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<meta name="vspubdate" content="07/01/97" />
<meta name="vscategory" content="Web and Software Development: Game Development,Web and Software Development: Graphics and Multimedia Development" />
<title>Michael Abrash's Graphics Programming Black Book Special Edition: The Idea of BSP Trees</title><!-- HEADER -->
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<title>Michael Abrash's Graphics Programming Black Book Special Edition: The Idea of BSP Trees</title>
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<p><br /></p>
<h2><a id="Heading1"></a>Chapter 59<br />
<h2 id="Heading1">Chapter 59<br />
The Idea of BSP Trees</h2>
<h3><a id="Heading2"></a>What BSP Trees Are and How to Walk Them</h3>
<h3 id="Heading2">What BSP Trees Are and How to Walk Them</h3>
<p>The answer is: Wendy Tucker.</p>
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<p>Before we begin, I&rsquo;d like to thank John Carmack, the technical wizard behind DOOM, for generously sharing his knowledge of BSP trees with me.</p>
<h3><a id="Heading3"></a>BSP Trees</h3>
<h3 id="Heading3">BSP Trees</h3>
<p>A BSP tree is, at heart, nothing more than a tree that subdivides space in order to isolate features of interest. Each node of a BSP tree splits an area or a volume (in 2-D or 3-D, respectively) into two parts along a line or a plane; thus the name &ldquo;Binary Space Partitioning.&rdquo; The subdivision is hierarchical; the root node splits the world into two subspaces, then each of the root&rsquo;s two children splits one of those two subspaces into two more parts. This continues with each subspace being further subdivided, until each component of interest (each line segment or polygon, for example) has been assigned its own unique subspace. This is, admittedly, a pretty abstract description, but the workings of BSP trees will become clearer shortly; it may help to glance ahead to this chapter&rsquo;s figures.</p>
<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"><a id="Heading4"></a>Visibility Determination</h4>
<h4 align="left" 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>
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Graphics Programming Black Book &copy; 2001 Michael Abrash
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