorderWidth:            3
        irit*Trans*Geometry:               =150x500+510+0
        irit*View*BorderWidth:             3
        irit*View*Geometry:                =500x500+0+0
@\end{verbatim}
@\item
 The Motif-based display drivers contain three types of gadgets which can be
 operated in the following manner. Scales: can be dragged or clicked outside
 button for single (mouse's middle button) or continuous (mouse's left
 button) action. Pushbuttons: activated by clicking the mouse's left button.
 The control panel: allowes rotation, translation of the objects in three
 axes, determine perspective ratio, viewing object from top, side, front or
 isometrically, determining scale factor and clipping settings, and operate
 the matrix stack.
   The environment window toggles between screen/object translation, depth
 cue on/off, orthographic/perspective projection, wireframe/solid display,
 single/doubble buffering,  showing/hiding normals, including/excluding
 surface mesh, surface isolines/polygons, and four/two per flat. Xglmdrvs
 allowes inclusion/exclusion of internal edges, and in xmtdrvs pro/anti
 aliasing. Scales set normals length, lines width, buttons sensitivity,
 the number of islolines and samples.
@\item
   The locations of windows as set via [-g] and [-G] and/or via the
 configuration file overwrites in x11drvs the Geometry X11 defaults.
 To use the Geometry X11 default use '-G " "' and '-g " "' or set the
 string to empty size in the configuration file.
@\item
   In os2drvs, only -G is used to specify the dimensions of the parent window
 that holds both the viewing and the transformation window.
@\end{itemize}
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\section{Utilities - General Usage}
!Utilities - General Usage
   The {\em IRIT} solid modeler is accompanied by quite a few utilities. They
 can be subdivided into two major groups. The first includes auxiliary tools
 such as illustrt and poly3d-h. The second includes filters such as irit2ray
 and irit2ps.
   All these tools operate on input files, and most of the time produce
 data files. In all utilities that read files, the dash ('-') can be used
 to read stdin.
 Example:
@\begin{verbatim}
 poly3d-h solid1.dat | irit2ps - > solid1.ps
@\end{verbatim}
   All the utilities have command line options. If an option is set by a '-x'
 then '-x-' resets the option. The command line options overwrite the settings
 in config files, and the reset option is useful for cases where the option
 is set by default, in the configuration file.
   All utilities can read a sequence of data files. However, the {\em last}
 transformation matrices found (VIEW\_MAT and PRSP\_MAT) are actually used.
 Example:
@\begin{verbatim}
 poly3d-h solid1.dat | x11drvs solid1.dat - solid1.mat
@\end{verbatim}
 x11drvs will display the original solid1.dat file with its hidden version,
 as computed by poly3d-h, all with the solid1.mat, ignoring all other matrices
 in the data stream.
 Under unix, compressed files with a postfix ".Z" will be {\em automatically}
 uncompressed on read and write. The following is legal under unix,
@\begin{verbatim}
 poly3d-h solid1.dat.Z | x11drvs solid1.dat.Z - solid1.mat
@\end{verbatim}
 where solid1.dat.Z was saved from within IRIT using the command
@\begin{verbatim}
 save( "solid1.dat.Z", solid1 );
@\end{verbatim}
 or similar. The unix system's "compress" and "zcat" are used for the purpose
 of (un)compressing the data via pipes. See also SAVE and LOAD.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\section{poly3d-h - Hidden Line Removing Program}
!poly3d-h - Hidden Line Removing Program
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{Introduction}
&Introduction
    poly3d-h is a program to remove hidden lines from a given polygonal model.
 Freeform objects are preprocessed into polygons with controlled fineness.
@See Figure~\ref{fig-poly3dh} for some output examples of using this tool.
@\begin{figure}
@\vspace{4.3in}
@\special{psfile=user_man/solid2h.ps hscale=50 vscale=50 hoffset=-20 voffset=50}
@\special{psfile=user_man/molecule.ps hscale=50 vscale=50 hoffset=130 voffset=-40}
@\special{psfile=user_man/dodechdr.ps hscale=50 vscale=50 hoffset=240 voffset=80}
@\caption{Some examples of the use of hidden line removal tool poly3d-h to
@         remove hidden lines.}
@\label{fig-poly3dh}
@\end{figure}
    The program performs 4 passes over the input:
 1. Preprocesses and maps all polygons in a scene, and sorts them.
 2. Generates edges out of the polygonal model and sorts them (preprocessing
    for the scan line algorithm) into buckets.
 3. Intersects edges, and splits edges with non-homogeneous visibility (the
    scan line algorithm).
 4. Applies a visibility test of each edge.
        This program can handle CONVEX polygons only. From {\em IRIT} one can
 ensure that a model consists of convex polygons only using the CONVEX command:
@\begin{verbatim}
  CnvxObj = convex( Obj );
@\end{verbatim}
 just before saving it into a file. Surfaces are always decomposed into
 triangles.
    poly3d-h output is in the form of polylines. It is a regular {\em IRIT} data
 file that can be viewed using any of the display devices, for example.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{Command Line Options}
&Command line options
@\begin{verbatim}
 poly3d-h [-b] [-m] [-i] [-e #Edges] [-H] [-4] [-W Width]
        [-F PolyOpti FineNess] [-q] [-o OutName] [-c] [-z] DFiles > OutFile
@\end{verbatim}
@\begin{itemize}
@\item
  {\bf -b}: BackFacing - if an object is closed (such as most models created by
       {\em IRIT}), back facing polygons can be deleted, therefore speeding up
       the process by at least a factor of two.
@\item
  {\bf -m}: More - provides some more information on the data file(s) parsed.
@\item
  {\bf -i}: Internal edges (created by {\em IRIT}) - default is not to
       display them, and this option will force displaying them as well.
@\item
  {\bf -e n}: Number of edges to use from each given polygon (default all).
       Handy as '-e 1 -4' for freeform data.
@\item
  {\bf -H}: Dumps both visible lines and hidden lines as separated objects.
       Hidden lines will be dumped using a different (dimmer) color and (a
       narrower) line width.
@\item
  {\bf -4}: Forces four polygons per almost flat region in the surface to
       polygon conversion. Otherwise two polygons only.
@\item
  {\bf -W Width}: Selects a default width for visible lines in inches.
@\item
  {\bf -F PolyOpti FineNess}: Optimality of polygonal approximation of
       surfaces. See the variable POLY\_APPROX\_OPT for the meaning of
       FineNess. See also -4.
@\item
  {\bf -q}: Quiet mode. No printing aside from fatal errors. Disables -m.
@\item
  {\bf -o OutName}: Name of output file. Default is stdout.
@\item
  {\bf -z}: Prints version number and current defaults.
@\item
  {\bf -c}: Clips data to screen (default). If disabled ('-c-'), data
       outside the view screen ([-1, 1] in x and y) are also processed.
@\end{itemize}
   Some of the options may be turned on in poly3d-h.cfg. They can be then
 turned off in the command line as '-?-'.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{Configuration}
&Configuration
   The program can be configured using a configuration file named poly3d-h.cfg.
   This is a plain ASCII file you can edit directly and set the parameters
 according to the comments there. 'poly3d-h -z' will display the current
 configuration as read from the configuration file.
   The configuration file is searched in the directory specified by the
 IRIT\_PATH environment variable. For example,
 'setenv IRIT\_PATH /u/gershon/irit/bin/'.
