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<h4 class="subsubsection"> 4.12.3.5 Instructions for Texture Mapper </h4>
<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>
<ul>
<li>
<code>orig</code> vector is <em>Vo</em>
</li><li>
<code>first</code> vector is <em>V1</em>
</li><li>
<code>second</code> vector is <em>V2</em>
</li><li>
<code>firstlen</code> is <em>L1</em>
</li><li>
<code>secondlen</code> is <em>L2</em>
</li><li>
Length of
<em>V1 - Vo</em>
is <em>l1</em>
</li><li>
Length of
<em>V2 - Vo</em>
is <em>l2</em>
</li></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>
<blockquote><p><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>)
</p></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>
<blockquote><p><em>Vu = (len1 / l1) * (V1-Vo)</em><br>
<em>Vv = (len2 / l2) * (V2-Vo)</em>
</p></blockquote>
<table><tr><td> </td><td><pre class="example"> / 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>
<blockquote><p><em>Vot = <Vo.x Vo.y Vo.z></em>
</p></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>
<blockquote><p><em>T = Mot * (O - Vot)</em>
</p></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>
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