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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: The Polygon Primeval</title><!-- HEADER -->
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-  <!--ISBN=1576101746//-->
-  <!--TITLE=Michael Abrash's Graphics Programming Black Book Special Edition//-->
-  <!--AUTHOR=Michael Abrash//-->
-  <!--PUBLISHER=The Coriolis Group, Inc.//-->
+  <title>Michael Abrash's Graphics Programming Black Book Special Edition: The Polygon Primeval</title>
   <meta name="chapter" content="38" />
   <meta name="pages" content="720-721" />
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   <p>Listing 38.1 first finds the top and bottom of the polygon, then works out from the top point to find the two ends of the top edge. If the ends are at different locations, the top is flat, which has two implications. First, it&rsquo;s easy to find the starting vertices and directions through the vertex list for the left and right edges. (To scan-convert them properly, we must first determine which edge is which.) Second, the top scan line of the polygon should be drawn without the rightmost pixel, because only the rightmost pixel of the horizontal edge that makes up the top scan line is part of a right edge.</p>
 
-  <p>If, on the other hand, the ends of the top edge are at the same location, the top is pointed. In that case, the top scan line of the polygon isn&rsquo;t drawn; it&rsquo;s part of the right-edge line that starts at the top vertex. (It&rsquo;s part of a left-edge line, too, but the right edge overrides.) When the top isn&rsquo;t flat, it&rsquo;s more difficult to tell in which direction through the vertex list the right and left edges go, because both edges start at the top vertex. The solution is to compare the slopes from the top vertex to the ends of the two lines coming out of it in order to see which is leftmost. The calculations in Listing 38.1 involving the various deltas do this, using a rearranged form of the slope-based equation:</p><!-- CODE SNIP //-->
+  <p>If, on the other hand, the ends of the top edge are at the same location, the top is pointed. In that case, the top scan line of the polygon isn&rsquo;t drawn; it&rsquo;s part of the right-edge line that starts at the top vertex. (It&rsquo;s part of a left-edge line, too, but the right edge overrides.) When the top isn&rsquo;t flat, it&rsquo;s more difficult to tell in which direction through the vertex list the right and left edges go, because both edges start at the top vertex. The solution is to compare the slopes from the top vertex to the ends of the two lines coming out of it in order to see which is leftmost. The calculations in Listing 38.1 involving the various deltas do this, using a rearranged form of the slope-based equation:</p>
   <pre>
 (DeltaYN/DeltaXN)&gt;(DeltaYP/DeltaXP)
-</pre><!-- END CODE SNIP //-->
+</pre>
 
   <p>Once we know where the left edge starts in the vertex list, we can scan-convert it a line segment at a time until the bottom vertex is reached. Each point is stored as the starting X coordinate for the corresponding scan line in the list we&rsquo;ll pass to <b>DrawHorizontalLineList</b>. The nearest X coordinate on each scan line that&rsquo;s on or to the right of the left edge is selected. The last point of each line segment making up the left edge isn&rsquo;t scan-converted, producing two desirable effects. First, it avoids drawing each vertex twice; two lines come into every vertex, but we want to scan-convert each vertex only once. Second, not scan-converting the last point of each line causes the bottom scan line of the polygon not to be drawn, as required by our rules. The first scan line of the polygon is also skipped if the top isn&rsquo;t flat.</p>
 
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   <p>Finis.</p>
 
-  <h3><a id="Heading7"></a>Oddball Cases</h3>
+  <h3 id="Heading7">Oddball Cases</h3>
 
   <p>Listing 38.1 handles zero-length segments (multiple vertices at the same location) by ignoring them, which will be useful down the road because scaled-down polygons can end up with nearby vertices moved to the same location. Horizontal line segments are fine anywhere in a polygon, too. Basically, Listing 38.1 scan-converts between active edges (the edges that define the extent of the polygon on each scan line) and both horizontal and zero-length lines are non-active; neither advances to another scan line, so they don&rsquo;t affect the edges being scanned.</p>
 
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     Graphics Programming Black Book &copy; 2001 Michael Abrash
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