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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: Quake's Visible-Surface Determination</title><!-- HEADER -->
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-  <!--TITLE=Michael Abrash's Graphics Programming Black Book Special Edition//-->
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-  <!--PUBLISHER=The Coriolis Group, Inc.//-->
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   <p>John says precalculating the PVS was a logical evolution of the approaches he had been considering, that there was no moment when he said &ldquo;Eureka!&rdquo; Nonetheless, it was clearly a breakthrough to a brand-new, superior design, a design that, together with a still-in-development sorted-edge rasterizer that completely eliminates overdraw, comes remarkably close to meeting the &ldquo;perfect-world&rdquo; specifications we laid out at the start.</p>
 
-  <h3><a id="Heading16"></a>Simplify, and Keep on Trying New Things</h3>
+  <h3 id="Heading16">Simplify, and Keep on Trying New Things</h3>
 
   <p>What does it all mean? Exactly what I said up front: Simplify, and keep trying new things. The precalculated PVS is simpler than any of the other schemes that had been considered (although precalculating the PVS is an interesting task that I&rsquo;ll discuss another time). In fact, at runtime the precalculated PVS is just a constrained version of the painter&rsquo;s algorithm. Does that mean it&rsquo;s not particularly profound?</p>
 
@@ -65,7 +58,7 @@
 
   <p>So far, it seems to have worked out pretty well for him.</p>
 
-  <h3><a id="Heading17"></a>Learn Now, Pay Forward</h3>
+  <h3 id="Heading17">Learn Now, Pay Forward</h3>
 
   <p>There&rsquo;s one other thing I&rsquo;d like to mention before I close this chapter. Much of what I&rsquo;ve learned, and a great deal of what I&rsquo;ve written, has been in the pages of <i>Dr. Dobb&rsquo;s Journal.</i> As far back as I can remember, <i>DDJ</i> has epitomized the attitude that sharing programming information is A Good Thing. I know a lot of programmers who were able to leap ahead in their development because of Hendrix&rsquo;s Tiny C, or Stevens&rsquo; D-Flat, or simply by browsing through <i>DDJ</i>&rsquo;s annual collections. (Me, for one.) Understandably, most companies understandably view sharing information in a very different way, as potential profit lost&mdash;but that&rsquo;s what makes <i>DDJ</i> so valuable to the programming community.</p>
 
@@ -73,7 +66,7 @@
 
   <p>So remember, when it&rsquo;s legally possible, sharing information benefits us all in the long run. You can pay forward the debt for the information you gain here and elsewhere by sharing what you know whenever you can, by writing an article or book or posting on the Net. None of us learns in a vacuum; we all stand on the shoulders of giants such as Wirth and Knuth and thousands of others. Lend your shoulders to building the future!</p>
 
-  <h3><a id="Heading18"></a>References</h3>
+  <h3 id="Heading18">References</h3>
 
   <p>Foley, James D., <i>et al.</i>, <i>Computer Graphics: Principles and Practice</i>, Addison Wesley, 1990, ISBN 0-201-12110-7 (beams, BSP trees, VSD).</p>
 
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     Graphics Programming Black Book &copy; 2001 Michael Abrash
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