The X-Philes (2nd Revision)/The X-Philes Number 1 (1995).iso/xphiles/hp48_1/suite3d

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From: Charles Patton <[e-mail]>
Subject:  v01i017:  suite3d - 3D Graphing Suite v1.0, Part01/01
Newsgroups: comp.sources.hp48
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Submitted-by: Charles Patton <[e-mail]>
Posting-number: Volume 1, Issue 17
Archive-name: suite3d/part01

BEGIN_DOC Suite3D.doc
@ Version 1.0 @

_Introduction_

     The programs contained in this document comprise a suite of 3D
graphing/viewing utilities for the HP-48 (an HP-28 version will be
forthcoming provided sufficient interest.)

     We had several requirements to consider in creating these
programs. Our aims were that they be (1) purely user code, (2)
relatively short, and (3) psychologically effective.  Aims (1) and (2)
are due to our target audience of educators, many of whom have little
contact with technology beyond their use of the HP-48 or HP-28. We
expect that, in many situations, one user will obtain the code in
printed form, enter it into their machine, and transmit it to others
via the infrared I/O.

     In exploring visualization techniques on a variety of machines we
found that increasing "realism" (read: ray-traced, Phong-shaded,
hidden-line, etc.) in the graphical presentation of functions of two
variables did not necessarily correlate with increasing ease of
comprehension. These programs represent the results of some of these
experiments (including time-to-completion as an important factor).

     We invite you to try them out and experiment yourself. All
suggestions, additions, corrections, insights, commentary, and
criticisms are welcome.

_Organization_

     Analogous to the built-in plotting routines, all the Suite3D
programs assume that the function of interest is stored in EQ.
Further, they assume that the function is represented as an expression
in the variables 'X' and 'Y' (e.g. u,v -> sin(u+v) is represented as
'SIN(X+Y)' in EQ). Insure that 'X' and 'Y' are formal (no variables
'X' and 'Y' along the current path).

     The viewing window is controlled (as usual) by PMIN and PMAX (or
XRNG and YRNG, though these may be inappropriately named for some
Suite3D programs.)

     Some of the programs have an associated <descriptor>PAR variable
analogous to PPAR. Default versions are supplied in this document.

     The programs here are organized into a single directory for
convenience.  Inter-dependence of the programs and other variables is
noted in the program description.

_Oversized PICTs_

     With the sole exception of YVIEW, all of the programs have
assumed that the PICT grob has the default size. Moreover, some of the
parameters coded into the programs were determined experimentally. In
consequence, don't expect any miracles to occur with these programs if
an oversized PICT is used. While it is quite possible encode automatic
scaling from the size of the PICT, we didn't find it useful enough to
include. If anyone has additional insights into this issue, we'd
welcome their input.

_Descriptions of the Programs_

SlopeField:
     The SlopeField program plots a lattice of line segments whose
slopes represent the function value at their centerpoint. Using
SlopeField to plot F(X,Y) allows your eye to pick out integral curves
of the differential equation dy/dx=F(x,y). It is quite useful in
understanding where the "arbitrary constant" in anti-derivatives comes
from.

psContour:
     The psContour program (pseudo-contour) program uses SlopeField to
produce a fast contour plot of the current function. By plotting the
direction field perpendicular to the gradient of the function it
allows your eye to pick out the integral curves (contours) without
actually plotting them. The apparent contours are evenly spaced
visually and so give no information on how steep the graph is at any
particular point.

YView:
     The YView program provides an oblique-view, perspective, 3D
surface plot (viewing toward increasing Y). The program assumes that
the variable VPAR contains the viewpoint coordinates, Xe, Ye, Ze,
together with view-volume bounds, Yfar and Ynear. VPAR, then, is
assumed to contain a list of numbers { Xe Ye Ze Yfar Ynear
hidden-line-p } where hidden-line-p is non-zero if you wish to use the
hidden-line facilities in the plot. If this is non-zero, RES (plotting
resolution) should be set to 0, or #2 for best effect.  The XRNG and
YRNG (really "ZRNG" in this case) are to be adjusted as usual.

     This is a simple "divide-by-depth" method for perspective
plotting where the viewplane is always 1 unit from the viewpoint and
is parallel to the x-z plane. Since the perspective transformation in
the case can be implemented by a simple change of coordinates,
plotting individual sections is no slower than ordinary plots.

     Note: To abort this routine, press the [ON] key and then press
the [ENTER] key.

ShapeToShade:
     The ShapeToShade program plots the function as a Phong-shaded
figure viewed from above with a light source in the "north west." It
assumes that the variable DPAR contains sixteen 4x4 GROBS to serve as
the dithering pattern. The dither patterns included are probably not the
best possible: insights along these lines are most welcome.

Movie:
     The Movie program plots 8 cross-sections of the function plot
varying the Y-value from Yfar to Ynear (as recorded in VPAR, see
YView). Having plotted these, it calls the utility program, uSMOV
(utility-show-movie), to play these back in sequence repeatedly.

     Note: To abort this routine in the plotting phase, press the [ON]
key and then press the [ENTER] key.  To end the movie press any key
(e.g. [ENTER]).

uSMOV:

     The uSMOV (utility show-movie) program takes <n> grobs from the
stack and shows them in sequence, thus producing a movie effect. It
can be stopped with any key press.

