Remove colour attributes from body and strip most of the font tags out
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James Gregory
parent
7e957c0bb4
commit
c1f88ddb41
362 changed files with 1632 additions and 1706 deletions
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@ -24,7 +24,7 @@
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<!--CHAPTER=42//-->
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<!--PAGES=778-781//-->
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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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@ -36,13 +36,13 @@
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</TABLE>
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</CENTER>
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<P><BR></P>
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<H3><A NAME="Heading4"></A><FONT COLOR="#000077">Tracing and Intensity in One</FONT></H3>
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<H3><A NAME="Heading4"></A>Tracing and Intensity in One</H3>
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<P>Horizontal, vertical, and diagonal lines do not require Wu antialiasing because they pass through the center of every pixel they meet; such lines can be drawn with fast, special-case code. For all other cases, Wu lines are traced out one step at a time along the major axis by means of a simple, fixed-point algorithm. The move along the minor axis with respect to a one-pixel move along the major axis (the line slope for lines with slopes less than 1, 1/slope for lines with slopes greater than 1) is calculated with a single integer divide. This value, called the “error adjust,” is stored as a fixed-point fraction, in 0.16 format (that is, all bits are fractional, and the decimal point is just to the left of bit 15). An error accumulator, also in 0.16 format, is initialized to 0. Then the first pixel is drawn; no weighting is needed, because the line intersects its endpoints exactly.
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</P>
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<P>Now the error adjust is added to the error accumulator. The error accumulator indicates how far between pixels the line has progressed along the minor axis at any given step; when the error accumulator turns over, it’s time to advance one pixel along the minor axis. At each step along the line, the major-axis coordinate advances by one pixel. The two bracketing pixels to draw are simply the two pixels nearest the line along the minor axis. For instance, if X is the current major-axis coordinate and Y is the current minor-axis coordinate, the two pixels to be drawn are (X,Y) and (X,Y+1). In short, the derivation of the pixels at which to draw involves nothing more complicated than advancing one pixel along the major axis, adding the error adjust to the error accumulator, and advancing one pixel along the minor axis when the error accumulator turns over.</P>
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<P>So far, nothing special; but now we come to the true wonder of Wu antialiasing. We know which pair of pixels to draw at each step along the line, but we also need to generate the two proper intensities, which must be inversely proportional to distance from the ideal line and sum to 1, and that’s a potentially time-consuming operation. Let’s assume, however, that the number of possible intensity levels to be used for weighting is the value NumLevels = 2<SUP>n</SUP> for some integer n, with the minimum weighting (0 percent intensity) being the value 2<SUP>n</SUP> -1, and the maximum weighting (100 percent intensity) being the value 0. Given that, lo and behold, the most significant n bits of the error accumulator select the proper intensity value for one element of the pixel pair, as shown in Figure 42.2. Better yet, 2<SUP>n</SUP>-1 minus the intensity of the first pixel selects the intensity of the other pixel in the pair, because the intensities of the two pixels must sum to 1; as it happens, this result can be obtained simply by flipping the n least-significant bits of the first pixel’s value. All this works because what the error accumulator accumulates is precisely the ideal line’s current distance between the two bracketing pixels.</P>
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<P><A NAME="Fig2"><!-- </A><A HREF="javascript:displayWindow('images/42-02.jpg',406,198 )"> --><IMG SRC="images/42-02.jpg"><BR><!-- </A>
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<BR><A HREF="javascript:displayWindow('images/42-02.jpg',406,198)"> --><FONT COLOR="#000077"><B>Figure 42.2</B></FONT></A> <I>Wu intensity calculations.</I>
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<BR><A HREF="javascript:displayWindow('images/42-02.jpg',406,198)"> --><B>Figure 42.2</B></A> <I>Wu intensity calculations.</I>
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</P>
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<P>The intensity calculations take longer to describe than they do to perform. All that’s involved is a shift of the error accumulator to right-justify the desired intensity weighting bits, and then an XOR to flip the least-significant n bits of the first pixel’s value in order to generate the second pixel’s value. Listing 42.1 illustrates just how efficient Wu antialiasing is; the intensity calculations take only three statements, and the entire Wu line-drawing loop is only nine statements long. Of course, a single C statement can hide a great deal of complexity, but Listing 42.6, an assembly implementation, shows that only 15 instructions are required per step along the major axis—and the number of instructions could be reduced to ten by special-casing and loop unrolling. Make no mistake about it, Wu antialiasing is fast.
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</P>
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@ -198,7 +198,7 @@ void DrawWuLine(int X0, int Y0, int X1, int Y1, int BaseColor, int NumLevels,
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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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