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Access ean13+5 in Java continued
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Part III: The Display List
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EXAMPLE 15-1
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var brightness:int = 0x80 + 0x80 * Math.random(); var color:int = brightness << 16 | brightness << 8 | brightness; face.graphics.beginFill(color, 0.8); face.graphics.drawRect(-size/2, -size/2, size, size); face.graphics.endFill(); addChild(face); } getChildAt(0).rotationY = 90; //left getChildAt(0).x = -size/2; getChildAt(1).rotationY = -90; //right getChildAt(1).x = size/2; getChildAt(2).z = -size/2; //front getChildAt(3).rotationY = 180; //back getChildAt(3).z = size/2; getChildAt(4).rotationX = 90; //bottom getChildAt(4).y = size/2; getChildAt(5).rotationX = -90; //top getChildAt(5).y = -size/2; } }
The three cubes are shown in Figure 15-5. The boringCube doesn t have a transformation of its own (except repositioning it so that it s visible), to contrast it from the Cubes, which have more complicated transformations. All three Cube instances hold together because their children are positioned in the parent Cube coordinate system, and the parent is what s being rotated and moved. All transformations are also relative to the origin of the coordinate system, which you were careful to place in the center of the cube. This makes the cube rotate around the center, which is far more predictable and easier to program. For more proof, you can easily modify the example by drawing a point at the origin of each Cube s coordinate system, or better yet, add three Shapes to show its own three axes.
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FIGURE 15-5
Three cubes, each with their own identical children and coordinate system. The parent coordinate systems are transformed in different ways. Displayed when you run Example 15-1.
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15: Working in Three Dimensions
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Another observation you can draw from this example is that the depth sorting is completely dependent on the display list s ordering, not on the object s position in 3D space. I ve intentionally used translucent cubes so that you can t tell the incorrect ordering with a glance. Just turn the blend mode back to normal and make the faces opaque, and you ll see that the display list ordering is in effect, including the fact that all faces in one cube are either above or below all faces in another cube, because they re separate DisplayObjectContainers with their own child layering.
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Geometry Revisited
There are new geometry classes in Flash Player 10 for 3D geometry, Vector3D and Matrix3D, found in the flash.geom package. (In the next section, you ll also touch on the PerspectiveProjection class in this package.) You ll nd both of these thoroughly explained in 34, but I ll quickly introduce Vector3D here. The Vector3D class represents a point in three dimensions, much like Point represents one in two dimensions. It contains x, y, and z properties. It also contains a fourth coordinate, w, to be ignored for now. Now, there s nothing that s forcing you to use this class only for coordinates. You can also use it to represent a vector in 3D. This vector has absolutely nothing to do with the Vector class in 9, Vectors. A vector in the geometric sense is a direction and a length you can think of it as an arrow pointing from the origin to (x, y, z), as Figure 15-6 demonstrates. The difference between a vector and a point is subtle. Say you re driving to New York City. A coordinate tells you where it is. A vector points you there. They both have the same values.
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FIGURE 15-6
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A vector and a point in 2D
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(5,15) 5,15
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Point
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Vector
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For instance, you d use a vector to encode a distance, a velocity, an acceleration, an Euler rotation, or in Example 15-2, an angular velocity.
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EXAMPLE 15-2
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http://actionscriptbible.com/ch15/ex2
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Using Vectors in 3D
package { import flash.display.*; import flash.events.MouseEvent; import flash.geom.*;
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Part III: The Display List
EXAMPLE 15-2
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public class ch15ex2 extends Sprite { public function ch15ex2() { stage.quality = StageQuality.LOW; stage.addEventListener(MouseEvent.CLICK, onClick); } protected function onClick(event:MouseEvent):void { var cube:Cube = new Cube(20); cube.x = event.localX; cube.y = event.localY; addChild(cube); var normalizedMousePosition2D:Point = new Point( stage.mouseX / stage.stageWidth * 2 - 1, stage.mouseY / stage.stageHeight * 2 - 1); cube.angularVelocity.x = Math.pow(normalizedMousePosition2D.y, 3) * 10; cube.angularVelocity.y = Math.pow(normalizedMousePosition2D.x, 3) * 10; } } } import flash.display.*; import flash.events.Event; import flash.geom.Vector3D; class Cube extends Sprite { public var angularVelocity:Vector3D; public function Cube(size:Number = 50, ang:Vector3D = null) { for (var side:int = 0; side < 6; side++) { var face:Sprite = new Sprite(); face.blendMode = BlendMode.MULTIPLY; var brightness:int = 0x80 + 0x80 * Math.random(); var color:int = brightness << 16 | brightness << 8 | brightness; face.graphics.beginFill(color, 0.8); face.graphics.drawRect(-size/2, -size/2, size, size); face.graphics.endFill(); addChild(face); } getChildAt(0).rotationY = 90; getChildAt(0).x = -size/2; getChildAt(1).rotationY = -90; getChildAt(1).x = size/2; getChildAt(2).z = -size/2; getChildAt(3).rotationY = 180; getChildAt(3).z = size/2; getChildAt(4).rotationX = 90; getChildAt(4).y = size/2; getChildAt(5).rotationX = -90; getChildAt(5).y = -size/2; this.angularVelocity = (ang) ang : new Vector3D(0, 0, 0); addEventListener(Event.ENTER_FRAME, onEnterFrame); } protected function onEnterFrame(event:Event):void { this.rotationX += angularVelocity.x; this.rotationY += angularVelocity.y; this.rotationZ += angularVelocity.z; } }