_Correspondence_

Correspondence on Suite3D suite be sent to Charles Patton at one of the
following addresses:

snail-mail:
          M.S. 5U-L9
          Hewlett-Packard Co.
          1000 N.E. Circle Blvd.
          Corvallis, OR 97330

e-mail:
          [e-mail]    (for Internet hosts)
          hplabs!hpcvrs!charliep (for UUCP hosts)

END_DOC
BYTES: #EEADh    3228.5

BEGIN_RPL Suite3D
%%HP: T(3)A(R)F(.);
DIR
  SlopeField
\<< EQ
   'PPAR(1)' EVAL C\->R
   'PPAR(2)' EVAL C\->R
   0 0 0 0 0 0 0
   \-> der left bot right top hstp vstp hofs vofs x y d
  \<< ERASE { # 0d # 0d } PVIEW
      right left - 13 / 'hstp' STO
      top bot - 8 / 'vstp' STO
      hstp .4 * 'hofs' STO
      vstp .4 * 'vofs' STO
      bot vstp 2 / + top
    FOR y
        y 'Y' STO
        left hstp 2 / + right
      FOR x
          x 'X' STO
          der \->NUM 'd' STO
          'IFTE(ABS(d*hofs)>vofs,
                vofs/d+i*vofs,
                hofs+i*hofs*d)' \->NUM
         x y R\->C
         DUP2 + 3 ROLLD SWAP - LINE
         hstp
      STEP
      vstp
    STEP
  \>> {X Y} PURGE {} PVIEW
\>>

  psContour
\<< EQ
  \<< \-> dx dy 'IFTE(dy==0,MAXR,-dx/dy)' \>>
  \-> eq slp
  \<< IFERR
        eq X \.d eq Y \.d
        2 \->LIST 'slp' APPLY
        {X Y } SHOW
        STEQ
        SlopeField
      THEN
        eq STEQ
        ERRM DOERR
      END eq STEQ
  \>>
\>>

  YView
\<< VPAR OBJ\->
@ include the (optional) hidden-line routine: @
  \<< \-> K
      \<< CASE K TYPE DUP 0 ==
          THEN DROP
           X K R\->C X -50 R\->C DUP2
               LINE TLINE
               K
      END
      1 ==
      THEN  K
      END
      K EVAL 1 \->LIST 'PRASE' APPLY
      END
       \>>
 \>>
    \-> Xe Ye Ze Yfar Ynear prase u hline
  \<< 'EQ' RCL 'u' \-> eq u
    \<< eq { 'X' '(X-Xe)*u+Xe' 'Y' 'u+Ye' } |
    Ze - 'u' / Ze +
    { X u } SHOW COLCT
      IF prase
      THEN { & 'hline(&)' } \|vMATCH DROP
      END
      IFERR
         'EQ' STO
     'X' INDEP ERASE
     Ynear Yfar - 8 /
     \-> stp
        \<<
        Yfar Ye -
        Ynear Ye -
        FOR u
            DRAW
        IF
          KEY
            THEN
              DROP
          "outa here" DOERR
            END stp
       STEP
       \>>
      THEN eq STEQ ERRM DOERR
      ELSE eq STEQ
      END {} PVIEW
     \>>
  \>>
\>>

  VPAR
{ 0 -.5 2 3.5 -.2 0}

 ShapeToShade
   \<< 'PPAR(1)' EVAL C\->R
       'PPAR(2)' EVAL C\->R 0 0 0
       \-> xmin ymin xmax ymax x y eq
       \<< xmax xmin - 32 / ymax ymin - 15 / 'x' 'y'
          \-> xstp ystp x y
      \<< EQ DUP X \.d .4 - 2 ^ SWAP
          Y \.d .4 - 2 ^ +
          1 + -.5 ^ {X x Y y} | 'eq' STO
              ERASE
          { # 0d # 0d } PVIEW # 0d ymin ymax
          FOR y
              # 0d xmin xmax
          FOR x
              DUP2 SWAP 2 \->LIST PICT SWAP
              eq \->NUM
              IF DUP TYPE 0 \=/
              THEN DROP 1
              END
              15 * IP DPAR SWAP
              16 - NEG GET REPL
              4 + xstp
           STEP
           DROP 4 + ystp
           STEP DROP
              {} PVIEW
     \>>
     \>>
  \>>

 DPAR
   { GROB 4 4 00400000
     GROB 4 4 00402000
     GROB 4 4 00604000
     GROB 4 4 00606000
     GROB 4 4 00606010
     GROB 4 4 10606080
     GROB 4 4 90606080
     GROB 4 4 90606090
     GROB 4 4 60909070
     GROB 4 4 E0909070
     GROB 4 4 F09090E0
     GROB 4 4 F09090F0
     GROB 4 4 F090B0F0
     GROB 4 4 F0B0D0F0
     GROB 4 4 F0B0F0F0
     GROB 4 4 F0F0F0F0
   }

  Movie
\<< PPAR EQ 'VPAR(4)' EVAL 'VPAR(5)' EVAL 0 0
    \-> ppar eq yfar ynear ystp y
    \<< 'y' 'y' STO
        eq {X Y} SHOW {Y y} |
        ynear yfar - 8 / 'ystp' STO
        IFERR
          STEQ
          'X' INDEP
          FUNCTION
          0 yfar ynear
          FOR y
            ERASE DRAW PICT RCL SWAP 1 +
            IF KEY
            THEN DROP "outa here" DOERR
            END
            ystp
          STEP
        THEN
          ppar 'PPAR' STO
          eq STEQ
          ERRM DOERR
        END
        ppar 'PPAR' STO
        eq STEQ
    \>> uSMOV
\>>

 uSMOV
\<< \-> n
    \<< {#0 #0} PVIEW
        DO
          n ROLL DUP PICT {#0 #0} ROT REPL
        UNTIL
          KEY
        END DROP
        n
    \>>
\>>

 EQ
'(Y^2*X-X^3)*.2'

 PPAR
{ (-6.5,-3.1) (6.5,3.2) X # 4d (0,0) FUNCTION Y }

END
END_RPL