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4.3.3 Transform Objects

Where a single 4x4 matrix is expected – as in the INST transform field, the camera's camtoworld transform and the Geomview xform* commands – use a transform object.

Note that a transform is distinct from a TLIST, which is a type of geometry. TLISTs can contain one or more 4x4 transformations; "transform" objects must have exactly one.

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.

Syntax for a transform object is

     <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)

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.

Some examples, in contexts where they might be used:

     # 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
     # 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 }

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7.2.125 transform

(transform objectID centerID frameID [rotate|translate|translate-scaled|scale] x y z [bbox-center|origin] [dt [smooth]])
Apply a motion (rotation, translation, scaling) to object objectID; 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 focus, 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 space command to change spaces. With type rotate x, y, and z are floats specifying angles in RADIANS. For types translate and translate-scaled x, y, and z are floats specifying distances in the coordinate system of the center object.

The next field is optional and may consist of the keyword bbox-center or the keyword origin and modifies the location of the origin of objectID's co-ordinate frame: bbox-center temporarily translates objectID's co-ordinate frame to the center of objectID's bounding box. origin is the default (and means not to modify objectID's co-ordinate frame) and bbox-center is only valid in Euclidean space.

The optional dt field allows a simple form of animation; if present, the object moves by just that amount during approximately dt seconds, then stops. If present and followed by the smooth 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.