15: Working in Three Dimensions in Java

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15: Working in Three Dimensions
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In Example 15-2, you use the x, y, and z properties of a Vector3D to represent the rotation to be added to each axis in each frame. Just like a Point, these properties can be set when calling the constructor. Don t worry about the event handling and animation here.
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Vector3D has a wonderful set of methods that do vector math; you may nd simple ones like add(), subtract(), scaleBy(), and distance() useful here. Once you start delving into
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projections and matrix multiplication, you d be better off heading to 34 to learn about 3D transformation matrices.
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The good news is that mouse position is mapped automatically and correctly onto 3D objects. A button in 3D can register a click no matter its angle. The mouse s position is always a 2D point in the display object s coordinate space, and Flash Player projects the mouse position onto a 3D display object without intervention from you. Although Example 15-3 uses the drawing API and mouse events, which are covered in later chapters, it does offer convincing proof that mouse positions are projected correctly in 3D space.
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package { import flash.display.Sprite; import flash.events.Event; public class ch15ex3 extends Sprite { protected var canvas:Canvas; public function ch15ex3() { canvas = new Canvas(400, 300); addChild(canvas); canvas.x = stage.stageWidth/2; canvas.y = stage.stageHeight/2; canvas.rotationY = 25; addEventListener(Event.ENTER_FRAME, onEnterFrame); } protected function onEnterFrame(event:Event):void { canvas.rotationY += 0.2; canvas.rotationX += 0.04; } } } import flash.display.Shape; import flash.display.Sprite; import flash.events.MouseEvent; import flash.geom.Rectangle; class Canvas extends Sprite { protected var fg:Shape, bg:Shape;
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Part III: The Display List
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protected var ink:int = 0; public function Canvas(w:Number, h:Number) { bg = new Shape(); bg.graphics.beginFill(0xe0e0e0, 1); bg.graphics.drawRect(0, 0, w, h); bg.x = -w/2; bg.y = -h/2; addChild(bg); fg = new Shape(); fg.x = -w/2; fg.y = -h/2; addChild(fg); fg.scrollRect = new Rectangle(-w/2, -h/2, w, h); addEventListener(MouseEvent.MOUSE_MOVE, onMouseMove); } protected function onMouseMove(event:MouseEvent):void { if (event.buttonDown) { ink++; fg.graphics.lineTo(event.localX, event.localY); } else { if (ink > 500) { fg.graphics.clear(); ink = 0; } fg.graphics.lineStyle(32, 0xffffff * Math.random(), 0.4); fg.graphics.moveTo(event.localX, event.localY); } } }
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Run the example, and you ll see a canvas in 3D that you can paint on as it rotates. Now, I wrote the Canvas code with no speci c concessions for 3D, but it works in 2D or 3D equally well. You ll notice that wherever you place your virtual pen in 3D, it s put on the canvas right below the mouse cursor as if your pen were an in nite line parallel to the z-axis.
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In many cases, ActionScript handles local, 2D coordinates and global, 3D coordinates by itself, as in Example 15-3. If need be, though, you can convert between two and three dimensions in ActionScript easily, using these methods of DisplayObject:
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globalToLocal3D() Takes a 2D global Point a point on the stage and nds out where that point is in 3D space relative to the DisplayObject. In other words, it nds what Vector3D points from the origin of the DisplayObject to the point on stage. local3DToGlobal() Takes a 3D Vector3D point in the local coordinate system and nds out where that point is drawn on stage in 2D.
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15: Working in Three Dimensions
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Example 15-4 will clarify these point projections. You ll track vertices on a rotating cube, using local3DToGlobal() to convert the vertex s position to its position on-screen. Then you ll draw on-screen where the vertex is. In this manner, you ll have some of the corners trace out a path as the cube rotates. EXAMPLE 15-4
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package { import flash.display.*; import flash.events.*; import flash.geom.*; public class ch15ex4 extends Sprite { protected var cube:Cube; protected var angularVelocity:Vector3D; protected var layers:Vector.<Shape> = new Vector.<Shape>(); protected var colors:Vector.<uint> = new <uint>[0xD97C2B,0x496B73]; protected var firstFrame:Boolean = true; public function ch15ex4() { cube = new Cube(200); cube.x = stage.stageWidth/2; cube.y = stage.stageHeight/2; addChild(cube); for (var i:int = 0; i < colors.length; i++) { layers[i] = new Shape(); addChild(layers[i]); } stage.addEventListener(MouseEvent.CLICK, onClick); addEventListener(Event.ENTER_FRAME, onEnterFrame); onClick(null); } protected function onClick(event:MouseEvent):void { var r:Function = function():Number {return Math.random() * 8 - 4}; angularVelocity = new Vector3D(r(), r(), r()); firstFrame = true; for (var i:int = 0; i < layers.length; i++) { layers[i].graphics.clear(); layers[i].graphics.lineStyle(0, colors[i], 1); } } protected function onEnterFrame(event:Event):void { cube.rotationX += angularVelocity.x; cube.rotationY += angularVelocity.y; cube.rotationZ += angularVelocity.z; for (var i:int = 0; i < layers.length; i++) { var p:Point = cube.local3DToGlobal(cube.vertices[i]); if (firstFrame) { layers[i].graphics.moveTo(p.x, p.y); } else {