   If the IRIT\_PATH variable is not set, the current directory is searched.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{Usage}
&Usage
   As this program is not interactive, usage is quite simple, and the only
 control available is using the command line options.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\section{poly3d-r - A Simple Data Rendering Program}
!poly3d-r - A Simple Data Rendering Program
 Retired. Sources can be found in the contrib directory, but this program is
 no longer supported. A new renderer is expected soon.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\section{Illustrt - Simple line illustration filter}
!Illustrt - Simple line illustration filter
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{Introduction}
&Introduction
 illustrt is a filter that processes IRIT data files and dumps out modified
 IRIT data files. illustrt can be used to make simple nice illustrations of
 data. The features of illustrt include depth sorting, hidden line clipping
 at intersection points, and vertex enhancements. illustrt is designed to
 closely interact with irit2ps, although it is not neceessary to use irit2ps
 on illustrt output.
@See Figure~\ref{fig-illustrt} for some output examples of using this tool.
@\begin{figure}
@\vspace{3in}
@\special{psfile=user_man/solid1.ps hscale=50 vscale=50 hoffset=0 voffset=-50}
@\special{psfile=user_man/icosahdr.ps hscale=50 vscale=50 hoffset=220 voffset=-50}
@\caption{Some examples of the use of the illustration tool illustrt.}
@\label{fig-illustrt}
@\end{figure}
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{Command Line Options}
&Command line options
@\begin{verbatim}
   illustrt [-I #IsoLines] [-S #SampPerCrv] [-s] [-M] [-P] [-p]
            [-l MaxLnLen] [-a] [-t TrimInter] [-o OutName] [-Z InterSameZ]
            [-m] [-z] DFiles
@\end{verbatim}
@\begin{itemize}
@\item
  {\bf -I \#IsoLines}: Specifies number of isolines per surface, per direction.
@\item
  {\bf -S \#SampPerCrv}: Specifies the samples per (iso)curve.
@\item
  {\bf -s}: sorts the data in Z depth order that emulates hidden line removal
        once the data are drawn.
@\item
  {\bf -M}: Dumps the control mesh/polygon as well.
@\item
  {\bf -P}: Dumps the curve/surface as isocurves.
@\item
  {\bf -p}: Dumps vertices of polygons/lines as points.
@\item
  {\bf -l MaxLnLen}: breaks long lines into shorter ones with maximal length
        of MaxLnLen. This option is necessary to achieve good depth depending
        line width in the '-d' option of irit2ps.
@\item
  {\bf -a}: takes into account the angle between the two (poly)lines that
        intersect when computing how much to trim. See also -t.
@\item
  {\bf -t TrimInter}: Each time two (poly)line segments intersect in the
        projection plane, the (poly)line that is farther away from the
        viewer is clipped TrimInter amount from both sides. See also -a.
@\item
  {\bf -o OutName}: Name of output file. Default is stdout.
@\item
  {\bf -Z InterSameZ}: The maximal Z depth difference of intersection curves
        to be be considered invalid.
@\item
  {\bf -m}: More talkative mode. Prints processing information.
@\item
  {\bf -z}: Prints version number and current defaults.
@\end{itemize}
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{Usage}
&Usage
    illustrt is a simple line illustration tool. It process geometry such
 as polylines and surfaces and dumps geometry with attributes that will make
 nice line illustrations. illustrt is geared mainly toward its use with
 irit2ps to create postscript illustrations. Here is a simple example:
@\begin{verbatim}
 illustrt -s -l 0.1 solid1.dat | irit2ps -W 0.05 -d 0.2 0.6 -u - > solid.ps
@\end{verbatim}
 make sure all segments piped into irit2ps are shorter than 0.1 and sort them
 in order to make sure hidden surface removal is correctly applied. Irit2ps
 is invoked with depth cueing activated, and a default width of 0.05.
    illustrt dumps out regular {\em IRIT} data files, so output can be handled
 like any other data set. illustrt does the following processing to the input
 data set:
@\begin{itemize}
@\item
  Converts surfaces to isocurves ('-I' flag) and isocurves and curves to
  polylines ('-S' flag), and converts polygons to polylines.
    Polygonal objects are considered closed and even though each edge is
  shared by two polygons, only a single one is generated.
@\item
  Finds the intersection location in the projection plane of all segments in
  the input data set and trims away the far segment at both sides of the
  intersection point by an amount controlled by the '-t' and '-a' flags.
@\item
  Breaks polylines and long lines into short segments, as specified via the
  '-l' flag, so that width depth cueing can be applied more accurately
  (see irit2ps's '-d' flag) as well as the Z sorting.
@\item
  Generates vertices of polygons in the input data set as points in output data
  controlled via the '-p' flag.
  set.
@\item
  Applies a Z sort to the output data, if '-s', so drawing in order of the data
  will produce a properly hidden surface removal drawing.
@\end{itemize}
 Here is a more complex example. Make sure tubular is properly set via
 "attrib(solid1, "tubular", 0.7);" and invoke:
@\begin{verbatim}
 illustrt -s -p -l 0.1 -t 0.05 solid1.dat |
     irit2ps -W 0.05 -d 0.2 0.6 -p h 0.05 -u - > solid.ps
@\end{verbatim}
 makes sure all segments piped into irit2ps are shorter than 0.1, generates
 points for the vertices, sorts the data in order to make sure hidden surface
 removal is correctly applied, and trims the far edge by 0.05 at an
 intersection point. Irit2ps is invoked with depth cueing activated and a
 default width of 0.05, points are drawn as hollowed circles of default
 size 0.05, and lines are drawn tubular.
 Objects in the input stream that have an attribute by the name of
 "IllustrtNoProcess" are passed to the output unmodified.
   Objects in the input stream that have an attribute by the name of
 "SpeedWave" will have a linear segments added that emulate fast
 motion with the following attributes
 "Randomness,DirX,DirY,DirZ,Length,Distance,LengthRandom,DistanceRandom,Width"
   Objects in the input stream that have an attribute by the name of
 "HeatWave" will have a spiral curves added that emulate a heat wave
 in the +Z axis with the following attributes
 "Randomness,Length,Distance,LengthRandom,DistanceRandom,Width".
 Examples:
@\begin{verbatim}
 attrib(Axis, "IllustrtNoProcess", "");
 attrib(Obj, "SpeedWave", "0.0005,1,0,0,5,3,3,2,0.05");
 attrib(Obj, "HeatWave", "0.015,0.1,0.03,0.06,0.03,0.002");
@\end{verbatim}
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\section{Dat2Bin - Data To Binary Data file filter}
!DAT2BIN - Data To Binary Data file filter
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{Command Line Options}
&Command line options
@\begin{verbatim}
   dat2bin [-t] [-z] DFiles
@\end{verbatim}
@\begin{itemize}
@\item
  {\bf -t}: Dumps data to stdout as text instead of binary.
  {\bf -z}: Print version number and current defaults.
@\end{itemize}
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{Usage}
&Usage
    It may be sometimes desired to convert .dat data files into a binary form,
 for example, for fast loading of files with large geometry. Binary files can
 be somewhat larger, are unreadable in editors but are much faster to load in.
 A binary file must have a '.bdt' file type.
