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Retidy, removing align=left from headings and empty paragraphs

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James Gregory 2013-12-30 15:37:13 +11:00
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<!DOCTYPE html>
<html xmlns="http://www.w3.org/1999/xhtml">
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<center>
<table border="1">
<tr>
<td><a href="58-05.html">Previous</a></td>
<td>
<a href="58-05.html">Previous</a>
</td>
<td><a href="index.html">Table of Contents</a></td>
<td>
<a href="index.html">Table of Contents</a>
</td>
<td><a href="59-02.html">Next</a></td>
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<a href="59-02.html">Next</a>
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<p><br /></p>
<h2 id="Heading1">Chapter 59<br />
The Idea of BSP Trees</h2>
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<p>Building a tree that subdivides space doesn&rsquo;t sound particularly profound, but there&rsquo;s a lot that can be done with such a structure. BSP trees can be used to represent shapes, and operating on those shapes is a simple matter of combining trees as needed; this makes BSP trees a powerful way to implement Constructive Solid Geometry (CSG). BSP trees can also be used for hit testing, line-of-sight determination, and collision detection.</p>
<h4 align="left" id="Heading4">Visibility Determination</h4>
<h4 id="Heading4">Visibility Determination</h4>
<p>For the time being, I&rsquo;m going to discuss only one of the many uses of BSP trees: The ability of a BSP tree to allow you to traverse a set of line segments or polygons in back-to-front or front-to-back order as seen from any arbitrary viewpoint. This sort of traversal can be very helpful in determining which parts of each line segment or polygon are visible and which are occluded from the current viewpoint in a 3-D scene. Thus, a BSP tree makes possible an efficient implementation of the painter&rsquo;s algorithm, whereby polygons are drawn in back-to-front order, with closer polygons overwriting more distant ones that overlap, as shown in Figure 59.1. (The line segments in Figure 1(a) and in other figures in this chapter, represent vertical walls, viewed from directly above.) Alternatively, visibility determination can be performed by front-to-back traversal working in conjunction with some method for remembering which pixels have already been drawn. The latter approach is more complex, but has the potential benefit of allowing you to early-out from traversal of the scene database when all the pixels on the screen have been drawn.</p>
<p><br /></p>
<center>
<table border="1">
<tr>
<td><a href="58-05.html">Previous</a></td>
<td>
<a href="58-05.html">Previous</a>
</td>
<td><a href="index.html">Table of Contents</a></td>
<td>
<a href="index.html">Table of Contents</a>
</td>
<td><a href="59-02.html">Next</a></td>
<td>
<a href="59-02.html">Next</a>
</td>
</tr>
</table>
</center>