APDL Public Domain 1/APDL_PD1A.iso/raytrace/rayshade/docs/olddocs/RayDoc

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Options

This appendix describes the commandline arguments accepted by rayshade.
These options override defaults as well as any values  or flags given in the
input file, and are thus useful for generating test and other unusual,
``non-standard'' renderings.

The general form of a rayshade command line is:

 rayshade [Options] [filename]

If given, the input file is read from  [filename].  By default, the input
file is read from the standard input. Recall that, by default, the image
file is written to the standard output; you will need to redirect the
standard output if you have  not chosen to write the image to a file
directly.  The name of the input file may be given anywhere on the command
line.

Command-line options fall into two broad categories: those that set
numerical or other values and thus must be followed by  further
arguments,and those that simply turn features on and off.  Rayshade's
convention is to denote the value-setting arguments  using capital letters,
and feature-toggling arguments using lower-case letters.

- A  frame
 Begin rendering (action) on the given frame.
The default starting frame is number zero.

- a
 Toggle writing of alpha channel.
This option is only available when the Utah Raster Toolkit is being used.

- C  R G B
 Set the adaptive ray tree pruning color.  If all channel contributions
falls below the given cutoff values, no further rays are  spawned. Overrides
the value specified via the cutoff keyword.

- c
 Continue an interrupted rendering.
When given, this option indicates that the image file being written to
contains a partially-completed image.  Rayshade will read  the image to
determine the scanline from which to continue the rendering. This option is
only available with the Utah Raster Toolkit. The  -O option must also be
used.

- D  depth
 Set maximum ray tree depth.
Overrides the value specified in the input file via the maxdepth keyword.

- E  separation
 Set eye separation for rendering of stereo pairs.
Overrides the value specified via the eyesep keyword.

- e
 Write exponential RLE file.
This option is only available for use with the Utah Raster Toolkit. See the
Utah Raster Toolkit's unexp manual page for details on  exponential RLE
files.

- F  freq
 Set frequency of status report.
Overrides the value given using the report keyword.

- G  gamma
 Use given gamma correction exponent writing writing color information to
the image file. The default value for gamma is 1.0.

- g
 Use a Gaussian pixel filter.
Overrides the filter selected through the use of the filter keyword.

- h
 Print a short use message.

- j
 Use jittered sampling to perform antialiasing.
This option overrides the adaptive keyword, if present, in the input file.

- l
 Render the left stereo pair image.

- m
 Write a sampling map to the alpha channel.
Rather than containing coverage information, the alpha channel values will
be restricted to zero, indicating no supersampling,  and full intensity,
indicating supersampling.  This option is only available if the Utah Raster
Toolkit is being used.

- N  frames
 Set the total number of frames to be rendered.
This option overrides any value specified through the use of the frames
keyword.  By default, a single frame is rendered.

- n
 Do not render shadows.

- O  outfile
 Write the image to the named file.
This option overrides the name given with the outfile keyword, if any, in
the input file.

- o
 Toggle the effect of object opacity on shadows.
This option is equivalent to specifying shadowtransp in the input file.  By
default, rayshade traces shadow rays through non- opaque objects.

- P  depth
 Use adaptive supersampling with the givenmaximum depth.
This option overrides the jittered keyword and the value associated the
adaptive keyword given in the input file, if any.

- P
 Specify the options that should be passed to the C preprocessor.
The C preprocessor, if available, is applied to all of the inputpassed to
rayshade.

- p
 Perform preview-quality rendering.
This option is equivalent to -n -S 1 -D 0.

- q
 Do not print warning messages.

- R  xsize ysize
 Produce an image xsize pixels wide by ysize pixels high.
This option overrides any screen size set by use of the screen keyword.

- r
 Render the right stereo pair image.

- S samples
 Use samples^2 jittered samples.
This option overrides any value set through the use of the samples keyword
in the input file.

- s
 Disable caching of  shadowing information.
It should not be necessary to ever use this option.

- T   r g b
 Set the contrast threshold in the three color channels for use in adaptive
supersampling. This option overrides any value given through the use of the
contrast keyword.


- V   filename
 Write verbose output to the named file.
This option overrides any file named through the use of the  report keyword.

- v
 Write verbose output.
When given, this option causes information about the options selected and
the objects defined to be included in the report file.

- W  minx miny maxx maxy
 Render the specified subwindow.  The parameters should fall between zero
and one. This option is provided to facilitate changing and/or examining a
small portion of an image without having to re-render the entire  image.


A View

When designing a rayshade input file, there are two main issues that must be
considered.  The first and more complex is the  selection of the objects to
be rendered and the appearances they should be assigned.  The second and
usually easier issue is the  choice of viewing parameters.  This chapter
deals with the latter problem; the majority of the following chapters
discuss aspects of objects and their appearances.

Rayshade uses a camera model to describe the geometric relationship between
the objects to be rendered and the image that is  produced.  This
relationship describes a perspective projection from world space onto the
image plane.

The geometry of the perspective projection may be thought of as an infinite
pyramid, known as the viewing frustum. The apex of  the frustum is defined
by the camera's position, and the main axis of the frustum by a ``look''
vector. The four sides of the pyramid are differentiated by their
relationship to a reference ``up'' vector from the camera's position.

The image ultimately produced by rayshade may then be thought of as the
projection of the objects closest to the eye onto a  rectangular screen
formed by the intersection of the pyramid with a plane orthogonal to the
pyramid's axis.  The overall shape of  the frustum (the lengths of the top
and bottom sides compared to left and right) is described by the horizontal
and vertical fields  of view.


Position

The three basic camera properties are its position, the direction in which
it is pointing, and its orientation.  The keywords for  specifying these
values are described below. The default values are designed to provide a
reasonable view of a sphere or radius 2 located at origin.  If these default
values are  used, the origin is projected onto the center of the image
plane, with the world x axis  running left-to-right, the z axis bottom-to-
top, and the y axis going ``into'' the screen.

eyep  evec (pos)
 Place the virtual camera at the given position.
The default camera position is (0, -8, 0).

lookp  evec{pos }
 Point the virtual camera toward the given position. The default look point
is the origin (0, 0, 0).  The look point and camera position must not be
coincident.

up  evec{direction }
 The ``up'' vector from the camera point is set to the given direction. This
up vector need not be orthogonal to the view vector, nor need it be
normalized.  The default up direction is (0, 0, 1).

Another popular standard viewing geometry, with the x axis running
left-to-right, the y axis bottom-to-top, and the z axis pointing  out of the
screen, may be obtained by setting the up vector to (0, 1, 0) and by placing
the camera on the positive z axis.


