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As an interesting aside, there is one transformation of a display object that I didn t mention earlier: skew. Skew doesn t have its own DisplayObject property like the ones I listed, but it can be added in all versions of Flash Player using the display object s transformation matrix (see 34), or visually in Flash Professional. Given that you can create the illusion of 3D by drawing a scene in a certain way (with a certain projection), there s actually another way to draw 3D that relies on skewing. This kind of drawing is a parallel projection. You may be familiar with parallel projections if you ve seen schematic drawings blueprints or played three-quarter, top-down games like SimCity, Final Fantasy Tactics, Diablo, and so on. The problem with parallel projections is that parallel lines never appear to converge. Parallel projections like these are mathematically pleasing, but you see in perspective where parallel lines eventually converge. (Imagine train tracks going off into the distance. At the horizon, they will have merged into a single point.) Perspective transforms just can t be done with a skew, because as you can see in Figure 15-1, skewing preserves parallel lines. So all it really takes to create the illusion of depth is a perspective transformation. Figure 15-1 shows two rectangles one skewed, and one with a perspective transform and the kinds of scenes that can be drawn with those different transformations.

12s2

FIGURE 15-1

(8-21)

where 2 2,n 1 and 2 2,n 1 are the upper and lower 100 2 percentage points of 1 the chi-square distribution with n 1 degrees of freedom, respectively. A con dence interval for has lower and upper limits that are the square roots of the corresponding limits in Equation 8-21.

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What all this boils down to is that you need a perspective transformation to convincingly fake three dimensions, and this kind of transformation is only available in Flash Player 10 and later. Now that you know what the trick is, take three giant steps back, because you re not going to have to apply it directly (in this chapter). When you use the third dimension in Flash Player s display list, it applies a perspective projection automatically. You just focus on positioning objects in three-dimensional space; Flash Player draws the convincing 2D perspective projection on-screen for you.

The 100(1

While Flash Player 9 can t do a perspective projection natively, of course, you can write code that approximates one. This four-point distortion is exactly how ActionScript 3D libraries work, in versions before Flash Player 10.

are (8-22)

This is a critical point: when using 3D in the display list, all you have to do is position and orient display objects in three dimensions. There are really no extra classes or steps required. You ll use DisplayObject and all its subclasses in the same way, except with a dimension added. Figure 15-2 is simply a block of TLF text (it could as easily be a TextField, Shape, or Video) rotated about the x-axis and positioned in 3D space, nothing more.

12s2

FIGURE 15-2

EXAMPLE 8-5

An automatic lling machine is used to ll bottles with liquid detergent. A random sample of 20 bottles results in a sample variance of ll volume of s2 0.0153 ( uid ounces)2. If the variance of ll volume is too large, an unacceptable proportion of bottles will be under- or over lled. We will assume that the ll volume is approximately normally distributed. A 95% upper-con dence interval is found from Equation 8-22 as follows:

In 14, Visual Programming and the Display List, you saw that the coordinate space that Flash Player uses is a Cartesian space with the origin at the top-left corner of the stage The x-axis increases to the right and the y-axis increases down Because of this, points in any quadrant but the bottom-right don t appear on-stage When you re using the 3D coordinate system, none of this changes A third, z-axis, is added The origin stays at the top-left corner, and the z-axis protrudes perpendicular to the stage, into and out of your display, with positive z being farther away from you, and negative z being closer to you By default, the perspective is set up so that the vanishing point is in the center of the stage, in nitely far off in positive z.

12s2

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