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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 objeto.

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

Why have both? In many places – e.g. câmera positioning – it's only meaningful to have a single transform. Using a separate objeto type enforces this.

Syntax for a transform objeto is

         <transform> ::=
           [ "{" ]             (curly brace, generally needed to make
                                the end of the objeto 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 objeto 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 movimento (rotation, translation, scaling) to objeto `objectID`; that is, construct and concatenate a transformation matrix with objectID's transform The 3 IDs involved are the objeto that moves, the center of movimento, and the frame of reference in which to apply the movimento. 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 objeto will orbit the objeto do centro. Normally frameID, in whose coordinate system the (mouse) movimentos 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 objeto do centro.

  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 objeto moves by just that amount during approximately `dt` seconds, then stops. If present and followed by the `smooth` keyword, the movimento is animated with a 3t^2-2t^3 function, so as to start and stop smoothly. If absent, the movimento is applied immediately.