View

Another important choice to be made is that of the field of view of the
camera.  The size of this field describes the angles  between the left and
right sides and top and bottom sidesof the frustum.

fov  hfov, vfov
 Specify the horizontal and vertical field of view, in degrees. The default
horizontal field of view is 45 degrees. If {em vfov} is omitted, as is the
general practice, the vertical field of view is  computed using the
horizontal field of view, the output image resolution, and the assumption
that a pixel samples a square area.   Thus, the values passed via the screen
keyword define the shape of the final image. If you are displaying on a
non-square pixeled  device, you must set the vertical field of view to
compensate for the ``squashing'' that will result.


Field

Under many circumstances, it is desirable to render objects in the image
suchthat they are in sharp focus on the image plane.   This is achieved by
using the default ``pinhole' camera.  In this mode, the camera's aperture is
a single point, and all light rays are  focused on the image plane.

Alternatively, one may widen the aperture in order to simulate depth of
field. In this case, rays are cast from various places on the  aperture disk
towards a point whose distance from the camera is equal to the focus
distance.  Objects that lay in the focal plane  will be in sharp focus.  The
farther an object is from the image plane, the more out-of-focus it will
appear to be. A wider aperture  will lead to a greater blurring of objects
that do not lay in the focal plane. When using a non-zero aperture radius,
it is best to use  jittered sampling in order to reduce aliasing.

aperture  radius
 Use an aperture with the given radius. The default radius is zero,
resulting in a pinhole camera model.

focaldist  distance
 Set the focal plane to be distance units from the camera. By default, the
focal distance is equal to the distance from the camera to the look point.


Rendering

Producing a stereo pair is a relatively simple process; rather than simply
rendering a single image, one creates two related images  which may then be
viewed on a stereo monitor, in a stereo slide viewer, or by using colored
glasses and an appropriate display  filter.

Rayshade facilitates the rendeing of stereo pairs by allowing you to specify
the distance between the camera positions used in  creating the two images.
The camera position given in the rayshade input file defines the midpoint
between the two camera   positions used to generate the images. Generally,
the remainder of the viewing parameters are kept constant.

eyesep  separation
 Specifies the camera separation to be used in rendering stereo pairs. There
is no default value. The separation may also be specified on the command
line through the -E option. The view to be  rendered (left or right) must be
specified on the command line by using the -l or -r options.

There are several things to keep in mind when generating stereo pairs.
Firstly, those objects that lie in from of the focal plane  will appear to
protrude from the screen when viewed in stereo, while objects farther than
the focal plane will recede into the  screen.  As it is usually easier to
look at stereo images that recede into the screen, you willusually want to
place the look point  closer to the camera than the objectof  primary
interest.

The degree of stereo effect is a function of the camera separation and the
distance from the camera to the look point. Too large a  separation will
result in a hyperstereo effect that will be hard to resolve, while too
little a value will result in no stereo effect at  all.  A separation equal
to one tenth the distance from the camera to the look point is often a good
choice.


Surfaces

Surfaces are used to control the interaction between light sources
andobjects.  A surface specification consists of information  about how the
light interacts with both the exterior and interior of an object . For
non-closed objects, such as polygons, the ``interior'' of an object is the
``other side'' of the object's surface relative to the  origin of a ray.

Rayshade usually ensures that a primitive's surface normal is pointing
towards the origin of the incident ray when performing  shading
calculations.  Exceptions to this rule are transparent primitives, for which
rayshade uses the direction of the surface  normal to determine if the
incident ray is entering or exiting the object. All non-transparent
primitives will, in effect, be double- sided.


description

A surface definition consists of a number of component keywords, each of
which is usually followed by either a single number or  a red-green-blue
color triple.   Each of the values in the color triple are normalized, with
zero indicating zero intensity, and one  indicating full intensity. If any
surface component is left unspecified, its value defaults to zero, with the
exception of the index of refraction, which is  assigned the default index
of refraction (normally 1.0).

Surface descriptions are used in rayshade to compute the color of a raythat
strikes the surface at a point evec{p }. The normal to  the surface at
evec{p },  evec{n }, is also computed.

ambient  evec{color }
 Use the given color to approximate those surface-surface  interactions
(e.g., diffuse interreflection) not modeled by the  raytracing process. A
surface's ambient color is always applied to a ray.  The color applied is
computed by multiplying the ambient color by the  intensity of the ambient
light source.

If  evec{p } is in shadow with respect to a given light source, that light
source makes no contribution to the shading of evec{p }.

diffuse  evec{color)
 Specifies the diffuse color The diffuse contribution from each non-shadowed
light source at evec{p } is equal to the diffuse color of the surface scaled
by the  cosine of the angle between evec{n } and the vector from evec{p } to
the light source.

specular  evec{color }
 Specifies the base color of specular reflections.

specpow  exponent
 Specifies the specular highlight exponent. The intensity of specular
highlights from light sources are scaled by the specular color of the
surface.

reflect  reflectivity
 Specifies the specular reflectivity of the surface.  If non-zero, reflected
rays will be spawned. The intensity of specularly reflected rays will be
proportional to the specular color of the surface scaled by the
reflectivity.

transp  transparency
 Specifies the specular transmissivity of the surface.  If non-zero,
transmitted (refracted) rays will be spawned.

body  evec{color }
 Specifies the body color of the object.  The body color affects the color
of rays that are transmitted through the object.

extinct  coefficient
 Specifies the extinction coefficient of the interior of the object.

The extinction coefficient is raised to a power equal to the distance the
transmitted ray travels through the object. The overall  intensity of
specularly transmitted rays will be proportional  to this factor multiplied
by the surface's body color multiplied by the  transparency of the object.

index  N
 Specifies the index of refraction.  The default value is equal to the index
of refraction of the atmosphere surrounding the eye.

translucency  translu  evec{color }  stexp
 Specifies the translucency, diffusely transmitted color, and Phong exponent
for transmitted specular highlights. If a light source illuminates a
translucent surface from the side opposite that from which a ray approaches,
illumination  computations are performed,   using the given color as the
surface's diffuse color, and the given exponent as the Phong highlight
exponent.  The resulting color is then scaled by the surface's translucency.



