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<H1><A ID="SECTION00100000000000000000"> Transformations</A> </H1>

<P> 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.

<P> <BR> <IMG STYLE="height: 196.25ex; vertical-align: -0.70ex; " SRC="img1.png" ALT="
\begin{defkey}{translate}{\evec{delta}}
Translate (move) by {\em delta}.
\end{defkey}
"> <BR>

<P> <BR> <IMG STYLE="height: 2.38ex; vertical-align: 176.40ex; " SRC="img2.png" ALT="
\begin{defkey}{rotate}{\evec{axis} $\theta$}
Rotate counter-clockwise about the given axis by $\theta$\ degrees.
\end{defkey}
"> <BR>

<P> <BR> <IMG STYLE="height: 2.17ex; vertical-align: 176.68ex; " SRC="img3.png" ALT="
\begin{defkey}{scale}{\evec{v}}
Scale by {\em v}.
\end{defkey}
"> <BR> All three scaling components must be non-zero, else degenerate matrices will result.

<P> <BR> <IMG STYLE="height: 2.17ex; vertical-align: 176.55ex; " SRC="img4.png" ALT="
\begin{defkey}{transform}{\evec{row1} \evec{row2} \evec{row3} [\evec{delta}]}
A....
.....ion matrix. If given, {\em delta}
specifies a translation vector.
\end{defkey}
"> <BR>

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

<P> <PRE> /* * 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 </PRE>

<P> Transformations may also be applied to textures:

<P> <PRE> plane 0 0 -4 0 0 1 texture checker red scale 2 2 2 rotate 0 0 1 45 </PRE>

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

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