 Example:
@\begin{verbatim}
   dat2bin b58polys.dat > b58polys.bdt
   dat2bin -t b58polys.bdt | more
@\end{verbatim}
 to convert a text file b58polys.dat into a binary file b58polys.bdt and
 to view the content of the binary file by converting it back to text. At
 this time data through pipes must be in text. That is, the following is
 {\em illegal}:
@\begin{verbatim}
   dat2bin b58polys.dat | xglmdrvs -
@\end{verbatim}
 It should be remembered that the binary format is not documented and
 it might change in the future. Moreover, it is machine dependent and can
 very well may be unreadible between different platforms.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\section{Dat2Irit - Data To IRIT file filter}
!DAT2IRIT - Data To IRIT file filter
  Converts '.dat' and '.bdt' data files to '.irt' {\em IRIT} scripts.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{Command Line Options}
&Command line options
@\begin{verbatim}
   dat2irit [-z] DFiles
@\end{verbatim}
@\begin{itemize}
@\item
  {\bf -z}: Print version number and current defaults.
@\end{itemize}
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{Usage}
&Usage
    It may be sometimes desired to convert .dat data files into a form that
 can be fed back to {\em IRIT} - a '.irt' file. This filter does exactly that.
 Example:
@\begin{verbatim}
   dat2irit b58.dat > b58-new.irt
@\end{verbatim}
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\section{Dxf2Irit - DXF (Autocad) To IRIT filter}
!DXF2IRIT - DXF (Autocad) To IRIT filter
   Due to lack of real documentation on the DXF format (for surfaces), this
 filter is not really complete. It only work for polygons, and is provided
 here only for those desperate enough to try and fix it...
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\section{Irit2Dxf - IRIT To DXF (Autocad) filter}
!IRIT2DXF - IRIT To DXF (Autocad) filter
   Due to lack of real documentation on the DXF format (for surfaces), this
 filter is not really complete. It works only for polygons, and is provided
 here only for those desperate enough to try and fix it...
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\section{Irit2Iv - IRIT To SGI's Inventor filter}
!IRIT2IV - IRIT To SGI's Inventor filter
 IV is the format used by the Inventor modeling/rendering package from SGI.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{Command Line Options}
&Command line options
@\begin{verbatim}
  irit2iv [-l] [-4] [-P] [-F PolyOpti FineNess] [-f PolyOpti SampPerCrv]
                                                             [-T] [-z] DFiles
@\end{verbatim}
@\begin{itemize}
@\item
  {\bf -l}: Linear - forces linear (degree two) surfaces to be approximated
       by a single polygon along their linear direction.
       Although, most of the time, linear direction can be exactly represented
       using a single polygon, even a bilinear surface can have a free form
       shape (saddle like) that is not representable using a single polygon.
       Note that although this option will better emulate the surface shape,
       it will create unnecessary polygons in cases where one is enough.
@\item
  {\bf -4}: Four - Generates four polygons per flat patch. Default is 2.
@\item
  {\bf -P}: Polygonize freeform shapes. Default is to leave freeform curves
       and surfaces as is.
@\item
  {\bf -F PolyOpti FineNess}: Optimality of polygonal approximation of
       surfaces. See the variable POLY\_APPROX\_OPT for the meaning of
       FineNess. See also -4.
@\item
  {\bf -f PolyOpti SampPerCrv}: Controls the method used to approximate curves
        into polylines. If PolyOpti == 0, equally spaced intervals are used.
        Otherwise, an adaptive subdivision that optimizes the samples is
        employed.
@\item
  {\bf -T}: Talkative mode. Prints processing information.
@\item
  {\bf -z}: Prints version number and current defaults.
@\end{itemize}
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{Usage}
&Usage
    Irit2Iv converts freeform surfaces and polygons into polygons and
 saved in iv Inventor's ascii file format.
 Example:
@\begin{verbatim}
 irit2iv solid1.dat > solid1.iv
@\end{verbatim}
    Surfaces are converted to polygons with fineness control:
@\begin{verbatim}
 irit2iv -F 0 16 - view.mat < saddle.dat > saddle.iv
@\end{verbatim}
    Note the use of '-' for stdin.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\section{Irit2Nff - IRIT To NFF filter}
!IRIT2NFF - IRIT To NFF filter
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{Command Line Options}
&Command line options
@\begin{verbatim}
  irit2nff [-l] [-4] [-c] [-F PolyOpti FineNess] [-o OutName] [-T] [-g]
                                                                  [-z] DFiles
@\end{verbatim}
@\begin{itemize}
@\item
  {\bf -l}: Linear - forces linear (degree two) surfaces to be approximated
       by a single polygon along their linear direction.
       Although, most of the time, linear direction can be exactly represented
       using a single polygon, even a bilinear surface can have a free-form
       shape (saddle-like) that is not representable using a single polygon.
       Note that although this option will better emulate the surface shape,
       it will create unnecessary polygons in cases where one is enough.
@\item
  {\bf -4}: Four - Generates four polygons per flat patch. Default is 2.
@\item
  {\bf -c}: Output files should be filtered by cpp. When set, the usually
       huge geometry file is separated from the main nff file that contains
       the surface properties and view parameters. By default all data,
       including the geometry, are saved into a single file with type extension
       '.nff'. Use of '-c' will pull out all the geometry into a file with
       the same name but a '.geom' extension, which will be included using the
       '\#include' command. The '.nff' file should, in that case, be
       preprocessed using cpp before being piped into the nff renderer.
@\item
  {\bf -F PolyOpti FineNess}: Optimality of polygonal approximation of
       surfaces. See the variable POLY\_APPROX\_OPT for the meaning of
       FineNess. See also -4.
@\item
  {\bf -o OutName}: Name of output file. By default the name of the first data
       file from the {\em DFiles} list is used.  See below on the output files.
@\item
  {\bf -g}: Generates the geometry file only. See below.
@\item
  {\bf -T}: Talkative mode. Prints processing information.
@\item
  {\bf -z}: Prints version number and current defaults.
@\end{itemize}
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{Usage}
&Usage
    Irit2Nff converts freeform surfaces into polygons in a format that can
 be used by an NFF renderer. Usually, one file is created with '.nff' type
 extension. Since the number of polygons can be extremely large, a '-c'
 option is provided, which separates the geometry from the surface
 properties and view specification, but requires preprocessing by cpp.
 The geometry is isolated in a file with extension '.geom' and included
 (via '\#include') in the main '.nff' file. The latter holds the surface
 properties for all the geometry as well as the viewing specification.
 This allows for the changing of shading or the viewing properties while
 editing small ('.nff') files.
    If '-g' is specified, only the '.geom' file is created, preserving the
 current '.nff' file. The '-g' flag can be specified only with '-c'.
    In practice, it may be useful to create a low resolution approximation
 of the model, change viewing/shading parameters in the '.nff' file until
 a good view and/or surface quality is found, and then run Irit2Nff once more
 to create a high resolution approximation of the geometry using '-g'.
 Example:
@\begin{verbatim}
 irit2nff -c -l -F 0 8 b58.dat
@\end{verbatim}
 creates b58.nff and b58.geom with low resolution (FineNess of 5).
 Once done with parameter setting, a fine approximation of the model can
 be created with:
@\begin{verbatim}
 irit2nff -c -l -g -F 0 64 b58.dat
@\end{verbatim}
 which will only recreate b58.geom (because of the -g option).
 One can overwrite the viewing matrix by appending a new matrix in the
 end of the command line, created by a display device:
@\begin{verbatim}
 xgldrvs b58.dat
 irit2nff -l -F 0 32 b58.dat irit.mat
@\end{verbatim}
 where irit.mat is the viewing matrix created by xgldrvs.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{Advanced Usage}
&Advanced Usage
   One can specify surface qualities for individual surfaces of a model.