Atmospheric effects

Any number of atmospheric effects may also be associated with a surface.
These effects will be applied to those rays that are  transmitted through
the surface.  Applying atmospheric effects to opaque objects is a waste of
input file.

fog  evec{color }  evec{thinness }
 Add exponential fog with the specified  thinness and color. Fog is
simulated by blending the color of the fog with the color of each ray.  The
amount of fog color blended into a ray color is  an exponentialfunction of
the distance from the ray origin to the point of intersection    divided by
the specified thinness for each  color channel. If the distance is equal to
thinness, a ray's new color will be half ofthe fog color plus half its
original color.

mist  evec{color }  evec{thinness }  zero scale
 Add global low-altitude mist of the specified color.  The color of a ray is
modulated by a fog with density that varies linearly  with the difference in
z coordinate (altitude) between the ray origin and the point of
intersection.  The thinness values specify the  transmissivity of the fog
for each color channel. The base altitude of the mist is given by {em zero},
and the apparent heightof the mist can be modulated using {em scale}, which
scales the difference in altitude used to compute the fog.



default Medium

The default medium is the medium which surrounds and encompasses all of the
objects in the scene; it is the ``air'' through which  eye rays usually
travel before hitting an object.  The properties of the default medium may
be modified through the use of the   atmosphere  keyword.

atmosphere  N  atmospheric effects
If given, N specifies the index of refraction of the default medium.  The
default is 1.0.  Any atmospheric effects listed are applied  to rays that
are exterior to every object in the scene (e.g., rays emanating from the
camera).

\begin{verbatim }
    /*
     * Red sphere on a grey plane, with fog.
     */
    eyep 0. -10. 2.
    atmosphere fog  .8 .8 .8 14. 14. 14.
    plane 0 0 0  0 0 1
    sphere diffuse 0.8 0 0   1.5  0 0 1.5
\end{verbatim }


Specification

Rayshade provides a number of ways to define surfaces and to bind these
surfaces to objects.  The most straight-forward method  of surface
specification is to simply list the surface properties to be used.
Alternatively, one may associate a name with a given surface. This name may
subsequently be used to refer to that surface.

surface  name { Surface Definition}
 Associate the given collection of surface attributes with the given name.

The binding of a collection of surface properties to a given object is
accomplished in a bottom-up manner; the surface that  ``closest'' in the
modeling tree to the primitive being rendered is the one that is used to
give the primitive its appearance.

An object that has no surface bound to it is assigned a default surface that
give an object the appearance of white plastic.

The first and most direct way to bind a surface to a primitive is by
specifying the surface to be bound to the primitive when it is
instantiated. This is accomplished by inserting a list of surface attributes
or a surface name after the primitive's type keyword and  before the actual
primitive data.

\begin{verbatim }
    /*
     * A red 'mud' colored sphere reseting on a
     * white sphere. To the right is a sphere with
     * default surface attributes.
     */
   surface mud ambient .03 0. 0.  diffuse .7 .3 0.
    sphere  ambient .05 .05 .05 diffuse .7 .7 .7   1. 0 0 0
    sphere mud  1. 0 0 2
    sphere 1. 1.5 0 0
\end{verbatim }

Here, we define a red surface named ``mud''.  We then instantiate a sphere,
which has a diffuse white surface bound to it.  The  next line instantiates
a sphere with the defined ``mud'' surface bound to it.  The last line
instantiates a sphere with no surface  bound to it; it is assigned the
default surface by rayshade.

The applysurf keyword may be used to set the default surface characteristics
for the aggregate object currently being defined.

applysurf {surface Specification}
 The specified surface is applied to all following instantiated objects that
do not have surfaces associated with them. The scope of this keyword is
limited to the aggregate currently being defined.

\begin{verbatim }
    /*
     * Mirrored ball and cylinder sitting on 'default' plane.
     */
    surface mirror .01 .01 .01  diffuse .05 .05 .05
            specular .8 .8 .8 speccoef 20  reflect 0.95

    plane 0 0 0  0 0 1
    applysurf mirror
    sphere 1 0 0 0
    cylinder 1  3 0 0  3 0 3
\end{verbatim }

For convenience, the name cursurf may be used to refer to the current
default surface.

The utility of bottom-up binding of surfaces lies in the fact that one may
be as adamant or as noncommittal about surface binding  as one sees fit when
defining objects.  For example, one could define a king chess piece
consisting of triangles that have no  surface bound to them, save for the
cross on top, which has a gold-colored surface associated with it.  One may
then instantiate  the king twice, once applying a black surface, and once
applying a white surface.  The result:  a black king and a white king, each
adorned with a golden cross.

\begin{verbatim }
    surface white ...
    surface black ...
    surface gold  ...
    ...
    define cross
            box x y z  x y z
            ...
    defend
    define king
            triangle x y z  x y z  x y z
            ...
            object gold cross
    defend

    object white king translate 1. 0 0
    object black king
\end{verbatim }





Objects

Objects in rayshade are composed of relatively simple  primitive objects.
These primitives may be used by themselves, or they  may be combined to form
more complex objects known as aggregates. A special family of aggregate
objects,  Constructive Solid Geometry or CSG objects, are the result of a
boolean operations  applied to primitive, aggregate, or CSG objects.

This chapter describes objects from a strictly geometric point of view.
Later chapters on surfaces, textures, and shading describe  how object
appearances are defined.

An instance is an object that has optionally been transformed and textured.
They are the entities that are actually rendered by  rayshade; when you
specify that, for example, a textured sphere is to be rendered, you are said
to be instantiating the textured  sphere. An instance is specified as a
primitive, aggregate, or CSG object that is followed by optional
transformation and texturing  information. Transformations and textures are
described in Chapters 7 and 8 respectively.


World Object

Writing a rayshade input file is principally a matter of defining a special
aggregate object, the World object, which is a list of the  objects in the
scene.  When writing a rayshade input file, all objects that are
instantiated outside of object-definition blocks are  added to the World
object; you need not (not should you) define the World object explicitly in
the input file.


Primitives

Primitive objects are the building box with which other objects are created.
Each primitive type has associated with it specialized methods for creation,
intersection with a ray, bounding box calculation, surface normal
calculation, ray enter/exit classification,  and for the computation 2D
texture coordinates termed  u-v coordinates. This latter method is often
referred to as the inverse mapping method.

While most of these methods should be of little concern to you, the inverse
mapping methods will affect the way in which certain  textures are applied
to primitives. Inverse mapping is a matter of computing normalized u and v
coordinates for a given point on  the surface of the primitive.  For planar
objects, the u and v coordinates of a point are computed by linear
interpolation based  upon the u and v coordinates assigned to vertices or
other known points on the primitive.  For non-planar objects, uv computation
can be considerably more involved.

