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<H1><A ID="SECTION00130000000000000000"> Mapping Functions</A> </H1>

<P> Mapping functions are used to apply two-dimensional textures to surfaces. Each mapping functions defines a different method of transforming a three dimensional point of intersection to a two dimensional <I>u</I> - <I>v</I> 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.

<P> The default mapping method is termed <I>u</I> - <I>v</I> mapping or <EM>inverse mapping</EM>. 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 <I>uv</I> method for the primitive that was hit.

<P> <BR> <IMG STYLE="height: 2.38ex; vertical-align: 176.27ex; " SRC="img17.png" ALT="
\begin{defkey}{map}{{\tt uv}}
Use the $uv$\ (inverse mapping) method associate...
...cted in order to map from 3D to determine
texturing coordinates.
\end{defkey}
"> <BR> The inverse mapping method for each primitive is described in Chapter 5.

<P> <BR> <IMG STYLE="height: 2.38ex; vertical-align: 176.27ex; " SRC="img18.png" ALT="
\begin{defkey}{map}{{\tt planar} [\evec{origin} \evec{vaxis} \evec{uaxis}]}
Us...
...\ axes, with
the (0,0) in texture space mapped to \evec{origin}.
\end{defkey}
"> <BR>

<P> <BR> <IMG STYLE="height: 2.38ex; vertical-align: 176.27ex; " SRC="img19.png" ALT="
\begin{defkey}{map}{{\tt cylindrical} [\evec{origin} \evec{vaxis} \evec{uaxis}]}...
......linder's axis, and \evec{uaxis} defines
where $u=0$\ is located.
\end{defkey}
"> <BR> 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 <I>z</I> axis, with uaxis equal to the <I>x</I> axis.

<P> <BR> <IMG STYLE="height: 2.38ex; vertical-align: 176.27ex; " SRC="img20.png" ALT="
\begin{defkey}{map}{{\tt spherical} [\evec{origin} \evec{vaxis} \evec{uaxis}]}
...
...ec{uaxis} intersects the sphere
defines where $u=0$\ is located.
\end{defkey}
"> <BR> By default, a spherical mapping projects points towards the origin, with vaxis defined to be the <I>z</I> axis and uaxis defined to be the <I>x</I> axis.

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