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Strip comments and inline ids onto h*

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James Gregory 2013-12-30 15:11:04 +11:00
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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: Raw Speed and More</title><!-- HEADER -->
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<title>Michael Abrash's Graphics Programming Black Book Special Edition: Raw Speed and More</title>
<meta name="chapter" content="53" />
<meta name="pages" content="1001-1003" />
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<p><br /></p>
<p><b>LISTING 53.2 OLIST.C</b></p><!-- CODE //-->
<p><b>LISTING 53.2 OLIST.C</b></p>
<pre>
/* Object list-related functions. */
#include &lt;stdio.h&gt;
@ -120,15 +113,15 @@ void SortObjects()
}
}
}
</pre><!-- END CODE //-->
</pre>
<h4 align="left"><a id="Heading6"></a>Rounding</h4>
<h4 align="left" id="Heading6">Rounding</h4>
<p>FIXED.ASM contains the equate <b>ROUNDING-ON</b>. When this equate is 1, the results of multiplications and divisions are rounded to the nearest fixed-point values; when it&rsquo;s 0, the results are truncated. The difference between the results produced by the two approaches is, at most, 2<sup><small>-16</small></sup>; you wouldn&rsquo;t think that would make much difference, now, would you? But it does. When the animation is run with rounding disabled, the cubes start to distort visibly after a few minutes, and after a few minutes more they look like they&rsquo;ve been run over. In contrast, I&rsquo;ve never seen any significant distortion with rounding on, even after a half-hour or so. I think the difference with rounding is not that it&rsquo;s so much more accurate, but rather that the errors are evenly distributed; with truncation, the errors are biased, and biased errors become very visible when they&rsquo;re applied to right-angle objects. Even with rounding, though, the errors will eventually creep in, and reorthogonalization will become necessary at some point.</p>
<p>The performance cost of rounding is small, and the benefits are highly visible. Still, truncation errors become significant only when they accumulate over time, as, for example, when rotation matrices are repeatedly concatenated over the course of many transformations. Some time could be saved by rounding only in such cases. For example, division is performed only in the course of projection, and the results do not accumulate over time, so it would be reasonable to disable rounding for division.</p>
<h4 align="left"><a id="Heading7"></a>Having a Ball</h4>
<h4 align="left" id="Heading7">Having a Ball</h4>
<p>So far in our exploration of 3-D animation, we&rsquo;ve had nothing to look at but triangles and cubes. It&rsquo;s time for something a little more visually appealing, so the demonstration program now features a 72-sided ball. What&rsquo;s particularly interesting about this ball is that it&rsquo;s created by the GENBALL.C program in the BALL subdirectory of X-Sharp, and both the size of the ball and the number of bands of faces are programmable. GENBALL.C spits out to a file all the arrays of vertices and faces needed to create the ball, ready for inclusion in INITBALL.C. True, if you change the number of bands, you must change the Colors array in INITBALL.C to match, but that&rsquo;s a tiny detail; by and large, the process of generating a ball-shaped object is now automated. In fact, we&rsquo;re not limited to ball-shaped objects; substitute a different vertex and face generation program for GENBALL.C, and you can make whatever convex polyhedron you want; again, all you have to do is change the <b>Colors</b> array correspondingly. You can easily create multiple versions of the base object, too; INITCUBE.C is an example of this, creating 11 different cubes.</p>
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<div align="center">
Graphics Programming Black Book &copy; 2001 Michael Abrash
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