Instead of Vectors of Vector3D objects, store vertices in a Vector of Numbers; you and Flash Player have to trust each other that those numbers refer to components of vertices, ordered in the proper manner, which is to say, x1 ,y1 ,z1 ,x2 ,y2 ,z2 , and so on. Once you store vertices this way, you can use the static Utils3D method projectVectors(), which projects a whole batch of points at once:

function projectVectors(projectionMatrix:Matrix3D, vertices:Vector.<Number>, projectedPoints:Vector.<Number>, textureCoords:Vector.<Number>):void

The projectionMatrix should be familiar as the matrix used to project vertices in 3D space onto screen space. The vertices argument contains the original 3D vertices to project, attened out into repeating sets of three x, y, and z coordinates as just described. The projectedPoints list, however, holds the result of the projection you must send in a valid, non-null Vector.<Number>, but the method itself sets its value this is an alternative to returning the value; notice that the return type is null. After the method is through, the projectedPoints list contains the vertices position on the screen in 2D, as a list of coordinate components ordered x1 ,y1 ,x2 ,y2 ,x3 ,y3 and so on with only two values per coordinate. Likewise, textureCoords is modi ed by the method. I ll explain how when I cover texture mapping; for now, you can send this parameter an empty but valid Vector.<Number>. In Example 40-2, you use vertices in a at layout to take advantage of projectVectors(). You also experiment with another, faster way of drawing the vertices. EXAMPLE 40-2

package { import flash.display.*; import flash.events.Event; import flash.geom.*; public class ch40ex2 extends Sprite { protected var perspective:PerspectiveProjection; protected var viewMatrix:Matrix3D; protected var modelMatrix:Matrix3D; protected var model:Plot3D; protected var projectedPoints:Vector.<Number> = new Vector.<Number>(); protected var texturePoints:Vector.<Number> = new Vector.<Number>(); protected var drawCommands:Vector.<int>; public function ch40ex2() { stage.quality = StageQuality.MEDIUM; this.x = stage.stageWidth/2; this.y = stage.stageHeight/2; perspective = new PerspectiveProjection(); perspective.fieldOfView = 50; perspective.projectionCenter = new Point(0, 0);

EXAMPLE 40-2

(continued)

viewMatrix = new Matrix3D(); viewMatrix.appendTranslation(0, 4, 11); viewMatrix.appendRotation(26, Vector3D.X_AXIS); viewMatrix.append(perspective.toMatrix3D()); modelMatrix = new Matrix3D(); model = new Plot3D(); model.plot(new Rectangle(-3, -3, 6, 6), 70); addEventListener(Event.ENTER_FRAME, onEnterFrame); } protected function onEnterFrame(event:Event):void { modelMatrix.appendRotation(2, Vector3D.Y_AXIS); var concatenatedMatrix:Matrix3D = modelMatrix.clone(); concatenatedMatrix.append(viewMatrix); Utils3D.projectVectors( concatenatedMatrix, model.vertices, projectedPoints, texturePoints); graphics.clear(); graphics.lineStyle(0, 1); if (!drawCommands) { drawCommands = new Vector.<int>(); for (var i:int = 0; i < projectedPoints.length; i+=2) { drawCommands.push(((i/2) % model.resolution == 0) GraphicsPathCommand.MOVE_TO : GraphicsPathCommand.LINE_TO); } } graphics.drawPath(drawCommands, projectedPoints); } } } import flash.geom.Rectangle; import flash.geom.Vector3D; class Plot3D { public var vertices:Vector.<Number>; public var tOffset:Number = 0; public var resolution:Number; public function plot(xzBounds:Rectangle, resolution:Number = 200):void { vertices = new Vector.<Number>(); this.resolution = resolution; var r:Rectangle = xzBounds; for (var z:Number = r.top; z < r.bottom; z += r.height/resolution) { for (var x:Number = r.left; x < r.right; x += r.width/resolution) { var y:Number = Math.sin(Math.pow(x, 2) + Math.pow(z, 2) + tOffset); vertices.push(x, y, z); } } } }

In the example, after projectVectors() lls up projectedPoints with the screen-space 2D points of the model, you batch up the drawing commands as well with drawPath(). If you remember from 35, drawPath() takes a list of commands and a list of points. You have the list of

points you d like to draw, so all that remains is a set of drawing commands; here I ve constructed one that connects all vertices at the same z value with a line. Finally, you pulled up all reusable Vectors to be instance variables, so that they don t have to be created anew every frame, an easy and effective optimization. Figure 40-1 shows the results for both Example 40-1 and Example 40-2.

FIGURE 40-1