// forked from makc3d's 3D Pythagoras tree (anaglyph) // forked from 3D Pythagoras tree - anaglyph version // Three-dimensional Pythagoras tree // First implementation ever, to my best knowledge :) // // Click anywhere to regenerate. // Check http://en.wikipedia.org/wiki/Pythagoras_tree for more info on subject. package { import flash.display.* import flash.events.* import flash.geom.ColorTransform; import alternativ5.engine3d.* import alternativ5.engine3d.controllers.* import alternativ5.engine3d.core.* import alternativ5.engine3d.display.* import alternativ5.engine3d.materials.* import alternativ5.engine3d.primitives.* import alternativ5.types.* use namespace alternativa3d; [SWF(width=465,height=465,frameRate=30,backgroundColor=0)] public class PythagorasTree3D extends Sprite { // tree elements (center positions, left and up vectors) // similar to http://wonderfl.kayac.com/code/18d2f77aeee90b0a3ae76dc5509a60f8bacad276 private var atA:Point3D = new Point3D, ltA:Point3D = new Point3D, upA:Point3D = new Point3D; private var atB:Point3D = new Point3D, ltB:Point3D = new Point3D, upB:Point3D = new Point3D; private var atC:Point3D = new Point3D, ltC:Point3D = new Point3D, upC:Point3D = new Point3D; private var atD:Point3D = new Point3D, ltD:Point3D = new Point3D, upD:Point3D = new Point3D; private var ltE:Point3D = new Point3D (-1, 0, 0), upE:Point3D = new Point3D (0, -1, 0); private var matD:Matrix3D = new Matrix3D; private var matE:Matrix3D = new Matrix3D; private var sA:Number, sB:Number, sC:Number; private var rA:Point3D = new Point3D, rB:Point3D = new Point3D, rC:Point3D = new Point3D; private function calculateElements (c1:Number, c2:Number):void { // using c1 and c2 in 0..1 range, select such a, b, c and d that a^2 + b^2 + c^2 = d^2 // this choise is almost completely free (we only need to make sure that d != 0) var a:Number = 0.1 + c1, c:Number = 1.1 - c1; // + var b:Number = ((c2 > 0.5) ? (c2 - 0.49) : (c2 - 0.51)) * 2; // + or - var d:Number = Math.sqrt (a * a + b * b + c * c); // + // define corresponding tree elements in some convenient frame // we are constrained by Pythagoras theorem, but orientation of planes is arbitrary // additionally, we want our tree to coincide with 2D one in boundary case of b = 0 atA.x = +a/2; atA.y = 0; atA.z = -a/2; ltA.x = +a/2; ltA.y = 0; ltA.z = 0; upA.x = 0; upA.y = 0; upA.z = -a/2; atC.x = -c/2; atC.y = b; atC.z = +c/2; ltC.x = 0; ltC.y = 0; ltC.z = -c/2; upC.x = -c/2; upC.y = 0; upC.z = 0; atD.x = +a/2; atD.y = +b/2; atD.z = +c/2; ltD.x = +a/2; ltD.y = -b/2; ltD.z = -c/2; upD.x = -c; upD.y = 0; upD.z = -a; upD.normalize (); upD.multiply (ltD.length); atD.subtract (upD); ltB.x = 0; ltB.y = -b/2; ltB.z = 0; upB.copy (upD); upB.normalize (); upB.multiply (Math.abs (b/2)); atB.copy (upB); atB.y = +b/2; // find transformation that aligns D element with 2x2 plane frame (E) // this 2x2 condition is there to use getRotations () method later var lxuD:Point3D = Point3D.cross (ltD, upD); lxuD.normalize (); lxuD.multiply (ltD.length); matD.a = -ltD.x; matD.e = -ltD.y; matD.i = -ltD.z; matD.b = -upD.x; matD.f = -upD.y; matD.j = -upD.z; matD.c = lxuD.x; matD.g = lxuD.y; matD.k = lxuD.z; var lxuE:Point3D = Point3D.cross (ltE, upE); matE.a = -ltE.x; matE.e = -ltE.y; matE.i = -ltE.z; matE.b = -upE.x; matE.f = -upE.y; matE.j = -upE.z; matE.c = lxuE.x; matE.g = lxuE.y; matE.k = lxuE.z; matD.invert (); matD.combine (matE); // transform A, B and C elements atA.subtract (atD); atA.transform (matD); ltA.transform (matD); upA.transform (matD); atB.subtract (atD); atB.transform (matD); ltB.transform (matD); upB.transform (matD); atC.subtract (atD); atC.transform (matD); ltC.transform (matD); upC.transform (matD); // calculate scales and normalize left/up vectors sA = ltA.length; ltA.normalize (); upA.normalize (); sB = ltB.length; ltB.normalize (); upB.normalize (); sC = ltC.length; ltC.normalize (); upC.normalize (); // finally, calculate corresponding rotations (re-using matE/lxuE variables) lxuE = Point3D.cross (ltA, upA); matE.a = -ltA.x; matE.e = -ltA.y; matE.i = -ltA.z; matE.b = -upA.x; matE.f = -upA.y; matE.j = -upA.z; matE.c = lxuE.x; matE.g = lxuE.y; matE.k = lxuE.z; matE.getRotations (rA); lxuE = Point3D.cross (ltB, upB); matE.a = -ltB.x; matE.e = -ltB.y; matE.i = -ltB.z; matE.b = -upB.x; matE.f = -upB.y; matE.j = -upB.z; matE.c = lxuE.x; matE.g = lxuE.y; matE.k = lxuE.z; matE.getRotations (rB); lxuE = Point3D.cross (ltC, upC); matE.a = -ltC.x; matE.e = -ltC.y; matE.i = -ltC.z; matE.b = -upC.x; matE.f = -upC.y; matE.j = -upC.z; matE.c = lxuE.x; matE.g = lxuE.y; matE.k = lxuE.z; matE.getRotations (rC); } private var planes:Array = [], planesDone:Array = []; private function step ():void { var pD:Plane = Plane (planes.shift ()); if (pD == null) return; planesDone.push (pD); var scale:Number = pD.transformation.a * pD.transformation.a + pD.transformation.e * pD.transformation.e + pD.transformation.i * pD.transformation.i; if (scale < 0.005) return; var pA:Plane = createPlane (); pA.rotationX = rA.x; pA.rotationY = rA.y; pA.rotationZ = rA.z; pA.scaleX = sA; pA.scaleY = sA; pA.scaleZ = sA; pA.x = atA.x; pA.y = atA.y; pA.z = atA.z; pD.addChild (pA); planes.push (pA); var pB:Plane = createPlane (); pB.rotationX = rB.x; pB.rotationY = rB.y; pB.rotationZ = rB.z; pB.scaleX = sB; pB.scaleY = sB; pB.scaleZ = sB; pB.x = atB.x; pB.y = atB.y; pB.z = atB.z; pD.addChild (pB); planes.push (pB); var pC:Plane = createPlane (); pC.rotationX = rC.x; pC.rotationY = rC.y; pC.rotationZ = rC.z; pC.scaleX = sC; pC.scaleY = sC; pC.scaleZ = sC; pC.x = atC.x; pC.y = atC.y; pC.z = atC.z; pD.addChild (pC); planes.push (pC); } private function regenerate (c1:Number, c2:Number):void { var p:Plane; // delete all the planes for each (p in planesDone) destroyPlane (p); planesDone.length = 0; planes.length = 0; // create base plane p = createPlane (); planes.push (p); scene.root.addChild (p); // do the math calculateElements (c1, c2); } private function destroyPlane (p:Plane):void { // this is supposed to make alternativa trash GC-friendly if (p.parent != null) p.parent.removeChild (p); if (p.hasSurface ("back")) p.setMaterialToSurface (null, "back"); if (p.hasSurface ("front")) p.setMaterialToSurface (null, "front"); p.moveAllFacesToSurface (null, true); } private function createPlane ():Plane { var p:Plane = new Plane (2, 2); p.cloneMaterialToAllSurfaces (new FillMaterial (0xFFFFFF, 0.5)); return p; } private function lightPlane (p:Plane):void { var face:Face = p.faces.peek () as Face; var dot:Number = face.globalNormal.x + face.globalNormal.y - face.globalNormal.z; if (dot < 0) dot = 0; if (dot > 1) dot = 1; var lum:Number = 0.6 + 0.4 * dot; var color:uint = 0x10101 * int (255 * lum); var mat1:FillMaterial = FillMaterial (Surface (p.surfaces ["front"]).material); mat1.color = color; var mat2:FillMaterial = FillMaterial (Surface (p.surfaces ["back"]).material); mat2.color = color; } private var scene:Scene3D; private var tripod:Object3D; private var viewL:View; private var viewR:View; public function PythagorasTree3D () { scene = new Scene3D; scene.root = new Object3D; viewL = new View; viewL.camera = new Camera3D; viewL.camera.z = -6; viewL.camera.rotationX = -0.6; viewL.camera.y = -9; tripod = new Object3D; scene.root.addChild (tripod); tripod.addChild (viewL.camera); viewL.width = 500; viewL.height = 465; addChild (viewL); viewL.x = -30; viewL.transform.colorTransform = new ColorTransform (1, 0, 0); viewR = new View; viewR.camera = new Camera3D; viewR.camera.x = 0.8; viewL.camera.addChild (viewR.camera); viewR.width = 500; viewR.height = 465; addChild (viewR); viewR.transform.colorTransform = new ColorTransform (0, 0.9, 1); viewR.blendMode = "add"; regenerate (0.1, 0.2); var s:Sprite = new Sprite; s.buttonMode = s.useHandCursor = true; s.graphics.beginFill (0, 0); s.graphics.drawRect (0, 0, 465, 465); addChild (s); s.addEventListener (MouseEvent.CLICK, onClick); addEventListener (Event.ENTER_FRAME, onEnterFrame); } private function onClick (e:MouseEvent):void { regenerate (mouseX / 465.0, mouseY / 465.0); } private function onEnterFrame (e:Event):void { // add 3 more planes var grow:Boolean = (planesDone.length < 2000); if (grow) step (); scene.calculate (); // apply lighting after global normals were set if (grow) for (var i:int = Math.max (0, planes.length - 3); i < planes.length; i++) lightPlane (planes [i]); } } }