 Several such attributes are supported by Irit2Nff and can be set within
 {\em IRIT}. See also the ATTRIB {\em IRIT} command.
   If a certain surface should be finer than the rest of the scene, one can
 set a "resolution" attribute which specifies the {\em relative} FineNess
 resolution of this specific surface.
 Example:
@\begin{verbatim}
 attrib( srf1, "resolution", 2 );
@\end{verbatim}
 will force srf1 to have twice the default resolution, as set via the '-f'
 flag.
   Almost flat patches are converted to polygons. The rectangle can be
 converted into two polygons (by subdividing along one of its diagonals) or
 into four by introducing a new point at the center of the patch. This
 behavior is controlled by the '-4' flag, but can be overwritten for
 individual surfaces by setting a "twoperflat" or a "fourperflat" attribute.
   NFF specific properties are controlled via the following attributes:
 "kd", "ks", "shine", "trans", "index". Refer to the NFF manual for detail.
 Example:
@\begin{verbatim}
 attrib( srf1, "kd", 0.3 );
 attrib( srf1, "shine", 30 );
@\end{verbatim}
   Surface color is controlled in two levels. If the object has an RGB
 attribute, it is used. Otherwise, a color, as set via the {\em IRIT} COLOR
 command, is used if set.
 Example:
@\begin{verbatim}
 attrib( tankBody, "rgb", "244,164,96" );
@\end{verbatim}
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\section{Irit2Plg - IRIT To PLG (REND386) filter}
!IRIT2PLG - IRIT To PLG (REND386) filter
 PLG is the format used by the rend386 real time renderer for the IBM PC.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{Command Line Options}
&Command line options
@\begin{verbatim}
  irit2plg [-l] [-4] [-F PolyOpti FineNess] [-T] [-z] DFiles
@\end{verbatim}
@\begin{itemize}
@\item
  {\bf -l}: Linear - forces linear (degree two) surfaces to be approximated
       by a single polygon along their linear direction.
       Although, most of the time, linear direction can be exactly represented
       using a single polygon, even a bilinear surface can have a free form
       shape (saddle like) that is not representable using a single polygon.
       Note that although this option will better emulate the surface shape,
       it will create unnecessary polygons in cases where one is enough.
@\item
  {\bf -4}: Four - Generates four polygons per flat patch. Default is 2.
@\item
  {\bf -F PolyOpti FineNess}: Optimality of polygonal approximation of
       surfaces. See the variable POLY\_APPROX\_OPT for the meaning of
       FineNess. See also -4.
@\item
  {\bf -T}: Talkative mode. Prints processing information.
@\item
  {\bf -z}: Prints version number and current defaults.
@\end{itemize}
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{Usage}
&Usage
    Irit2Plg converts freeform surfaces and polygons into polygons in a
 format that can be used by the REND386 renderer.
 Example:
@\begin{verbatim}
 irit2plg solid1.dat > solid1.plg
@\end{verbatim}
    Surfaces are converted to polygons with fineness control:
@\begin{verbatim}
 irit2plg -F 0 16 - view.mat < saddle.dat > saddle.plg
@\end{verbatim}
    Note the use of '-' for stdin.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\section{Irit2Ps - IRIT To PS filter}
!IRIT2PS - IRIT To PS filter
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{Command Line Options}
&Command line options
@\begin{verbatim}
  irit2ps [-l] [-4] [-s Size] [-I #UIso[:#VIso[:#WIso]]] [-F PolyOpti FineNess]
          [-f PolyOpti SampPerCrv] [-M] [-G] [-P] [-W LineWidth]
          [-w WidenLen WidenWidth] [-b R G B] [-c] [-C] [-T] [-i] [-o OutName]
          [-d [Zmin Zmax]] [-D [Zmin Zmax]] [-p PtType PtSize] [-u] [-z] DFiles
@\end{verbatim}
@\begin{itemize}
@\item
  {\bf -l}: Linear - forces linear (degree two) surfaces to be approximated
        by a single polygon along their linear direction.
         Although most of the time, linear direction can be exactly represented
        using a single polygon, even a bilinear surface can have a free-form
        shape (saddle-like) that is not representable using a single polygon.
          Note that although this option will better emulate the surface shape,
        it will create unnecessary polygons in cases where one is enough.
@\item
  {\bf -4}: Four - Generates four polygons per flat patch. Default is 2.
@\item
  {\bf -s Size}: Controls the size of the postscript output in inches.
        Default is to fill the entire screen.
@\item
  {\bf -I \#UIso[:\#VIso[:\#WIso]]}: Specifies the number of isolines per
        surface/trivariate, per direction. If \#VIso or \#WIso is not
        specified, \#UIso is used for \#VIso etc.
@\item
  {\bf -F PolygonOpti FineNess}: Optimality of polygonal approximation of
        surfaces. See the variable POLY\_APPROX\_OPT for the meaning of
        FineNess. See also -4.
@\item
  {\bf -f PolyOpti SampPerCrv}: Controls the method used to approximate curves
        into polylines. If PolyOpti == 0, equally spaced intervals are used.
        Otherwise, an adaptive subdivision that optimizes the samples is
        employed.
@\item
  {\bf -M}: Dumps the control mesh/polygon as well.
@\item
  {\bf -G}: Dumps the curve/surface (as freeform geometry). Default. See -I,
        -C, -f for control on polyline approximation.
@\item
  {\bf -P}: Dumps the curve/surface (as polygons). See -F, -l, -4 for control
        on polygonal approximation.
@\item
  {\bf -W \#LineWidth}: Sets the line drawing width in inches. Default is
        as thin as possible. This option will overwrite only those objects
        that do {\em not} have a "width" attribute. See also -d. If LineWidth
        is negative its absolute value is used to scale the current width
        of the object if has one, or the default width otherwise.
@\item
  {\bf -w WidenLen WidenWidth}: If end points of polylines should be made
        wider, and if so to what width.
@\item
  {\bf -b R G B}: Sets a colored background. RGB are three integers prescribing
        the Red, Green, and Blue coefficients. if no -c (i.e. a gray level
        drawing) this color is converted to a gray level using RGB to
        T.V. Y(IQ) channel conversion.
@\item
  {\bf -c}: Creates a {\em color} postscript file.
@\item
  {\bf -C}: Curve mode. Dumps freeform curves and surfaces as cubic
       Bezier curves. Higher order curves and surfaces and/or rationals are
       approximated by cubic Bezier curves. This option generates data
       files that are roughly a third of piecewise linear postscript files
       (by disabling this feature, -C-), but takes a longer time to compute.
@\item
  {\bf -T}: Talkative mode. Prints processing information.
@\item
  {\bf -i}: Internal edges (created by {\em IRIT}) - the default is not to
       display them, and this option will force displaying them as well.
@\item
  {\bf -o OutName}: Name of output file. Default is stdout.
@\item
  {\bf -d [Zmin Zmax]}: Sets the ratios between the depth cue and the width of
        the dumped data. See also -W, -p. Closer lines/points will be drawn
        wider/larger. Zmin and Zmax are optional. The object's bounding
        box is otherwise computed and used.
@\item
  {\bf -D [Zmin Zmax]}: Same as -d, but depth cue the color or gray scale
        instead of width. You might need to consider the sorting option
        of the illustrt tool (-s of illustrt) for proper drawings.
        Only one of -d and -D can be used.
@\item
  {\bf -p PtType PtSize}: Specifies the way points are drawn.