This section briefly describes each primitive and the syntax that should be
used to create an instance of the primitive. It also  describes the inverse
mapping method, if any, for each type.

blob  thresh  st  r  evec{p }  [st  r  evec{p }  ldots]
Defines a blob with consisting of a threshold equal to  thresh and a group
of one or ore metaballs.  Each  metaball is defined by its position
evec{p }, radius  r, and strength  st. For now, see the source code for more
explicit documentation. There is no inverse mapping method for blobs.

box  evec{corner1 }  evec{corner2 }
Creates an axis-aligned bo which has  evec{corner1 } and  evec{corner2 } as
opposite corners. Transformations may be applied to the box if a
non-axis-aligned instance is required.  There is no inverse mapping method
for  boxes.

sphere  radius  evec{center }
Creates a sphere with the given radius and centered at the given position.
Note that ellipsoids may be created by applying the proper scaling to a
sphere.  Inverse mapping on the sphere is accomplished  by computing the
longitude and latitude of the point on the sphere, with the u value
corresponding to longitude and v to latitude. On an untransformed sphere,
the z axis defines the poles, and the x axis intersects the sphere at u = 0,
v = 0.5.  There are  degeneracies at the poles: the south pole contains all
points of latitude 0., the north all points of latitude 1.

torus  rmajor  rminor  evec{center }  evec{up }
Creates a torus centered at evec{center } by rotating a circle with the
given minor radius around the center at a  distance equal to the major
radius.  In tori inverse mapping, the u value is computed using the angle of
rotation about the up vector, and the v value is computing the  angle of
rotation around the tube, with v=0 occuring on the innermost point of the
tube.

triangle  evec{p1 }  evec{p2 }  evec{p3 }
Creates a triangle with the given vertices.

triangle  evec{p1 }  evec{n1 }  evec{p2 }  evec{n2 }  evec{p3 }  evec{n3 }
Creates a Phong-shaded triangle with the given vertices and vertex normals.
For both Phong- and flat-shaded triangles, the u axis is the vector from
evec{p1 } to evec{p2 }, and the v axis the vector from  evec{p1 } to
evec{p3 }.  There is a degeneracy at evec{p3 }, which contains all points
with v = 1.0.  This default mapping may be  modified using the triangleuv
primitive described below.

triangleuv  evec{p1 } evec{n1 } evec{uv1} evec{p2 } evec{n2 } evec{uv2 } evec{p3 } evec{n3 } evec{uv3 }
Creates a Phong-shaded triangle with the given vertices, vertex normals.
When performing texturing, the uv  given for each vertex are used instead of
the default values. When computing uv coordinates within the interior of the
triangle, linear interpolation of the coordinates associated with each
triangle vertex is used.

poly  evec{p1 } evec{p2 } evec{p3 } [evec{p4 } ldots ]
Creates a polygon with the given vertices. The vertices should be given in
counter-clockwise order as one is  looking at the ``top'' side of the
polygon.  The number of vertices in a polygon is limited only by available
memory. Inverse mapping for arbitrary polygons is problematical. Rayshade
punts and equate u with the x coordinate of the point of  intersection, and
v with the y coordinate.

hf   file
Creates a height field defined by the altitude data stored in the named
file.  The height field is based upon  perturbations of the unit square in
the z=0 plane, and is rendered as a surface tessellated by right isosceles
triangles. See Appendix B for a discussion of the format of a height field
file. Height field inverse mapping is straight-forward:  u is the x
coordinate of the point of intersection, v the y coordinate.

plane  evec{point } evec{normal }
Creates a plane that passes through the given point and has the specified
normal. Inverse mapping on the plane is identical to polygonal inverse
mapping.

cylinder  radius evec{bottom } evec{top }
Creates a cylinder that extends from  evec{bottom } to  evec{top } and has
the indicated radius.  Cylinders are  rendered without endcaps. The
cylinder's axis defines the v axis.  The u axis wraps around the cylinder,
with u=0 dependent upon the orientation of the  cylinder.

cone  rad_{bottom }  evec{bottom }  rad_{top }  evec{top }
Creats a (truncated) cone that extends from evec{bottom } to evec{top }.
The cone will have a radius of  rad_{bottom } at evec{bottom } and a radius
of rad_{top } at  evec{top }. Cones are rendered without endcaps. Cone
inverse mapping is analogous to cylinder mapping.

disc radius  evec{pos }  evec{normal }
Creates a disc centered at the given position and with the indicated surface
normal. Discs are useful for placing endcaps on cylinders and cones. Inverse
mapping for the disc is based on the computation of the  normalized polar
coordinates of the point of intersection.  The normalized radius of the
point of intersection is assigned to u,  while the normalized angle from a
reference vector is assigned to v.


Objects

An aggregate is a collection of primitives, aggregate, and CSG objects.  An
aggregate, once defined, may be instantiated at will,  which means that
copies that are optionally transformed and textured may be made. If a scene
calls for the presence of many geometrically identical objects, only one
such object need be defined; the one defined  object may then be
instantiated many times.

An aggregate is one of several possible types.  These aggregate types are
differentiated by the type of ray/aggregate intersection  algorithm (often
termed an acceleration technique or efficiency scheme that is used.

Aggregates are defined by giving a keyword that defines the type of the
aggregate, followed by a series of object instantiations  and surface
definitions, and terminated using the end keyword. If a defined object
contains no instantiations, a warning message is printed.

The most basic type of aggregate, the list, performs intersection testing in
the simplest possible way:  Each object in the list is  tested for
intersection with the ray in turn, and the closest intersection is returned.

list  ldots  end
Create a List object containing those objects instantiated between the
list/end pair.

The grid aggregate divides the region of space it occupies into a number of
discrete box-shaped voxels.  Each of these voxels  contains a list of the
objects that intersect the voxel.  This discretization makes it possible to
restrict the objects tested for  intersection to those that are likely to
hit the ray, and to test the objects in nearly ``closest-first'' order.

grid  xvox  yvox  zvox  ldots  end
Create a Grid objects composed of  xvox by  yvox by zvox voxels containing
those objects instantiated between  the grid/end pair.

It is usually only worthwhile to ``engrid'' rather large, complex
collections of objects.  Grids also use a great deal more memory  than List
objects.


Solid Geometry

Constructive Solid Geometry is the process of building solid objects from
other solids. The three CSG operators are Union,  Intersection, and
Difference.  Each operator acts upon two objects and produces a single
object result. By combining multiple  levels of CSG operators, complex
objects can be produced from simple primitives.

The union of two objects results in an object that encloses the space
occupied by the two given objects. Intersection results in an  object that
encloses the space where the two given objects overlap.  Difference is an
order dependent operator; it results in the  first given object minus the
space where the second intersected the first.

