quaternion
Free rotation using Quaternions
package { import flash.display.Bitmap; import flash.events.Event; import flash.events.MouseEvent; import org.papervision3d.core.geom.renderables.Vertex3D; import org.papervision3d.core.math.Number3D; import org.papervision3d.core.math.Plane3D; import org.papervision3d.core.math.Quaternion; import org.papervision3d.lights.PointLight3D; import org.papervision3d.materials.BitmapMaterial; import org.papervision3d.objects.DisplayObject3D; import org.papervision3d.objects.primitives.Sphere; import org.papervision3d.view.BasicView; [SWF(width="640", height="480", backgroundColor="#000000", frameRate="60")] public class QuaternionExample extends BasicView { private const XYPLANE:Number3D = new Number3D(0, 0, 1); private const RADIUS:Number = 400; private const SPEED:Number = .05; private var plane3D:Plane3D = new Plane3D(XYPLANE, Number3D.ZERO);; private var sphere:Sphere; [Embed(source="assets/lake_640.jpg")] private var materialAsset:Class; public function QuaternionExample() { var light:PointLight3D = new PointLight3D(); var bitmap:Bitmap = new materialAsset() as Bitmap; var material:BitmapMaterial = new BitmapMaterial(bitmap.bitmapData); sphere = new Sphere(material, RADIUS, 30, 30); scene.addChild(sphere); startRendering(); stage.addEventListener(MouseEvent.CLICK, clickHandler); } private function clickHandler(event:MouseEvent):void { //quick reset sphere.copyTransform(new DisplayObject3D()); } override protected function onRenderTick(event:Event=null):void { var ray:Number3D = camera.unproject(viewport.containerSprite.mouseX, viewport.containerSprite.mouseY); ray = Number3D.add(ray, camera.position); var cameraVertex3D:Vertex3D = new Vertex3D(camera.x, camera.y, camera.z); var rayVertex3D:Vertex3D = new Vertex3D(ray.x, ray.y, ray.z); var intersectPoint:Vertex3D = plane3D.getIntersectionLine(cameraVertex3D, rayVertex3D); var velocityX:Number = intersectPoint.x * SPEED; var velocityY:Number = intersectPoint.y * SPEED; var velocityZ:Number = intersectPoint.y * SPEED; var difference:Number3D = new Number3D(-velocityX, -velocityY, -velocityZ); var distance:Number = Math.sqrt(difference.x * difference.x + difference.y * difference.y); var rotationAxis:Number3D = Number3D.cross(difference, XYPLANE); rotationAxis.normalize(); var rotation:Quaternion = Quaternion.createFromAxisAngle(rotationAxis.x, rotationAxis.y, rotationAxis.z, distance/RADIUS); rotation.normalize(); sphere.transform.calculateMultiply3x3(rotation.matrix, sphere.transform); renderer.renderScene(scene, camera, viewport); } } }
I hope to be able to do a write-up explaining Quaternions next week.
Using Slerp to move around a Sphere
package { import flash.events.Event; import org.papervision3d.core.math.Quaternion; import org.papervision3d.core.utils.Mouse3D; import org.papervision3d.events.InteractiveScene3DEvent; import org.papervision3d.lights.PointLight3D; import org.papervision3d.materials.ColorMaterial; import org.papervision3d.materials.shadematerials.FlatShadeMaterial; import org.papervision3d.objects.primitives.Plane; import org.papervision3d.objects.primitives.Sphere; import org.papervision3d.view.BasicView; import org.papervision3d.view.layer.ViewportLayer; import org.papervision3d.view.layer.util.ViewportLayerSortMode; [SWF(width="640", height="480", backgroundColor="#000000", frameRate="60")] public class SlerpExample extends BasicView { private const RADIUS:Number = 400; private var planeQuat:Quaternion = new Quaternion(); private var mouseQuat:Quaternion = new Quaternion(); private var slerpQuat:Quaternion = new Quaternion(); private var plane:Plane; private var sphere:Sphere; private var mouse3D:Mouse3D; private var slerp:Number = 0; public function SlerpExample() { viewport.interactive = true; Mouse3D.enabled = true; mouse3D = viewport.interactiveSceneManager.mouse3D; var light:PointLight3D = new PointLight3D(); var material:FlatShadeMaterial = new FlatShadeMaterial(light, 0xffffff); material.interactive = true; plane = new Plane(new ColorMaterial(0xcc0000), 50, 50); plane.z = -RADIUS; viewport.containerSprite.sortMode = ViewportLayerSortMode.INDEX_SORT; var planeViewportLayer:ViewportLayer = new ViewportLayer(viewport, plane); planeViewportLayer.layerIndex = 1; viewport.containerSprite.addLayer(planeViewportLayer); sphere = new Sphere(material, RADIUS, 30, 30); sphere.addEventListener(InteractiveScene3DEvent.OBJECT_CLICK, objectClickHandler); scene.addChild(sphere); scene.addChild(plane); startRendering(); } private function resetQuats():void { slerp = 0; planeQuat = Quaternion.createFromMatrix(plane.transform); mouseQuat = Quaternion.createFromMatrix(mouse3D.transform); } private function objectClickHandler(event:InteractiveScene3DEvent):void { resetQuats(); } override protected function onRenderTick(event:Event=null):void { slerp += (1 - slerp) * .1; slerpQuat = Quaternion.slerp(planeQuat, mouseQuat, slerp); plane.transform = slerpQuat.matrix; plane.moveBackward(RADIUS); renderer.renderScene(scene, camera, viewport); } } }
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