        PtType can be one of H, F, C for Hollow circle, Full Circle, or
        Cross. PtSize specifies the size of the point to be drawn, in inches.
        Vectors will also be drawn as points, but with an additional thin
        line to the origin. See also -d.
@\item
  {\bf -u}: Forces a unit matrix transformation, i.e. no transformation.
@\item
  {\bf -z}: Prints version number and current defaults.
@\end{itemize}
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{Usage}
&Usage
    Irit2Ps converts freeform surfaces and polygons into a postscript file.
 Example:
@\begin{verbatim}
 irit2ps solid1.dat > solid1.ps
@\end{verbatim}
    Surfaces are converted to polygons with fineness control:
@\begin{verbatim}
 irit2ps -f 0 32 -c -W 0.01 saddle.dat > saddle.ps
@\end{verbatim}
 creates a postscript file for the saddle model, in color, and with
 lines 0.01 inch thick.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{Advanced Usage}
&Advanced Usage
   One can specify several attributes that affect the way the postscript
 file is generated. The attributes can be generated within {\em IRIT}.
 See also the ATTRIB {\em IRIT} command.
   If a certain object should be thinner or thicker than the rest of the scene,
 one can set a "width" attribute which specifies the line width in inches of
 this specific object.
 Example:
@\begin{verbatim}
 attrib( srf1, "width", 0.02 );
@\end{verbatim}
 will force srf1 to have this width, instead of the default as set via the
 '-W' flag.
 If a (closed) object, a polygon for example, needs to be filled, a "fill"
 attribute should be set, with a value equal to the gray level desired.
 Example:
@\begin{verbatim}
 attrib( poly, "fill", 0.5 );
@\end{verbatim}
 will fill poly with \%50 gray.
 If an object, a polygon for example, needs to be painted in a gray level
 instead of black, a "gray" attribute should be set, with a value equal
 to the gray level desired.
 Example:
@\begin{verbatim}
 attrib( poly, "gray", 0.5 );
@\end{verbatim}
 will draw poly with \%50 gray.
 Dotted or dashed line effects can be created using a "dash" attribute which
 is a direct PostScript dash string. A simple form of this string is "[a b]"
 in which a is the drawing portion (black) in inches, followed by b inches
 of white space. See the postScript manual for more about the format of this
 string. Here is an example for a dotted-dash line.
@\begin{verbatim}
 attrib( poly, "dash", "[0.006 0.0015 0.001 0.0015] 0" );
@\end{verbatim}
   Surface color is controlled (for color postscript only - see -c) in two
 levels. If the object has an RGB attribute, it is used. Otherwise, a color as
 set via the {\em IRIT} COLOR command is used.
 Example:
@\begin{verbatim}
 attrib( Ball, "rgb", "255,0,0" );
@\end{verbatim}
    An object can be drawn as ``tubes'' instead of full lines. The ratio
 between the inner and the outer radii of the tube is provided as the
 TUBULAR attribute:
@\begin{verbatim}
 attrib( final, "tubular", 0.7 );
@\end{verbatim}
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\section{Irit2Ray - IRIT To RAYSHADE filter}
!IRIT2RAY - IRIT To RAYSHADE filter
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{Command Line Options}
&Command line options
@\begin{verbatim}
  irit2ray [-l] [-4] [-G GridSize] [-F PolyOpti FineNess]
           [-f PolyOpti SampPerCrv] [-o OutName] [-g] [-p Zmin Zmax] [-P]
           [-M] [-T] [-I #UIso[:#VIso[:#WIso]]] [-s ObjSeq#] [-z] DFiles
@\end{verbatim}
@\begin{itemize}
@\item
  {\bf -l}: Linear - forces linear (degree two) surfaces to be approximated
        by a single polygon along their linear direction.
         Although most of the time, linear direction can be exactly represented
        using a single polygon, even a bilinear surface can have a free-form
        shape (saddle-like) that is not representable using a single polygon.
          Note that although this option will better emulate the surface shape,
        it will create unnecessary polygons in cases where one is enough.
@\item
  {\bf -4}: Four - Generates four polygons per flat patch. Default is 2.
@\item
  {\bf -G GridSize}: Usually objects are grouped as {\em lists} of polygons.
        This flags will coerce the usage of the RAYSHADE {\em grid} structure,
        with {\em GridSize} being used as the grid size along the object
        bounding box's largest dimension.
@\item
  {\bf -F PolygonOpti FineNess}: Optimality of polygonal approximation of
        surfaces. See the variable POLY\_APPROX\_OPT for the meaning of
        FineNess. See also -4.
@\item
  {\bf -f PolyOpti SampPerCrv}: Controls the method used to approximate curves
        into polylines. If PolyOpti == 0, equally spaced intervals are used.
        Otherwise, an adaptive subdivision that optimizes the samples is
        employed.
@\item
  {\bf -o OutName}: Name of output file. By default the name of the first data
        file from the {\em DFiles} list is used.  See below on the output
        files.
@\item
  {\bf -g}: Generates the geometry file only. See below.
@\item
  {\bf -p Zmin Zmax}: Sets the ratios between the depth cue and the width of
        the dumped {\em polylines}. See also -P. Closer lines will be drawn
        wider.
@\item
  {\bf -P}: Forces dumping polygons as polylines with thickness controlled
        by -p.
@\item
  {\bf -M}: If -P (see -P and -p) then converts the control mesh/polygon
        to polylines which are represented as a sequence of truncated
        cones.
@\item
  {\bf -T}: Talkative mode. Prints processing information.
@\item
  {\bf -I \#UIso[:\#VIso[:\#WIso]]}: Specifies the number of isolines per
        surface/trivariate, per direction. If \#VIso or \#WIso is not
        specified, \#UIso is used for \#VIso etc.
@\item
  {\bf -s ObjSeq\#}: Sets object sequence number if no object name. Default 1.
@\item
  {\bf -z}: Prints version number and current defaults.
@\end{itemize}
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{Usage}
&Usage
    Irit2Ray converts freeform surfaces into polygons in a format that can
 be used by RAYSHADE. Two files are created, one with a '.geom' extension and
 one with '.ray'. Since the number of polygons can be extremely large,
 the geometry is isolated in the '.geom' file and is included
 (via '\#include') in the main '.ray' file. The latter holds the surface
 properties for all the geometry as well as viewing and RAYSHADE specific
 commands. This allows for the changing of the shading or the viewing
 properties while editing small ('.ray') files.
    If '-g' is specified, only the '.geom' file is created, preserving the
 current '.ray' file.
    In practice, it may be useful to create a low resolution approximation
 of the model, change the viewing/shading parameters in the '.ray' file until
 a good view and/or surface quality is found, and then run Irit2Ray once more
 to create a high resolution approximation of the geometry using '-g'.
 Example:
@\begin{verbatim}
 irit2ray -l -F 0 8 b58.dat
@\end{verbatim}
 creates b58.ray and b58.geom with low resolution (FineNess of 5).
   At such low resolution it can very well may happen that triangles will have
 normals "over the edge" since a single polygon may approximate a highly
 curved surface. That will cause RAYSHADE to issue an
 "Inconsistent triangle normals" warning. This problem will not exist if
 high fineness is used.
   One can ray trace this scene using a command similar to:
@\begin{verbatim}
 RAYSHADE -p -W 256 256 b58.ray > b58.rle
@\end{verbatim}
 Once done with parameter setting for RAYSHADE, a fine approximation of the
 model can be created with:
@\begin{verbatim}
 irit2ray -l -g -F 0 64 b58.dat
@\end{verbatim}
 which will only recreate b58.geom (because of the -g option).