In Rayshade:

CSG in rayshade will generally operate properly when applied to conjunction
with on boxes, spheres, tori, and blobs. These  primitives are by nature
consistent, as they all enclose a portion of space (no hole from the
"inside" to the "outside"), have surface  normals which point outward (they
are not "inside-out"), and do not have any extraneous surfaces.

CSG objects may also be constructed from aggregate objects. These aggregates
contain whatever is listed inside, and may  therefore be inconsistent. For
example, an object which contains a single triangle will not produce correct
results in CSG models,  because the triangle does not enclose space.
However, a collection of four triangles which form a pyramid does enclose
space,  and if the triangle normals are oriented correctly, the CSG
operators should work correctly on the pyramid.

CSG objects are specified by surrounding the objects upon which to operate,
as well as any associated surface-binding  commands, by the operator verb on
one side and the end keyword on the other:

union  object  Object  Object  ldots  end
Specify a new object defined as the union of the given objects.

difference  object  Object  Object  ldots  end
Specify a new object defined as the difference of the given objects.

intersect  object  Object  Object  ldots  end
Specify a new object defined as the intersection of the given objects.

Note that the current implementation does not support more that two objects
in a CSG list (but it is planned for a future version).

* The following aren simple CSG objects using the four consistent
* primitives:
*
* union box ... difference ...

csg Problems:

A consistent CSG model is one which is made up of solid objects with no
dangling surfaces.  In rayshade, it is quite easy to  construct inconsistent
models, which will usually appear incorrect in the final images. In
rayshade, CSG is implemented by maintaining the tree structure of the CSG
operations.  This tree is traversed, and the  operators therein applied, on
a per-ray basis. It is therefore difficult to verify the consistency of the
model ``on the fly.'' One class of CSG problems occur when surfaces of
objects being operated upon coincide.  For example, when subtracting a box
from another box to make a square cup, the result will be wrong if the tops
of the two boxes coincide.  To correct this, the inner  box should be made
slightly taller than the outer box. A related problem that must be avoided
occurs when two coincident  surfaces are assigned different surface
properties.

It may seem that the union operator is unnecessary, since listing two
objects together in an aggregate results in an image that  appears to be the
same. While the result of such a short-cut may appear the same on the
exterior, the interior of the resulting  object will contain extraneous
surfaces. The following examples show this quite clearly.

\begin{verbatim }
    difference
      box -2 0 -3  2 3 3
      union  /* change to list; note bad internal surfaces */
        sphere 2 1 0 0
        sphere 2 -1 0 0
      end
    end rotate 1 0 0 -40  rotate 0 0 1 50
\end{verbatim }

The visual evidence of an inconsistent CSG object varies depending upon the
operator being used. When subtracting a consistent  object from and
inconsistent one, the resulting object will appear to be the union of the
two objects, but the shading will be  incorrect. It will appear to be
inside-out in places, while correct in other places.  The inside-out
sections indicate the areas where  the problems occur. Such problems are
often caused by polygons with incorrectly specified normals, or by surfaces
that exactly coincide (which  appear as partial ``swissh-cheese'' objects).

The following example illustrates an attempt to subtract a sphere from a
pyramid defined using an incorrectly facing triangle.   Note that the
resulting image obviously points to which triangle is reversed.

\begin{verbatim }
    name pyramid list
        triangle 1 0 0  0 1 0  0 0 1
        triangle 1 0 0  0 0 0  0 1 0
        triangle 0 1 0  0 0 0  0 0 1
        triangle 0 0 1  1 0 0  0 0 0  /* wrong order */
    end

    difference
        object pyramid scale 3 3 3 rotate 0 0 1 45
            rotate 1 0 0 -30 translate 0 -3.5 0
        sphere 2.4 0 0 0
    end
\end{verbatim }

By default, cylinders and cones do not have end caps, and thus are not
consistent primitives.  One must usually add endcaps by  listing the
cylinder or cone with (correctly-oriented) endcap discs in an aggregate.


Objects

A name may be associated with any primitive, aggregate, or CSG object
through the use of the name keyword:

name  objname Instance
Associate objname with the given object.  The specified object is not
actually instantiated; it is only stored  under the given name.

An object thus named may then be instantiated (with possible additional
transforming and texturing) via the object keyword:

object  objname Transformations Textures
Instantiate a copy of the object associated with objname. If given, the
transformations and textures are  composed with any already associated with
the object being instantiated. Texturing

Textures are used to modify the appearance of an object through the use of
procedural functions. A texture may modify any  surface characteristic,such
as diffuse color, reflectivity, or transparency, or it may  modify the
surface normal (``bump mapping'')  in order to give the appearance of a
rough surface.

Any number of textures may be associated with an object.  If more than one
texture is specified, they are applied in the order  given.  This allowsone
to compose texturing functions and create, for example a tiled marble ground
plane using the checker and  marble textures.

Textures are associated with objects by following the object specification
bya number of lines of the form:

texture  name  Texturing Arguments  Transformations

Transformations may be applied to the texture in order to, for example,
shrink or grow feature size, change the orientation of  features, and change
the position of features.

Several of the texturing functions take the name of a colormap as an
argument. A colormap is 256-line ASCII file, with each line  containing
three space-separated values ranging from 0 to 255. Each line gives the red,
green, and blue values for a single entry  in the colormap.


Functions

blotch  BlendFactor  surface
Produces a mildly interesting blotchy-looking surface. BlendFactor is used
to control the interpolation between the default  surface characteristics
and the characteristics of the given surface.  A value of 0 results in a
roughly 50-50 mix of the two  surfaces.  Higher values result in a great
portion of the default surface characteristics.

bump  scale
Apply a random bump map.  The point of intersection is passed to DNoise().
The returned normalized vector is weighted by   scale and the result is
added to the normal vector at the point of intersection

checker surface
Applies a 3D checkerboard texture.  Every point that falls within an
``even'' unit cube will be assigned the characteristics of the  named
surface applied to it, while points that fall within ``odd'' cubes will have
its usual surface characteristics.  Be wary of  strange effects due to
roundoff error that occur when a planar checkered surface lies in a plane of
constant integral value (e.g.,  z=0) in texture space. In such cases, simply
translate the texture to ensure that the planar surface is not coincident
with an integral plane in texture space (e.g., translate 0 0 0.1).

cloud  scale H  lambda octaves cthresh lthresh tscale
This texture is a variant on Geoff Gardner's ellipsoid-texturing algorithm.
It should be applied to unit spheres centered at the  origin. Thesespheres
may, of course, be transformed at will to form the appropriately-shaped
cloud or tree.

