Remove colour attributes from body and strip most of the font tags out
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James Gregory
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362 changed files with 1632 additions and 1706 deletions
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59-01.html
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59-01.html
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<!--CHAPTER=59//-->
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<!--PAGES=1095-1099//-->
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<!--UNASSIGNED1//-->
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<!--UNASSIGNED2//--></HEAD><BODY LINK=#0000FF ALINK=#000099 VLINK=#0000FF BGCOLOR=#FFFFFF>
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<!--UNASSIGNED2//--></HEAD><body>
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<CENTER>
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<TABLE BORDER>
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</TABLE>
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</CENTER>
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<P><BR></P>
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<H2><A NAME="Heading1"></A><FONT COLOR="#000077">Chapter 59<BR>The Idea of BSP Trees
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</FONT></H2>
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<H3><A NAME="Heading2"></A><FONT COLOR="#000077">What BSP Trees Are and How to Walk Them</FONT></H3>
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<H2><A NAME="Heading1"></A>Chapter 59<BR>The Idea of BSP Trees</H2>
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<H3><A NAME="Heading2"></A>What BSP Trees Are and How to Walk Them</H3>
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<P>The answer is: Wendy Tucker.
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</P>
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<P>The question that goes with that answer isn’t particularly interesting to anyone but me—but the manner in which I came up with the answer is.</P>
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<P>The problem is, though, that neither you nor I will ever do anything great without inspiration and intuitive leaps, and especially not without stepping away from what’s known and venturing into territories beyond. The way to do that is not by trying harder but, paradoxically, by trying less hard, stepping back, and giving your right brain room to work, then listening for and nurturing whatever comes of that. On a small scale, that’s how I remembered Wendy’s name, and on a larger scale, that’s how programmers come up with products that are more than me-too, checklist-oriented software.</P>
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<P>Which, for a couple of reasons, brings us neatly to this chapter’s topic, Binary Space Partitioning (BSP) trees. First, games are probably the sort of software in which the right-brain element is most important—blockbuster games are almost always breakthroughs in one way or another—and some very successful games use BSP trees, most notably id Software’s megahit DOOM. Second, BSP trees aren’t intuitively easy to grasp, and considerable ingenuity and inventiveness is required to get the most from them.</P>
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<P>Before we begin, I’d like to thank John Carmack, the technical wizard behind DOOM, for generously sharing his knowledge of BSP trees with me.</P>
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<H3><A NAME="Heading3"></A><FONT COLOR="#000077">BSP Trees</FONT></H3>
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<H3><A NAME="Heading3"></A>BSP Trees</H3>
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<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 “Binary Space Partitioning.” The subdivision is hierarchical; the root node splits the world into two subspaces, then each of the root’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’s figures.
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</P>
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<P>Building a tree that subdivides space doesn’t sound particularly profound, but there’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>
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<H4 ALIGN="LEFT"><A NAME="Heading4"></A><FONT COLOR="#000077">Visibility Determination</FONT></H4>
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<H4 ALIGN="LEFT"><A NAME="Heading4"></A>Visibility Determination</H4>
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<P>For the time being, I’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’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.
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</P><P><BR></P>
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<CENTER>
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<hr width="90%" size="1" noshade>
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<div align="center">
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<font face="Verdana,sans-serif" size="1">Graphics Programming Black Book © 2001 Michael Abrash</font>
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Graphics Programming Black Book © 2001 Michael Abrash
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</div>
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<!-- all of the reference materials (books) have the footer and subfoot reveresed -->
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<!-- reference_subfoot = footer -->
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