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<a name="transform"></a>
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<h4 class="subsection">4.3.3 Transform Objects</h4>
<p>Where a single 4x4 matrix is expected – as in the <code>INST</code>
<code>transform</code> field, the camera's <code>camtoworld</code> transform and the
Geomview <code>xform*</code> commands – use a transform object.
<p>Note that a transform is distinct from a <code>TLIST</code>, which is a type
of geometry. <code>TLIST</code>s can contain one or more 4x4 transformations;
"transform" objects must have exactly one.
<p>Why have both? In many places – e.g. camera positioning – it's only
meaningful to have a single transform. Using a separate object type
enforces this.
<p>Syntax for a transform object is
<pre class="example"> <transform> ::=
[ "{" ] (curly brace, generally needed to make
the end of the object unambiguous.)
[ "transform" ] (optional keyword; unnecessary if the type
is determined by the context, which it
usually is.)
[ "define" <name> ]
(defines a transform named <name>, setting
its value from the stuff which follows)
<sixteen floating-point numbers>
(interpreted as a 4x4 homogeneous transform
given row by row, intended to apply to a
row vector multiplied on its LEFT, so that e.g.
Euclidean translations appear in the bottom row)
|
"<" <filename> (meaning: read transform from that file)
|
":" <name> (meaning: use variable <name>,
defined elsewhere; if undefined the initial
value is the identity transform)
[ "}" ] (matching curly brace)
</pre>
<p>The whole should be enclosed in { braces }. Braces are not essential
if exactly one of the above items is present, so e.g. a 4x4 array of
floats standing alone may but needn't have braces.
<p>Some examples, in contexts where they might be used:
<pre class="example"> # Example 1: A GCL command to define a transform
# called "fred"
(read transform { transform define fred
1 0 0 0
0 1 0 0
0 0 1 0
-3 0 1 1
}
)
</pre>
<pre class="example"> # Example 2: A camera object using transform
# "fred" for camera positioning
# Given the definition above, this puts the camera at
# (-3, 0, 1), looking toward -Z.
{ camera
halfyfield 1
aspect 1.33
camtoworld { : fred }
}
</pre>
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<h4 class="subsection">7.2.125 transform</h4>
<p><a name="index-transform-133"></a>
<dl>
<dt><code>(transform objectID centerID frameID [rotate|translate|translate-scaled|scale] x y z [bbox-center|origin] [dt [smooth]])</code><dd>Apply a motion (rotation, translation, scaling) to object <code>objectID</code>;
that is, construct and concatenate a transformation matrix with
objectID's transform The 3 IDs involved are the object
that moves, the center of motion, and the frame of reference
in which to apply the motion. The center is easiest understood
for rotations: if centerID is the same as objectID then it will
spin around its own axes; otherwise the moving object will orbit
the center object. Normally frameID, in whose coordinate system
the (mouse) motions are interpreted, is <code>focus</code>, the current camera.
Translations can be scaled proportional to the
distance between the target and the center. Support for
spherical and hyperbolic as well as Euclidean space is
built-in: use the <code>space</code> command to change spaces. With type
<code>rotate</code> x, y, and z are floats specifying angles in RADIANS.
For types <code>translate</code> and <code>translate-scaled</code> x, y, and z are
floats specifying distances in the coordinate system of the
center object.
<p>The next field is optional and may consist of the keyword
<code>bbox-center</code> or the keyword <code>origin</code> and modifies the
location of the origin of <var>objectID</var>'s co-ordinate frame:
<code>bbox-center</code> temporarily translates <var>objectID</var>'s co-ordinate
frame to the center of <var>objectID</var>'s bounding box. <code>origin</code> is
the default (and means not to modify <var>objectID</var>'s co-ordinate frame)
and <code>bbox-center</code> is only valid in Euclidean space.
<p>The optional <code>dt</code> field allows a simple form of
animation; if present, the object moves by just that amount during
approximately <code>dt</code> seconds, then stops. If present and followed by
the <code>smooth</code> keyword, the motion is animated with a 3t^2-2t^3
function, so as to start and stop smoothly. If absent, the motion is
applied immediately.
</dl>
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