A sample of normalized  fBm (see the fbm texture) is generated at the point
of intersection.  This sample is used to modulate the  surface transparency.
The final transparency if a function of the sample value,  the proximity of
the point of intersection to the  edge of the sphere (as seen from the ray
origin), and three parameters to control the overall  ``density.'' The
proximity of the point to the sphere edge is determined by  evaluating a
limb function, which varies from 0 on the  limb to 1 at the center of the
sphere.

transp = 1. - \frac{- cthresh - (lthresh - cthresh)(1 - limb)}{tscale }

fbm  offset scale H lambda octaves thresh colormap
Generate a sample of discretized fractional Brownian motion (fBm) and uses
it to scale the diffuse and ambient component of an  object's surface.

-Scale is used to scale the value returne the fBm function.
-Offset allows one to control  minimum value of the fBm function.
-H is the {m Holder exponent} used in the fBm function (a value of 0.5 works
well). $\lambda$ is used to control  lacunarity,   and specifies  the
frequency difference between successive samples of the fBm basis function (a
value of 2.0 will suffice).    -Octaves specifies the numberof octaves
(samples) to take of the fBm basis function (in this case, Noise()). Between
five and  seven octaves usually works well. {em Thresh} is used to specify a
lower bound onthe output of the fBm function. Any value  lower than thresh
is set to zero. If a colormap is named, a 256-entry colormap is read from
the named file, and the sample of fBm is scaled by 255 and is used as  an
index into thecolormap. The resulting colormap entry is used to scale the
ambient and diffuse components of the object's  surface.

fbmbump  offset  scale  H  lambda  octaves
Similar to the  fbm texture. Rather than modifying the color of a surface,
this texture acts as a bump map.

gloss  glossiness
Gives reflective surfaces a glossy appearance. This texture erturbs the
object's surace normal such that the normal ``samples'' a  cone of unit
height with radius 1. - glossiness.  A value of 1 results in perfect
mirror-like reflections, while a value of 0 results in  extremely fuzzy
reflections.  For best results, jittered sampling should be used to render
scenes that make use of this texture.

marble  colormap
Gives a surface a marble-like appearance. The texture is implemented as
roughly parallel alternating veins of marble, each of  which is separated by
1/7 of a unit and runs perpendicular to the Z axis. If a colormap is named,
the surface's ambient and diffuse  colors will be scaled using the RGB
values in the colormap. If no colormap is given, the diffuse and ambient
components are  simply scaled by the value of the marble function. One may
transform the texture to control the density and orientation of the  marble
veins.

sky  scale  H  lambda  octaves  cthresh  ltresh
Similar to the  fbm texture. Rather than modifying the color of a surface,
this texture modulates its transparency. cthresh is the  value of the fBm
function above which the surface is totally opaque. Below lthresh, the
surface is totally transparent.

stripe  surface  size  bump Mapping
Apply a ``raised'' stripe pattern to the surface. The surface properties
used to color the stripe are those of the given surface. The  width of the
stripe, as compared to the unit interval, is given by  size. The magnitude
of bump controls the extent to which the  bump appears to be displaced from
the rest of the surface. If negative, the stripe will appear to sink into
the surface; if negative, it  will appear to stand out of the surface.

Mapping functions are described below.

wood
Gives a surface a wood-like appearance. The feature size of this texture is
approximately 0.01 of a unit, making it often necessary  to scale the
texture in order to achieve the desired appearance.


Texturing

Rayshade also supports an  image texture.  This texture allows you to use
images to modify the characteristics of a surface. You  can use
three-channel images to modify the any or all of the ambient, diffuse, and
specular colors of a surface.

If you are using the Utah Raster Toolkit, you can also use single-channel
images to modify surface reflectance, transparency, and  the specular
exponent. You can also use a single-channel image to apply a bump map to a
surface.

In all but the bump-mapping case, a component is modified by multiplying the
given value by the value computed by the  texturing function. When using the
Utah Raster Toolkit, surface characteristics are modified in proportion to
the value of the   alpha channel in the image. If there is no {em
alpha}channel, or you are not using the Utah Raster Toolkit,  alpha is
assumed to  be everywhere equal to 1.

component  component
The named component will be modified.

Possible surface components are:

ambient   (modify ambient color),
diffuse     (modify diffuse color),
specular  (modify specular color),
specpow  (modify specular exponent),
reflect     (modify reflectivity),
transp     (modify transparency),
bump      (modify surface normal).

The specpow,  reflect,  transp, and  bump components require the use of a
single-channel image. range  high low Specify the range of values to which
the values in the image should be mapped.  An value of 1 will be mapped
high, 0 to  low.   Intermediate values will be linearly interpolated.

smooth
When given, pixel averaging will be performed in order to smooth the sampled
image.  If not specified, no averaging will occur.

textsurf  surface Specification
For use when modifying surface colors, this keyword specifies that the given
surface should be used as the base to be modified  when the alpha value in
the image is non-zero.  When alpha is zero, the object's unmodified default
surface characteristics are  retained.

The usual behavior is for the object's default surface properties to be used.

tile  un vn
Specify how the image should be tiled (repeated) along the u and v axes. If
positive, the value of un gives the number of times the  image should be
repeated along the u axis, starting from the origin of the texture, and
positive vn gives the number of times it  should be repeated along the v
axis. If either valueis zero, the image is repeated infinitely along the
appropriate axis.

Tiling is usually only a concern when linear mapping is being used, though
it may also be used if image textures are being scaled.  By default em un
and em vn are both zero.

 A mapping function may also be associated with an image texture.


Functions

Mapping functions are used to apply two-dimensional textures to surfaces.
Each mapping functions defines a different method of  transforminga three
dimensional point of intersection to a two dimensional u-v pair termed
texturing coordinates. Typically, the arguments to a mapping method define a
center of a projection and two non-parallel axes that define a local
coordinate system.

The default mapping method is termed u-v mapping or inverse mapping.
Normally, there is a different inverse mapping method  for each primitive
type (see chapter 5).

When inverse mapping is used, the point of intersection is passed to the uv
method for the primitive that was hit.

map  uv
Use the uv (inverse mapping) method associated with the object that was
intersected in order to map from 3D to determine  texturing coordinates.