 Interesting effects can be created using the depth cue support and polyline
 conversion of irit2ray. For example
@\begin{verbatim}
 irit2ray -G 5 -P -p -0.0 0.5 solid1.dat
@\end{verbatim}
 will dump solid1 as a set of polylines (represented as truncated cones in
 RAYSHADE) with varying thickness according to the $z$ depth. Another example
@\begin{verbatim}
 irit2ray -G 5 -P -p -0.1 1.0 saddle.dat
@\end{verbatim}
 which dumps the isolines extracted from the saddle surface with varying
 thickness.
   Each time a data file is saved in {\em IRIT}, it can be saved with the
 viewing matrix of the last INTERACT by saving the VIEW\_MAT object as well.
 I.e.:
@\begin{verbatim}
 save( "b58", b58 );
@\end{verbatim}
   However one can overwrite the viewing matrix by appending a new matrix
 in the end of the command line, created by the display devices:
@\begin{verbatim}
 os2drvs b58.dat
 irit2ray -l -F 0 16 b58.dat irit.mat
@\end{verbatim}
 where irit.mat is the viewing matrix created by os2drvs. The output name,
 by default, is the last input file name, so you might want to provide an
 explicit name with the -o flag.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{Advanced Usage}
&Advanced Usage
   One can specify surface qualities for individual surfaces of a model.
 Several such attributes are supported by Irit2Ray and can be set within
 {\em IRIT}. See also the ATTRIB {\em IRIT} command.
   If a certain surface should be finer than the rest of the scene, one can
 set a "resolution" attribute which specifies the {\em relative} FineNess
 resolution of this specific surface.
 Example:
@\begin{verbatim}
 attrib( srf1, "resolution", 2 );
@\end{verbatim}
 will force srf1 to have twice the default resolution, as set via the '-f'
 flag.
   Almost flat patches are converted to polygons. The rectangle can be
 converted into two polygons (by subdividing along one of its diagonals) or
 into four by introducing a new point at the patch center. This behavior is
 controlled by the '-4' flag, but can be overwritten for individual surfaces
 bu setting "twoperflat" or "fourperflat".
   RAYSHADE specific properties are controlled via the following attributes:
 "specpow", "reflect", "transp", "body", "index", and "texture". The value of
 this attributes must be strings as it is copied verbatim. Refer to
 RAYSHADE's manual for their meaning.
  Example:
@\begin{verbatim}
 attrib( srf1, "transp", "0.3" );
 attrib( srf1, "texture", "wood" );
@\end{verbatim}
   Surface color is controlled in two levels. If the object has an RGB
 attribute, it is used. Otherwise a color as set via the {\em IRIT} COLOR
 command is being used if set.
 Example:
@\begin{verbatim}
 attrib( tankBody, "rgb", "244,164,96" );
@\end{verbatim}
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\section{Irit2Scn - IRIT To SCENE (RTrace) filter}
!IRIT2Scn - IRIT To SCENE (RTrace) filter
 SCENE is the format used by the RTrace ray tracer. This filter was donated
 by Antonio Costa ([e-mail]), the author of RTrace.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{Command Line Options}
&Command line options
@\begin{verbatim}
  irit2scn [-l] [-4] [-F PolyOpti FineNess] [-o OutName] [-g] [-T] [-z] DFiles
@\end{verbatim}
@\begin{itemize}
@\item
  {\bf -l}: Linear - forces linear (degree two) surfaces to be approximated
       as a single polygon along their linear direction.
         Although most of the time, linear direction can be exactly represented
       using a single polygon, even a bilinear surface can have a free-form
       shape (saddle-like) that is not representable using a single polygon.
         Note that although this option will better emulate the surface shape,
       it will create unnecessary polygons in cases where one is enough.
@\item
  {\bf -4}: Four - Generates four polygons per flat patch.
@\item
  {\bf -F PolyOpti FineNess}: Optimality of polygonal approximation of
       surfaces. See the variable POLY\_APPROX\_OPT for the meaning of
       FineNess. See also -4.
@\item
  {\bf -o OutName}: Name of output file. By default the name of the first data
       file from {\em DFiles} list is used.  See below on the output files.
@\item
  {\bf -g}: Generates the geometry file only. See below.
@\item
  {\bf -T}: Talkative mode. Prints processing information.
@\item
  {\bf -z}: Prints version number and current defaults.
@\end{itemize}
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{Usage}
&Usage
    Irit2Scn converts freeform surfaces and polygons into polygons in a format
 that can be used by RTrace. Two files are created, one with a '.geom'
 extension and one with '.scn'. Since the number of polygons can be extremely
 large, the geometry is isolated in the '.geom' file and is included
 (via '\#include') in the main '.scn' file. The latter holds the surface
 properties for all the geometry as well as viewing and RTrace specific
 commands. This allows for the changing of the shading or the viewing
 properties while editing small ('.scn') files.
    If '-g' is specified, only the '.geom' file is created, preserving the
 current '.scn' file.
    In practice, it may be useful to create a low resolution approximation
 of the model, change the viewing/shading parameters in the '.scn' file
 until a good view and/or surface quality is found, and then run Irit2Scn once
 more to create a high resolution approximation of the geometry using '-g'.
 Example:
@\begin{verbatim}
 irit2scn -l -F 0 8 b58.dat
@\end{verbatim}
 creates b58.scn and b58.geom with low resolution (FineNess of 5).
   One can ray trace this scene after converting the scn file to a sff file,
 using scn2sff provided with the RTrace package.
 Once done with the parameter setting of RTrace, a fine approximation of the
 model can be created with:
@\begin{verbatim}
 irit2scn -l -g -F 0 64 b58.dat
@\end{verbatim}
 which will only recreate b58.geom (because of the -g option).
   One can overwrite the viewing matrix by appending a new matrix
 in the end of the command line, created by the display devices:
@\begin{verbatim}
 wntdrvs b58.dat
 irit2scn -l -F 0 8 b58.dat irit.mat
@\end{verbatim}
 where irit.mat is the viewing matrix created by wntdrvs. The output name,
 by default, is the last input file name, so you might want to provide an
 explicit name with the -o flag.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{Advanced Usage}
&Advanced Usage
   One can specify surface qualities for individual surfaces of a model.
 Several such attributes are supported by Irit2Scn and can be set within
 {\em IRIT}. See also the ATTRIB {\em IRIT} command.
   If a certain surface should be finer than the rest of the scene, one can
 set a "resolution" attribute which specifies the {\em relative} FineNess
 resolution of this specific surface.
 Example:
@\begin{verbatim}
 attrib( srf1, "resolution", 2 );
@\end{verbatim}
 will force srf1 to have twice the default resolution, as set via the '-f'
 flag.
   Almost flat patches are converted to polygons. The patch can be converted
 into two polygons (by subdividing along one of its diagonals) or into four
 by introducing a new point at the patch center. This behavior is controlled
 by the '-4' flag, but can be overwritten for individual surfaces bu setting
 "twoperflat" or "fourperflat".
   RTrace specific properties are controlled via the following attributes:
 "SCNrefraction", "SCNtexture", "SCNsurface. Refer to the RTrace manual for
 their meaning.
