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<H4> 7.6.6.5 Instructions for Texture Mapper </H4>
<!--docid::SEC385::-->
<P>
In the Crystal Space map file,
the `<SAMP>ORIG</SAMP>', `<SAMP>FIRST</SAMP>', and `<SAMP>SECOND</SAMP>' vertex keywords describe the
texture plane. What Crystal Space does internally is to create a
transformation matrix/vector which translates object space (3D coordinates) to
texture space (<EM>u,v</EM> coordinates). Here is how this works.
</P><P>
First a few definitions:
</P><P>
<UL>
<LI>
<CODE>ORIG</CODE> vector is <EM>Vo</EM>
<LI>
<CODE>FIRST</CODE> vector is <EM>V1</EM>
<LI>
<CODE>SECOND</CODE> vector is <EM>V2</EM>
<LI>
<CODE>FIRST_LEN</CODE> is <EM>L1</EM>
<LI>
<CODE>SECOND_LEN</CODE> is <EM>L2</EM>
<LI>
Length of
<EM>V1 - Vo</EM>
is <EM>l1</EM>
<LI>
Length of
<EM>V2 - Vo</EM>
is <EM>l2</EM>
</UL>
<P>
<EM>Vo</EM>, <EM>V1</EM> and <EM>V2</EM> are vertices in object space. These define
the local coordinate system for texture space. So we have the following
mapping:
</P><P>
<BLOCKQUOTE>
<EM>Vo</EM> ==> (<EM>0</EM>,<EM>0</EM>)<BR>
<EM>V1</EM> ==> (<EM>L1</EM>,<EM>0</EM>)<BR>
<EM>V2</EM> ==> (<EM>0</EM>,<EM>L2</EM>)
</BLOCKQUOTE>
<P>
It is important to realize that the coordinate (0,0) in texture space is the
top-left coordinate of the texture and (1,1) is the bottom-right corner. The
coordinate (2,2) is thus the bottom-right corner of a tiled texture (2x2
times).
</P><P>
The conversion to the matrix happens as follows:
</P><P>
<BLOCKQUOTE>
<EM>Vu = (len1 / l1) * (V1-Vo)</EM><BR>
<EM>Vv = (len2 / l2) * (V2-Vo)</EM>
</BLOCKQUOTE>
<TABLE><tr><td> </td><td class=example><pre> / Vu.x Vv.x 1 \
Mot = | Vu.y Vv.y 1 |
\ Vu.z Vv.z 1 /
</pre></td></tr></table><P>
The last column represents the <EM>W</EM> texture component which is not used.
</P><P>
<BLOCKQUOTE>
<EM>Vot = <Vo.x Vo.y Vo.z></EM>
</BLOCKQUOTE>
<P>
So <EM>Mot</EM> and <EM>Vot</EM> are the transformation matrix/vector to go from
object to texture space. Use these as follows:
</P><P>
<BLOCKQUOTE>
<EM>T = Mot * (O - Vot)</EM>
</BLOCKQUOTE>
<P>
With <EM>O</EM> being the object space vector that you want to convert and
<EM>T</EM> the texture space vector. Only the <EM>x</EM> and <EM>y</EM> components
are used of <EM>T</EM>. <EM>x</EM> represents <EM>u</EM> and <EM>y</EM> represents
<EM>v</EM>.
</P><P>
Using the last equation you can convert every point of your polygon to texture
space.
</P><P>
<A NAME="Texture Mapping Animations"></A>
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