The inverse mapping method for each primitive is described in Chapter 5.

map  linear  evec{origin }  evec{vaxis }  evec{uaxis }
Use a linear mapping method. The 2D texture is transformed so that its u
axis is given by evec{uaxis } and its v axis by vaxis. The  texture is
projected along the vector defined by the cross product of the u and v axes,
with the (0,0) in texture space mapped to  evec{origin }.

map  cylindrical  evec{origin }  evec{vaxis }  evec{uaxis }
Use a cylindrical mapping method.  The point of intersectionis projected
onto an imaginary cylinder, and the location of the  projected point is used
to determine the texture coordinates. If given, evec{origin } and evec{vaxis
} define the cylinder's axis,  and evec{uaxis } defines where u=0 is
located. See the description of the inverse mapping method for the cylinder
in Chapter 5.  By default, the point of intersection is projected  onto a
cylinder that runs through the origin along the z axis, with evec{uaxis }
equal to the x axis.

map  spherical  evec{origin }  evec{vaxis }  evec{uaxis }
Use a spherical mapping method.  The intersection point is projected onto an
imaginary sphere, and the location of the projected  point is used to
determine the texturing coordinates in a manner identical to that used in
the inverse mapping method for the  sphere primitive. If given, the center
of the projection is evec{origin }, evec{vaxis } defines the sphere axis,
and the point where the non-parallel  evec{uaxis } intersects the sphere
defines where u=0 is located. By default, a spherical mapping projects
points towards the origin, with evec{vaxis } defined to be the z axis and
evec{uaxis }  defined to be the x axis.


Sources

The lighting in a scene is determined by the number, type, and nature of the
light sources defined in the input file.  Available light  sources range
from simple directional sources to more realistic but computationally costly
quadrilateral area light sources.   Typically, you will want to use point or
directional light sources while developing images.  When final renderings
are made,  these simple light sources may be replaced by the more complex
ones.

No matter what kind of light source you use, you will need to specify its
intensity. In this chapter, an Intensity is either a red- green-blue triple
indicating the color of the light source, or a single value that is
interpreted as the intensity of a ``white'' light. In the current version of
rayshade, the intensity of a light does not decrease as one moves farther
from it.

If you do not define a light source, rayshade will create a directional
light source of intensity 1.0 defined by the vector (1., -1.,  1.). This
default light source is designed to work well when default viewing
parameters and surface values are being used.

You may define any number of light sources, but keep in mind that it will
require more time to render images that include many  light sources.  It
should also be noted that the light sources themselves will not appear in
the image, even if they are placed in  frame.


Source Types

The amount of ambient light present in a scene is controlled by a pseudo
light source of type ambient.

light  Intensity  ambient
Define the amount of ambient light present in the entire scene.

There is only one ambient light source; its default intensity is {1 , 1, 1}.
If more than one ambient light source is defined, only  the last instance is
used.  A surface's ambient color is multiplied by the intensity of the
ambient source to give the total ambient  light reflected from the surface.

Directional sources are described by a direction alone, and are useful for
modeling light sources that are effectively infinitely far  away from the
objects they illuminate.

light  Intensity  directional  evec{direction }
Define a light source with the given intensity that is defined to be in the
given direction from every point it illuminates.  The  direction need not be
normalized.

Point sources are defined as a single point in space.  They produce shadows
with sharp edges and are a good replacement for  extended and other
computationally expensive light source.

light  Intensity  point  evec{pos }
Place a point light source with the given intensity at the given position.

Spotlights are useful for creating dramatic localized lighting effects. They
are defined by their position, the direction in which  they are pointing,
and the width of the beam of light they produce.

light  Intensity  spot evec{pos }  evec{to }  alpha  theta_{in }  theta_{out }
Place a spotlight at evec{pos }, oriented as to be pointing at evec{to }.
The intensity of the light falls off as (cosine theta)^{alpha  }, where
theta is the angle between the spotlight's main axis and the vector from the
spotlight to the point being illuminated.   theta_{in } and  theta_{out }
may be used to control the radius of the cone of light produced by the
spotlight. theta_{in } is the the angle at which the light source begins to
be attenuated.  At theta_{out }, the spotlight intensity is zero. This
affords control over how ``fuzzy'' the edges of the spotlight are.  If
neither angle is given, they both are effectively set to 180  degrees.

Extended sources are meant to model spherical light sources.  Unlike point
sources, extended sources actually possess a radius,  and as such are
capable or producing shadows with fuzzy edges (penumbrae).  If you do not
specifically desire penumbrae in  your image, use a point source instead.

light  Intensity  extended  radius  evec{pos }
Create an extended light source at the given position and with the given
radius. The shadows cast by extended sources are modeled by taking samples
of the source at different locations on its surface.  When  the source is
partially hidden from a given point in space, that point is in partial
shadow with respect to the extended source, and  the sampling process is
usually able to determine this fact.

Quadrilateral light sources are computationally more expensive than extended
light sources, but are more flexible and produce  more realistic results.
This is due to the fact that an area source is approximated by a number of
point sources whose positions are jittered to reduce  aliasing. Because each
of these point sources has shading calculations performed individually, area
sources may be placed  relatively close to the objects it illuminates, and a
reasonable image will result.

light  Intensity  area  evec{p1 }  evec{p2 }  usamp  evec{p3 }  vsamp
Create a quadrilateral area light source. The u axis is defined by the
vector from  evec{p1 } to evec{p2 }.  Along this axis a total  of usamp
samples will be taken. The v axis of the light source is defined by the
vector from evec{p1 } to evec{p3 }.  Along this  axis a total of vsamp
samples will be taken.

The values of usamp and vsamp are usually chosen to be proportional to the
lengths of the u and v axes.  Choosing a relatively  high number of samples
will result in a good approximation to a ``real'' quadrilateral source.
However, because complete  lighting calculations are performed for each
sample, the computational cost is directly proportional to the product of
usamp and  vsamp.


Shadows

In order to determine the color of a point on the surface of any object, it
is necessary to determine if that point is in shadow with  respect to each
defined light source.  If the point is totally in shadow with respect to a
light source, then the light source makes no  contribution to the point's
final color.

This shadowing determination is made by tracing rays from the point of
intersection to each light source.  These ``shadow feeler''  rays can add
substantially to the overall rendering time.  This is especially true if
extended or area light sources are used.  If at  any point you wish to
disable shadow determination on a global scale, there is a command-line
option -n that allows you to do so.   It is also possible to disable the
casting of shadows onto given objects through the use of the noshadow
keyword in surface  descriptions.  In addition, the noshadow keyword may be
given following the definition of a light source, causing the light source
to cast no shadows onto any surface.

Determining if a point is in shadow with respect to a light source is
relatively simple if all the objects in a scene are opaque.  In  this case,
one simply traces a ray from the point to the light source. If the ray hits
an object before it reaches the light source, then the point is in shadow.

