Misc/abrash-black-book
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James Gregory 2013-12-30 12:25:34 +11:00
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@ -38,7 +38,7 @@
<P><BR></P>
<P>An insertion sort that scans backward through the AET from the current edge rather than forward from the start of the AET could be quite a bit faster, because edges rarely move more than one or two positions through the AET. However, scanning backward requires a doubly linked list, rather than the singly linked list used in Listing 40.1. I&#146;ve chosen to use a singly linked list partly to minimize memory requirements (double-linking requires an extra pointer field) and partly because supporting back links would complicate the code a good bit. The main reason, though, is that the potential rewards for the complications of back links and insertion sorting aren&#146;t great enough; profiling a variety of polygons reveals that less than ten percent of total time is spent sorting the AET.
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<TABLE WIDTH="100%"><TD WIDTH="5%" VALIGN="TOP"><IMG SRC="images/40-01i.jpg"><TD WIDTH="95%"><SMALL><I>The potential 1 to 5 percent speedup gained by optimizing AET sorting just isn&#146;t worth it in any but the most demanding application&#151;a good example of the need to keep an overall perspective when comparing the theoretical characteristics of various approaches.</I></SMALL>
<TABLE WIDTH="100%"><TD WIDTH="5%" VALIGN="TOP"><IMG SRC="images/i.jpg"><TD WIDTH="95%"><SMALL><I>The potential 1 to 5 percent speedup gained by optimizing AET sorting just isn&#146;t worth it in any but the most demanding application&#151;a good example of the need to keep an overall perspective when comparing the theoretical characteristics of various approaches.</I></SMALL>
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<H3><A NAME="Heading8"></A><FONT COLOR="#000077">Nonconvex Polygons</FONT></H3>
<P>Nonconvex polygons can be filled somewhat faster than complex polygons. Because edges never cross or switch positions with other edges once they&#146;re in the AET, the AET for a nonconvex polygon needs to be sorted only when new edges are added. In order for this to work, though, edges must be added to the AET in strict left-to-right order. Complications arise when dealing with two edges that start at the same point, because slopes must be compared to determine which edge is leftmost. This is certainly doable, but because of space limitations and limited performance returns, I haven&#146;t implemented this in Listing 40.1.