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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: Adding a Dimension</title><!-- HEADER -->
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-  <!--PUBLISHER=The Coriolis Group, Inc.//-->
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   <meta name="chapter" content="50" />
   <meta name="pages" content="931-935" />
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   <p><br /></p>
 
-  <h2><a id="Heading1"></a>Chapter 50<br />
+  <h2 id="Heading1">Chapter 50<br />
   Adding a Dimension</h2>
 
-  <h3><a id="Heading2"></a>3-D Animation Using Mode X</h3>
+  <h3 id="Heading2">3-D Animation Using Mode X</h3>
 
   <p>When I first started programming micros, more than 11 years ago now, there wasn&rsquo;t much money in it, or visibility, or anything you could call a promising career. Sometimes, it was a way to accomplish things that would never have gotten done otherwise because minicomputer time cost too much; other times, it paid the rent; mostly, though, it was just for fun. Given free computer time for the first time in my life, I went wild, writing versions of all sorts of software I had seen on mainframes, in arcades, wherever. It was a wonderful way to learn how computers work: Trial and error in an environment where nobody minded the errors, with no meter ticking.</p>
 
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   <p>In a sense, I&rsquo;ve saved the best for last, because, to my mind, real-time 3-D animation is one of the most exciting things of any stripe that can be done with a computer&mdash;and because, with today&rsquo;s hardware, it can in fact be done. Nay, it can be done amazingly well.</p>
 
-  <h3><a id="Heading3"></a>References on 3-D Drawing</h3>
+  <h3 id="Heading3">References on 3-D Drawing</h3>
 
   <p>There are several good sources for information about 3-D graphics. Foley and van Dam&rsquo;s <i>Computer Graphics: Principles and Practice</i> (Second Edition, Addison-Wesley, 1990) provides a lengthy discussion of the topic and a great many references for further study. Unfortunately, this book is heavy going at times; a more approachable discussion is provided in <i>Principles of Interactive Computer Graphics</i>, by Newman and Sproull (McGraw-Hill, 1979). Although the latter book lacks the last decade&rsquo;s worth of graphics developments, it nonetheless provides a good overview of basic 3-D techniques, including many of the approaches likely to work well in realtime on a PC.</p>
 
   <p>A source that you may or may not find useful is the series of six books on C graphics by Lee Adams, as exemplified by <i>High-Performance CAD Graphics in C</i> (Windcrest/Tab, 1986). (I don&rsquo;t know if all six books discuss 3-D graphics, but the four I&rsquo;ve seen do.) To be honest, this book has a number of problems, including: Relatively little theory and explanation; incomplete and sometimes erroneous discussions of graphics hardware; use of nothing but global variables, with cryptic names like &ldquo;array3&rdquo; and &ldquo;B21;&rdquo; and&mdash;well, you get the idea. On the other hand, the book at least touches on a great many aspects of 3-D drawing, and there&rsquo;s a lot of C code to back that up. A number of people have spoken warmly to me of Adams&rsquo; books as their introduction to 3-D graphics. I wouldn&rsquo;t recommend these books as your only 3-D references, but if you&rsquo;re just starting out, you might want to look at one and see if it helps you bridge the gap between the theory and implementation of 3-D graphics.</p>
 
-  <h3><a id="Heading4"></a>The 3-D Drawing Pipeline</h3>
+  <h3 id="Heading4">The 3-D Drawing Pipeline</h3>
 
   <p>Each 3-D object that we&rsquo;ll handle will be built out of polygons that represent the surface of the object. Figure 50.1 shows the stages a polygon goes through enroute to being drawn on the screen. (For the present, we&rsquo;ll avoid complications such as clipping, lighting, and shading.) First, the polygon is transformed from object space, the coordinate system the object is defined in, to world space, the coordinate system of the 3-D universe. Transformation may involve rotating, scaling, and moving the polygon. Fortunately, applying the desired transformation to each of the polygon vertices in an object is equivalent to transforming the polygon; in other words, transformation of a polygon is fully defined by transformation of its vertices, so it is not necessary to transform every point in a polygon, just the vertices. Likewise, transformation of all the polygon vertices in an object fully transforms the object.</p>
 
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     Graphics Programming Black Book &copy; 2001 Michael Abrash
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