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Pixel Bender is a pixel shader (or fragment shader, sometimes) system developed for use across Adobe Creative Suite products. In theory, you can use the same shader as a lter in Photoshop, After Effects, and during runtime in Flash Player. A pixel shader is a short program whose output is the color of a given pixel. When an area affected by a pixel shader needs to be rendered, the system runs the program on each pixel that needs to appear on-screen, and it faithfully renders that pixel as the color returned by the program. In this way, the aggregate effect of the pixel shader is to color, or shade, the region. You can also bend Pixel Bender to your will and make it run on nonimage data. In the general case, a single Pixel Bender program is called a kernel.

The stem-and-leaf display and the histogram provide general visual impressions about a data set, while numerical quantities such as x or s provide information about only one feature of the data. The box plot is a graphical display that simultaneously describes several important features of a data set, such as center, spread, departure from symmetry, and identi cation of unusual observations or outliers. A box plot displays the three quartiles, the minimum, and the maximum of the data on a rectangular box, aligned either horizontally or vertically. The box encloses the interquartile range with the left (or lower) edge at the rst quartile, q1, and the right (or upper) edge at the third quartile, q3. A line is drawn through the box at the second quartile (which is the 50th percentile or the median), q2 x. A line, or whisker, extends from each end of the box. The lower whisker is a line from the rst quartile to the smallest data point within 1.5 interquartile ranges from the rst quartile. The upper whisker is a line from the third quartile to the largest data point within 1.5 interquartile ranges from the third quartile. Data farther from the box than the whiskers are plotted as individual points. A point beyond a whisker, but less than 3 interquartile ranges from the box edge, is called an outlier. A point more than 3 interquartile ranges from the box edge is called an extreme outlier. See Fig. 6-13. Occasionally, different symbols, such as open and lled circles, are used to identify the two types of outliers. Sometimes box plots are called box-and-whisker plots.

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Whisker extends to smallest data point within 1.5 interquartile ranges from first quartile First quartile Second quartile Third quartile

In reality, each product that uses Pixel Bender has some speci c limitations that mean some shaders won t be entirely portable. This chapter focuses on the kinds of Pixel Bender programs that run in Flash Player. You ll see that, currently, Flash Player imposes some serious limitations on Pixel Bender kernels that make them best kept simple.

Figure 6-14 Box plot for compressive strength data in Table 6-2.

Pixel shaders aren t like the kinds of programs that you learn to write in the rest of this book. Like regular expressions, they are tools perfectly suited for their singular task. Regular expressions don t look anything like the rest of ActionScript, and they are executed in their own fashion, to ef ciently and concisely manipulate strings. Similarly, Pixel Bender shaders use a language of their own, the Pixel Bender kernel language, and are executed in a manner completely unlike ActionScript code, all in the service of quickly generating graphics. To write a pixel shader, you have to think like a pixel shader.

Figure 6-14 presents the box plot from Minitab for the alloy compressive strength data shown in Table 6-2. This box plot indicates that the distribution of compressive strengths is fairly symmetric around the central value, because the left and right whiskers and the lengths of the left and right boxes around the median are about the same. There are also two mild outliers on either end of the data. Box plots are very useful in graphical comparisons among data sets, because they have high visual impact and are easy to understand. For example, Fig. 6-15 shows the comparative box plots for a manufacturing quality index on semiconductor devices at three manufacturing plants. Inspection of this display reveals that there is too much variability at plant 2 and that plants 2 and 3 need to raise their quality index performance. EXERCISES FOR SECTION 6-5

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