 Example:
@\begin{verbatim}
 attrib( srf1, "SCNrefraction", 0.3 );
@\end{verbatim}
   Surface color is controlled in two levels. If the object has an RGB
 attribute, it is used. Otherwise a color as set via {\em IRIT} COLOR command
 is used if set.
 Example:
@\begin{verbatim}
 attrib( tankBody, "rgb", "244,164,96" );
@\end{verbatim}
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\section{Irit2Xfg - IRIT To XFIG filter}
!IRIT2Xfg - IRIT To XFIG filter
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{Command Line Options}
&Command line options
@\begin{verbatim}
  irit2xfg [-s Size] [-t XTrans YTrans] [-I #UIso[:#VIso[:#WIso]]]
       [-f PolyOpti SampPerCrv] [-F PolyOpti FineNess] [-M] [-G] [-T]
       [-i] [-o OutName] [-z] DFiles
@\end{verbatim}
@\begin{itemize}
@\item
  {\bf -s Size}: Size in inches of the page. Default is 7 inches.
@\item
  {\bf -t XTrans YTrans}: X and Y translation. of the image. Default is (0, 0).
@\item
  {\bf -I \#UIso[:\#VIso]}: Specifies the number of isolines per surface, per
        direction. If \#VIso is not specified, \#UIso is used for \#VIso as
        well.
@\item
  {\bf -f PolyOpti SampPerCrv}: Controls the method used to approximate curves
        into polylines. If PolyOpti == 0, equally spaced intervals are used.
        Otherwise, an adaptive subdivision that optimizes the samples is
        employed.
@\item
  {\bf -F PolygonOpti FineNess}: Optimality of polygonal approximation of
        surfaces. See the variable POLY\_APPROX\_OPT for the meaning of
        FineNess. See also -4. This enforces the dump of freefrom geometry
        as polygons.
@\item
  {\bf -M}: Dumps the control mesh/polygon as well.
@\item
  {\bf -G}: Dumps the freeform geometry.
@\item
  {\bf -T}: Talkative mode. Prints processing information.
@\item
  {\bf -i}: Internal edges (created by {\em IRIT}) - default is not to
       display them, and this option will force displaying them as well.
@\item
  {\bf -o OutName}: Name of output file. By default the name of the first data
       file from {\em DFiles} list is used.  See below on the output files.
@\item
  {\bf -z}: Prints version number and current defaults.
@\end{itemize}
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\subsection{Usage}
&Usage
    Irit2Xfg converts freeform surfaces and polygons into polylines in a format
 that can be used by XFIG.
 Example:
@\begin{verbatim}
 irit2Xfg -l -f 0 16  saddle.dat > saddle.xfg
@\end{verbatim}
   However, one can overwrite the viewing matrix by appending a new matrix
 in the end of the command line, created by the display devices:
@\begin{verbatim}
 x11drvs b58.dat
 irit2Xfg -l -f 0 16 b58.dat irit.mat > saddle.xfg
@\end{verbatim}
 where irit.mat is the viewing matrix created by x11drvs.
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
@\section{Data File Format}
!DATAFILE Format
   This section describes the data file format used to exchange data between
 {\em IRIT} and its accompanying tools.
@\begin{verbatim}
 [OBJECT {ATTRS} OBJNAME
     [NUMBER n]
   | [VECTOR x y z]
   | [CTLPT POINT_TYPE {w} x y {z}]
   | [STRING "a string"]
   | [MATRIX m00 ... m03
             m10 ... m13
             m20 ... m23
             m30 ... m33]
     ;A polyline should be drawn from first point to last. Nothing is drawn
     ;from last to first (in a closed polyline, last point is equal to first).
   | [POLYLINE {ATTRS} #PTS                   ;#PTS = number of points.
         [{ATTRS} x y z]
         [{ATTRS} x y z]
            .
            .
            .
         [{ATTRS} x y z]
     ]
     ;Defines a closed planar region. Last point is NOT equal to first,
     ;and a line from last point to first should be drawn when the boundary
     ;of the polygon is drawn.
   | [POLYGON {ATTRS} #PTS
         [{ATTRS} x y z]
         [{ATTRS} x y z]
            .
            .
            .
         [{ATTRS} x y z]
     ]
     ;Defines a "cloud" of points.
   | [POINTLIST {ATTRS} #PTS
         [{ATTRS} x y z]
         [{ATTRS} x y z]
            .
            .
            .
         [{ATTRS} x y z]
     ]
     ;Defines a Bezier curve with #PTS control points. If the curve is
     ;rational, the rational component is introduced first.
   | [CURVE BEZIER {ATTRS} #PTS POINT_TYPE
         [{ATTRS} {w} x y z ...]
         [{ATTRS} {w} x y z ...]
            .
            .
            .
         [{ATTRS} {w} x y z ...]
     ]
     ;Defines a Bezier surface with #UPTS * #VPTS control points. If the
     ;surface is rational, the rational component is introduced first.
     ;Points are printed row after row (#UPTS per row), #VPTS rows.
   | [SURFACE BEZIER {ATTRS} #UPTS #VPTS POINT_TYPE
         [{ATTRS} {w} x y z ...]
         [{ATTRS} {w} x y z ...]
            .
            .
            .
         [{ATTRS} {w} x y z ...]
     ]
     ;Defines a Bezier trivariate with #UPTS * #VPTS * #WPTS control
     ;points. If the trivariate is rational, the rational component is
     ;introduced first. Points are printed row after row (#UPTS per row),
     ;#VPTS rows, #WPTS layers (depth).
   | [TRIVAR BEZIER {ATTRS} #UPTS #VPTS #WPTS POINT_TYPE
         [{ATTRS} {w} x y z ...]
         [{ATTRS} {w} x y z ...]
            .
            .
            .
         [{ATTRS} {w} x y z ...]
     ]
     ;Defines a Bspline curve of order ORDER with #PTS control points. If the
     ;curve is rational, the rational component is introduced first.
     ;Note length of knot vector is equal to #PTS + ORDER.
     ;If curve is periodic KVP prefix the knot vector that has length of
     ;'Length + Order + Order - 1'.
   | [CURVE BSPLINE {ATTRS} #PTS ORDER POINT_TYPE
         [KV{P} {ATTRS} kv0 kv1 kv2 ...]                    ;Knot vector
         [{ATTRS} {w} x y z ...]
         [{ATTRS} {w} x y z ...]
            .
            .
            .
         [{ATTRS} {w} x y z ...]
     ]
     ;Defines a Bspline surface with #UPTS * #VPTS control points, of order
     ;UORDER by VORDER. If the surface is rational, the rational component
     ;is introduced first.
     ;Points are printed row after row (#UPTS per row), #VPTS rows.
     ;If surface is periodic in some direction KVP prefix the knot vector
     ;that has length of 'Length + Order + Order - 1'.
   | [SURFACE BSPLINE {ATTRS} #UPTS #VPTS UORDER VORDER POINT_TYPE
         [KV{P} {ATTRS} kv0 kv1 kv2 ...]                ;U Knot vector
         [KV{P} {ATTRS} kv0 kv1 kv2 ...]                ;V Knot vector
         [{ATTRS} {w} x y z ...]
         [{ATTRS} {w} x y z ...]
            .
            .
            .
         [{ATTRS} {w} x y z ...]
     ]
     ;Defines a Bspline trivariate with #UPTS * #VPTS * #WPTS control
     ;points. If the trivariate is rational, the rational component is
     ;introduced first. Points are printed row after row (#UPTS per row),
     ;#VPTS rows, #WPTS layers (depth).
