Part VIII: Graphics Programming and Animation in Java

Writer UPC - 13 in Java Part VIII: Graphics Programming and Animation
Part VIII: Graphics Programming and Animation
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3D Transformations
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In Flash Player 10 and later, DisplayObjects can be drawn in three dimensions. In 15, Working in Three Dimensions, you learned how to position and orient 3D objects with DisplayObject properties. But just like their 2D brethren, 3D DisplayObjects can be transformed with transformation matrices. Using the transformation API in 3D is generally more powerful, and applicable, than in 2D. This is partially because the relative and absolute orientation of objects is increasingly hard to visualize and keep consistent in three dimensions, and partially because of the extended set of tools that the flash.geom package provides in Flash Player 10 and later.
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FP10. All topics covered in this section apply to Flash Player 10 and later.
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This section provides a refresher on some basic 3D math concepts that were only touched on in 15, making sure to include matrix math in the mix. This section covers not only af ne transforms in 3D, but perspective projection transforms. With an overview of the theory, you can dive into the classes that aid 3D geometry in ActionScript 3.0, comparing them to similar classes that exist for 2D geometry.
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Basic 3D Concepts Review
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Before beginning, I want you to know that there are far better resources on 3D math than what you are about to read. I m going to review some concepts at breakneck speed, mostly to introduce terminology and jog your memory. If you are new to 3D, there are many online and of ine resources for learning the essential yet dif cult concepts involved. For beginners, I recommend 3D Math Primer for Graphics and Game Development by Fletcher Dunn and Ian Parberry (http://gamemath.com/). It starts at square one and has an easy pace without skimping on explanation. It contains problem sets so you can test yourself. Best of all, it s mercifully short and mostly sticks to the real foundation material. Go get it as a companion if you are learning 3D concepts for the rst time. Online, the gamedev.net forums (http://gamedev.net/) are an endless treasure trove of information on graphics programming and beyond. Now s a good time to review some of the terms and concepts needed to operate in 3D. For now it s important not to think about any ActionScript 3.0 classes you may have seen with similar names and just focus on the mathematical concepts. The class names and topics don t translate perfectly; the correct classes will be covered shortly.
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Coordinate System
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The coordinate system for 3D graphics in Flash Player 10 is a Cartesian space with three axes: x, y, and z. The origin is at the top-left corner of the screen. The +x axis proceeds toward the right of the screen, and the +y axis goes down the screen. The +z axis points away from you into the screen, and z extends out of the screen, toward you, the viewer. The plane of the screen is where z = 0. The global coordinate space is pictured in Figure 34-1.
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34: Geometric and Color Transformations
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FIGURE 34-1
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Global coordinate space superimposed on a screen
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Points
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In an n-dimensional Cartesian coordinate system, a location is described by n numbers. Each describes a component of the location along one of the space s axes. For instance, in two dimensions, a point is described by two numbers. You write this (x, y). The x value describes the point s position along the x-axis; the y value describes its position along the y axis. In three dimensions, you add a third axis, z, so you require a third variable to locate a point along the z-axis. A three-dimensional point has three values and is written (x, y, z). A real point, of course, uses real values in place of the variables, such as (5, 5, 5), pictured in Figure 34-2. The dotted lines help you visualize the point s position in three dimensions.
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FIGURE 34-2
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