Remove colour attributes from body and strip most of the font tags out
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James Gregory
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362 changed files with 1632 additions and 1706 deletions
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36-01.html
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36-01.html
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@ -24,7 +24,7 @@
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<!--CHAPTER=36//-->
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<!--PAGES=679-683//-->
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<!--UNASSIGNED1//-->
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<!--UNASSIGNED2//--></HEAD><BODY LINK=#0000FF ALINK=#000099 VLINK=#0000FF BGCOLOR=#FFFFFF>
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<!--UNASSIGNED2//--></HEAD><body>
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<CENTER>
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<TABLE BORDER>
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@ -36,9 +36,8 @@
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</TABLE>
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</CENTER>
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<P><BR></P>
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<H2><A NAME="Heading1"></A><FONT COLOR="#000077">Chapter 36<BR>The Good, the Bad, and the Run-Sliced
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</FONT></H2>
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<H3><A NAME="Heading2"></A><FONT COLOR="#000077">Faster Bresenham Lines with Run-Length Slice Line Drawing</FONT></H3>
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<H2><A NAME="Heading1"></A>Chapter 36<BR>The Good, the Bad, and the Run-Sliced</H2>
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<H3><A NAME="Heading2"></A>Faster Bresenham Lines with Run-Length Slice Line Drawing</H3>
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<P>Years ago, I worked at a company that asked me to write blazingly fast line-drawing code for an AutoCAD driver. I implemented the basic Bresenham’s line-drawing algorithm; streamlined it as much as possible; special-cased horizontal, diagonal, and vertical lines; broke out separate, optimized routines for lines in each octant; and massively unrolled the loops. When I was done, I had line drawing down to a mere five or six instructions per pixel, and I handed the code over to the AutoCAD driver person, content in the knowledge that I had pushed the theoretical limits of the Bresenham’s algorithm on the 80x86 architecture, and that this was as fast as line drawing could get on a PC. That feeling lasted for about a week, until Dave Miller, who these days is a Windows display-driver whiz at Engenious Solutions, casually mentioned Bresenham’s faster run-length slice line-drawing algorithm.
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</P>
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<P>Remember Bill Murray’s safety tip in <I>Ghostbusters</I>? It goes something like this. Harold Ramis tells the Ghostbusters not to cross the beams of the antighost guns. “Why?” Murray asks.</P>
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@ -88,12 +87,12 @@ else
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<P>Think of it this way: A program is a state machine. It takes a set of inputs and produces a corresponding set of outputs by passing through a set of states. Your primary job as a programmer is to implement the desired state machine. Your additional job as a performance programmer is to minimize the lengths of the paths through the state machine. This means performing as many tests and calculations as possible outside the loops, so that the loops themselves can do as little work—that is, pass through as few states—as possible.
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</P>
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<P>Which brings us full circle to Bresenham’s run-length slice line-drawing algorithm, which just happens to be an excellent example of a minimized state machine. In case you’re fuzzy on the good/bad performance thing, that’s “good”—as in <I>fast</I>.</P>
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<H3><A NAME="Heading3"></A><FONT COLOR="#000077">Run-Length Slice Fundamentals</FONT></H3>
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<H3><A NAME="Heading3"></A>Run-Length Slice Fundamentals</H3>
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<P>First off, I have a confession to make: I’m not sure that the algorithm I’ll discuss is actually, precisely Bresenham’s run-length slice algorithm. It’s been a long time since I read about this algorithm; in the intervening years, I’ve misplaced Bresenham’s article, and have been unable to unearth it. As a result, I had to derive the algorithm from scratch, which was admittedly more fun than reading about it, and also ensured that I understood it inside and out. The upshot is that what I discuss may or may not be Bresenham’s run-length slice algorithm—but it surely is fast.
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</P>
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<P>The place to begin understanding the run-length slice algorithm is the standard Bresenham’s line-drawing algorithm. (I discussed the standard Bresenham’s line-drawing algorithm at length in the previous chapter.) The basis of the standard approach is stepping one pixel at a time along the major axis (the longer dimension of the line), while maintaining an integer error term that indicates at each major-axis step how close the line is to advancing halfway to the next pixel along the minor axis. Figure 36.1 illustrates standard Bresenham’s line drawing. The key point here is that a calculation and a test are performed once for each step along the major axis.</P>
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<P><A NAME="Fig1"><!-- </A><A HREF="javascript:displayWindow('images/36-01.jpg',408,194 )"> --><IMG SRC="images/36-01.jpg"><BR><!-- </A>
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<BR><A HREF="javascript:displayWindow('images/36-01.jpg',408,194)"> --><FONT COLOR="#000077"><B>Figure 36.1</B></FONT></A> <I>Standard Bresenham’s line drawing.</I>
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<BR><A HREF="javascript:displayWindow('images/36-01.jpg',408,194)"> --><B>Figure 36.1</B></A> <I>Standard Bresenham’s line drawing.</I>
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<P><BR></P>
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<CENTER>
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<TABLE BORDER>
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@ -107,7 +106,7 @@ else
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<hr width="90%" size="1" noshade>
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<div align="center">
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<font face="Verdana,sans-serif" size="1">Graphics Programming Black Book © 2001 Michael Abrash</font>
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Graphics Programming Black Book © 2001 Michael Abrash
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</div>
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<!-- all of the reference materials (books) have the footer and subfoot reveresed -->
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<!-- reference_subfoot = footer -->
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