     ;If trivariate is periodic in some direction KVP prefix the knot vector
     ;that has length of 'Length + Order + Order - 1'.
   | [TRIVAR BSPLINE {ATTRS} #UPTS #VPTS #WPTS UORDER VORDER WORDER POINT_TYPE
         [KV{P} {ATTRS} kv0 kv1 kv2 ...]                ;U Knot vector
         [KV{P} {ATTRS} kv0 kv1 kv2 ...]                ;V Knot vector
         [KV{P} {ATTRS} kv0 kv1 kv2 ...]                ;W Knot vector
         [{ATTRS} {w} x y z ...]
         [{ATTRS} {w} x y z ...]
            .
            .
            .
         [{ATTRS} {w} x y z ...]
     ]
     ;Defines a trimmed surface. Encapsulates a surface (can be either a
     ;Bspline or a Bezier surface) and prescribes its trimming curves.
     ;There can be an arbitrary number of trimming curves (either Bezier
     ; or Bspline). Each trimming curve contains an arbitrary number of
     ;trimming curve segments, while each trimming curve segment contains
     ;a parameteric representation optionally followed by a Euclidean
     ;representation of the trimming curve segment.
   | [TRIMSRF
         [SURFACE ...
         ]
         [TRIMCRV
             [TRIMCRVSEG
                 [CURVE ...
                 ]
             ]
                .
                .
                .
             [TRIMCRVSEG
                 [CURVE ...
                 ]
             ]
         ]
             .
             .
             .
         [TRIMCRV
             [TRIMCRVSEG
                 [CURVE ...
                 ]
             ]
                .
                .
                .
             [TRIMCRVSEG
                 [CURVE ...
                 ]
             ]
         ]
     ]
 POINT_TYPE -> E1 | E2 | E3 | E4 | E5 | P1 | P2 | P3 | P4 | P5
 ATTRS -> [ATTRNAME ATTRVALUE]
          | [ATTRNAME]
          | [ATTRNAME ATTRVALUE] ATTRS
@\end{verbatim}
 Some notes:
 * This definition for the text file is designed to minimize the
   reading time and space. All information can be read without backward
   or forward referencing.
 * An OBJECT must noever hold different geometry or other entities.
   I.e. CURVEs, SURFACEs, and POLYGONs must all be in different OBJECTs.
 * Attributes should be ignored if not needed. The attribute list may have
   any length and is always terminated by a token that is NOT '\verb+[+'. This
   simplifies and disambiguates the parsing.
 * Comments may appear between '\verb+[+OBJECT ...\verb+]+' blocks, or
   immediately after OBJECT OBJNAME, and only there.
   A comment body can be anything not containing the '\verb+[+' or the
   '\verb+]+' tokens (signals start/end of block). Some of the comments in
   the above definition are {\em illegal} and appear there only of the sake
   of clarity.
 * It is preferred that geometric attributes such as NORNALs will be saved in
   the geometry structure level (POLYGON, CURVE or vertices) while graphical
   and others such as COLORs will be saved in the OBJECT level.
 * Objects may be contained in other objects to an arbitrary level.
 Here is an example that exercises most of the data format:
@\begin{verbatim}
 This is a legal comment in a data file.
 [OBJECT DEMO
     [OBJECT REAL_NUM
         And this is also a legal comment.
         [NUMBER 4]
     ]
     [OBJECT A_VECTOR
         [VECTOR 1 2 3]
     ]
     [OBJECT CTL_POINT
         [CTLPT E3 1 2 3]
     ]
     [OBJECT STR_OBJ
         [STRING "string"]
     ]
     [OBJECT UNIT_MAT
         [MATRIX
            1 0 0 0
            0 1 0 0
            0 0 1 0
            0 0 0 1
         ]
     ]
     [OBJECT [COLOR 4] POLY1OBJ
         [POLYGON [PLANE 1 0 0 0.5] 4
             [-0.5 0.5 0.5]
             [-0.5 -0.5 0.5]
             [-0.5 -0.5 -0.5]
             [-0.5 0.5 -0.5]
         ]
         [POLYGON [PLANE 0 -1 0 0.5] 4
             [0.5 0.5 0.5]
             [-0.5 0.5 0.5]
             [-0.5 0.5 -0.5]
             [0.5 0.5 -0.5]
         ]
     ]
     [OBJECT [COLOR 63] ACURVE
         [CURVE BSPLINE 16 4 E2
             [KV 0 0 0 0 1 1 1 2 3 4 5 6 7 8 9 10 11 11 11 11]
             [0.874 0]
             [0.899333 0.0253333]
             [0.924667 0.0506667]
             [0.95 0.076]
             [0.95 0.76]
             [0.304 1.52]
             [0.304 1.9]
             [0.494 2.09]
             [0.722 2.242]
             [0.722 2.318]
             [0.38 2.508]
             [0.418 2.698]
             [0.57 2.812]
             [0.57 3.42]
             [0.19 3.572]
             [0 3.572]
         ]
     ]
     [OBJECT [COLOR 2] SOMESRF
         [SURFACE BEZIER 3 3 E3
             [0 0 0]
             [0.05 0.2 0.1]
             [0.1 0.05 0.2]
             [0.1 -0.2 0]
             [0.15 0.05 0.1]
             [0.2 -0.1 0.2]
             [0.2 0 0]
             [0.25 0.2 0.1]
             [0.3 0.05 0.2]
         ]
     ]
@\end{verbatim}
@\section{Bugs and Limitations}
!BUGS and LIMITATIONS
   Like any program of more than one line, it is far from being perfect.
 Some limitations, as well as simplifications, are laid out below.
 *  If the intersection curve of two objects falls exactly on polygon
    boundaries, for all polygons, the system will scream that the two objects
    do not intersect at all. Try to move one by EPSILON into the other.
    I probably should fix this one - it is supposed to be relatively easy.
 *  Avoid degenerate intersections that result with a point or a line.
    They will probably cause wrong propagation of the inner and outer part of
    one object relative to the other. Always extend your object beyond the
    other object.
 *  If two objects have no intersection in their boundary, {\em IRIT} assumes they
    are disjoint: a union simply combines them, and the other Boolean
    operators return a NULL object. One should find a FAST way (3D Jordan
    theorem) to find the relation between the two (A in B, B in A, A
    disjoint B) and according to that, make a decision.
 *  Since the boolean sum implementation constructs ruled surfaces with
    uniform speed, it might return a somewhat incorrect answer, given
    non-uniform input curves.
 *  The parser is out of hand and is difficult to maintain. There are several
    memory leaks there that one should fix.
 *  The X11 driver has no menu support (any easy way to have menus using
    Xlib!?).
 *  IBM R6000 fails to run the drivers in -s- mode.
 *  Rayshade complains a lot about degenerate polygons on irit2ray output.
    To alleviate the problem, change the 'equal' macro in common.h in libcommon
    of rayshade from EPSILON (1e-5) to 1e-7 or even lower.
 *  On the motif-based drivers (xmtdrvs etc.) clicking the mouse left and
    right of the scale's button produces stepped transformations. This
    step size is constant, and is not proportional to the distance between
    the mouse's position and the position of the button. The reason for the
    flaw is incorrect callback information returned from the scale in
    repeattive mode.
 *  Binary data files are not documented, nor will they be. They might
    change in the future and are in fact machine dependend. Hence, one
    platform might fail to read the other's binary data file.
@\end{document}