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Retidy, removing align=left from headings and empty paragraphs

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James Gregory 2013-12-30 15:37:13 +11:00
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@ -1,5 +1,4 @@
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<!DOCTYPE html>
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
@ -19,17 +18,21 @@
<center>
<table border="1">
<tr>
<td><a href="39-05.html">Previous</a></td>
<td>
<a href="39-05.html">Previous</a>
</td>
<td><a href="index.html">Table of Contents</a></td>
<td>
<a href="index.html">Table of Contents</a>
</td>
<td><a href="40-02.html">Next</a></td>
<td>
<a href="40-02.html">Next</a>
</td>
</tr>
</table>
</center>
<p><br /></p>
<h2 id="Heading1">Chapter 40<br />
Of Songs, Taxes, and the Simplicity of Complex Polygons</h2>
@ -51,7 +54,7 @@
<p>Before we dive into complex polygon filling, I&rsquo;d like to point out that the code in this chapter, like all polygon filling code I&rsquo;ve ever seen, requires that the caller describe the type of the polygon to be filled. Often, however, the caller doesn&rsquo;t know what type of polygon it&rsquo;s passing, or specifies complex for simplicity, because that will work for all polygons; in such a case, the polygon filler will use the slow complex-fill code even if the polygon is, in fact, a convex polygon. In Chapter 41, I&rsquo;ll discuss one way to improve this situation.</p>
<h4 align="left" id="Heading4">Active Edges</h4>
<h4 id="Heading4">Active Edges</h4>
<p>The basic premise of filling a complex polygon is that for a given scan line, we determine all intersections between the polygon&rsquo;s edges and that scan line and then fill the spans between the intersections, as shown in Figure 40.1. (Section 3.6 of Foley and van Dam&rsquo;s <i>Computer Graphics</i>, Second Edition provides an overview of this and other aspects of polygon filling.) There are several rules that might be used to determine which spans are drawn and which aren&rsquo;t; we&rsquo;ll use the odd/even rule, which specifies that drawing turns on after odd-numbered intersections (first, third, and so on) and off after even-numbered intersections.</p>
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<p>Maintaining the AET from one scan line to the next involves three steps: First, we must add to the AET any edges that start on the current scan line, making sure to keep the AET X-sorted for efficient odd/even scanning. Second, we must remove edges that end on the current scan line. Third, we must advance the X coordinates of active edges with the same sort of error term-based, Bresenham&rsquo;s-like approach we used for convex polygons, again ensuring that the AET is X-sorted after advancing the edges.</p>
<p><br /></p>
<center>
<table border="1">
<tr>
<td><a href="39-05.html">Previous</a></td>
<td>
<a href="39-05.html">Previous</a>
</td>
<td><a href="index.html">Table of Contents</a></td>
<td>
<a href="index.html">Table of Contents</a>
</td>
<td><a href="40-02.html">Next</a></td>
<td>
<a href="40-02.html">Next</a>
</td>
</tr>
</table>
</center>