Shadow determination becomes more complicated if there are one or more
objects with non-zero transparency between the point  and the light source.
Transparent objects may not completely block the light from a source, but
merely attenuate it. In such cases,  it is necessary to compute the amount
of attenuation at each intersection and to continue the shadow ray until it
either reaches the  light source or until the light is completely
attenuated.

By default, rayshade computes shadow attenuation by assuming that the index
of refraction of the transparent object is the same  as that of the medium
through which the ray is traveling. To disable partial shadowing due to
transparent objects, the   shadowtransp keyword should be given somewhere in
the input file.

shadowtransp
The intensity of light striking a point is  not affected by intervening
transparent objects.

If you enclose an object behind a transparent surface, and you wish the
inner object to be illuminated, you must not use the   shadowtransp keyword
or the  -o option.


Transformations

Rayshade supports the application of linear transformations to objects and
textures. If more than one transformation is specified,  the total resulting
transformation is computed and applied.

translate  evec{delta }
Translate (move) by delta.

rotate  evec{axis }  theta
Rotate counter-clockwise about the given axis by theta degrees.

scale  evec{v }
Scale by v.
All three scaling components must be non-zero, else degenerate matrices will
result.

transform  evec{row1 }  evec{row2 }  evec{row3 }  [ evec{delta ]
Apply the given 3-by-3 transformation matrix.  If given,  delta specifies a
translation vector.

Transformations should be specified in the order in which they are to be
applied immediately following the item to be  transformed.  For example:

\begin{verbatim }
        /*
         * Ellipsoid, rotated cube
         */
        sphere 1. 0 0 0   scale 2. 1. 1. translate 0 0 -2.5
        box 0 0 0 .5 .5 .5
           rotate 0 0 1 45 rotate 1 0 0 45 translate 0 0 2.5
\end{verbatim }

Transformations may also be applied to textures:

\begin{verbatim }
   plane 0 0 -4  0 0 1
     texture checker red scale 2 2 2 rotate 0 0 1 45
\end{verbatim }

Note that transformation parameters may be specified using of animated
expressions, causing the transformations themselves to  be animated. See
Appendix B for further details.


Field Files

This appendix describes the format of the files that store data for the
height field primitive. The format is an historical relic; a  better format
is needed.

Height field data is stored in binary form. The first record in the file is
a 32-bit integer giving the square root of number of data  points in the
file. We'll call this number the size of the height field.

The size is followed by altitude ('z') values stored as 32-bit floating
pointvalues. The 0th value in the file specifies the 'z'  coordinate of the
lower-left corner of the height field (0, 0). The next specifies the Z
coordinate for '(1/(size-1), 0)'. The last  specifiesthe coordinate for
'(1., 1.)'. In other words, the 'i^{th }' value in the heightfield file
specifies the 'z' coordinate for the  point whose 'x' coordinate is '(i \%
size) / (size -1)', and whose 'y' coordinate is '(i / size) / (size -1)'.
Non-square height fields may be rendered by specifying altitude values less
than or equal to the magic value '-1000'. Triangles  that have any vertex
lessthan or equal in altitude to this value are not rendered.

While this file format is compact, it sacrifices portability for ease of
use. While creating and handling height field files is simple,  transporting
a height field from one machine to another is problematical due to the fact
that differences in byte order and floating- point format between machines
is not taken into account.

These problems could be circumvented by writing the height field file in a
fixed-point format, taking care to write the bytes that  encode a given
value in a consistent way from machine to machine. An even better idea would
be to write a set of tools for  manipulating arbitrary 2D arrays of
floating-point values in a compact, portable way, allowing for comments and
the like in the  file\ldots








Animation

Rayshade provides basic animation animation support by allowing time-varying
transformations to be associated with primitives  and aggregate objects.
Commands are provided for controlling the amount of time between each frame,
the speed of the camera  shutter, and the total number of frames to be
rendered.

By default, rayshade renders a single frame, with the shutter open for an
instant (0 units of time, in fact).  The shutter speed in no  way changes
the light-gathering properties of the camera, i.e. frames rendered using a
longer exposure will not appear brighter  than those with a shorter
exposure.  The only change will be in the potential amount of movement that
the frame ``sees'' during  the time that the shutter is open.

Each ray cast by \rayshade samples a particular moment in time. The time
value assigned to a ray ranges from the starting time of  the current frame
to the starting time plus the amount of time the shutter is open.  When a
ray encounters an object or texture that  possesses an animated
transformation, the transformed entity is moved into whatever position is
appropriate for the ray's current  time value before intersection, shading,
or texturing computations are performed.

The starting time of the current frame is computed using the length of each
frame the current frame number, and the starting time  of the first frame.

shutter  t
Specifies that the shutter is open for t units of time for each exposure. A
larger value of  t will lead to more motion blur in the final image.   Note
that t may be greater than the actual length of a frame.   By default, t is
zero, which prevents all motion blur.

framelength   frameinc
Specifies the time increment between frames.
The default time between frames is 1 unit.

starttime  time
Specifies the starting time of the first frame.
By default,  time is zero.

Variables may be defined thorugh the use of the define keyword:

define  name  value
Associate  name with the given  value.  Value may be a constant or a
parenthesized expression. The variable name may thereafter be used in
expressions in the input file.

An animated transformation is one for which animated expressions have been
used to define one or more of its parameters (e.g.  the angle through which
a rotation occurs).  An animated expression is one that makes use of a
time-varying (``animated'')  variable or function.

There are two supported animated variables. The first, time, is equal to the
current time. When a ray encounters an animated  transformation defined
using an expression containing  time, the ray substitutes its time value
into the expression before  evaluation. Using the  time variable in an
animated expression is the most basic way to create blur-causing motion.

The second animated variable,  frame, is equal to the current frame number.
Unlike the  time variable,  frame takes on a single  value for the duration
of each frame.  Thus, transforms animated through the use of the  frame
variable will not exhibit motion  blurring.

Also supported is the linear function.  This function uses time implicitly
to interplate between two values.

linear  Stime, Sval, Etime, Eval
Linearly interpolate between Sval at time Stime and Eval at time Etime. If
the current time is less than Stime, the function returns  Sval.  If the
current time is greater than Etime,  Eval is returned.

The following example shows the use of the time variable to animate a sphere
by translating it downwards over five frames. Note  thet the shutter keyword
is used to set the shutter duration in order to induce motion blurring.

\begin{verbatim }
    frames 5
    shutter 1
    sphere 1 0 0 2 translate 0 0 (-time)
\end{verbatim }