2008 November 24 | pv3d.org

Archive for November 24th, 2008

Understanding Papervision3D: Matrix3D

Monday, November 24th, 2008 | how it works | Comments

This post will cover how you use a Matrix3D to scale, pitch, yaw, roll, and translate 3d objects:

Every 3d object within Papervision3D has a Matrix3D that defines its scale, pitch, yaw, roll, x, y, and z (changing x, y, and z is referred to as “translation” because they move a group of points equally). You will find the Matrix3D in the “transform” property of your 3d object.

The default 4 column by 4 row Matrix 3d with no scale, yaw, pitch, roll, or translation is set up as follows:

1, 0, 0, 0
0, 1, 0, 0
0, 0, 1, 0
0, 0, 0, 1

These values are stored in the “transform” property of your 3d object using a “n”, a integer defining the row, and an integer for the column:

n11, n12, n13, n14
n21, n22, n23, n24
n31, n32, n33, n34
n41, n42, n43, n44

For example: cube.transform.n11

Scale, pitch, yaw, and roll are handled in the first 3 columns and rows of the matrix (play with the explorer above to figure out how it works):

1, 0, 0
0, 1, 0
0, 0, 1

x, y, and z are all handled first 3 numbers in the last column:

0
0
0

The last row hangs around to make Matrix multiplication possible. Have fun playing with the explorer to get a hang of how 3d objects are moved around. I hope to cover some of the Matrix3D math functions in the future.

Tags: matrix

Drag and Release

Monday, November 24th, 2008 | examples | Comments

Sproing! I’ll go into “camera.unproject” and “rays” in more detail in the future.

source

package
{
	import flash.events.Event;
	import flash.events.MouseEvent;
 
	import gs.TweenMax;
	import gs.easing.Elastic;
 
	import org.papervision3d.core.geom.Lines3D;
	import org.papervision3d.core.geom.renderables.Line3D;
	import org.papervision3d.core.geom.renderables.Vertex3D;
	import org.papervision3d.core.math.Number3D;
	import org.papervision3d.events.InteractiveScene3DEvent;
	import org.papervision3d.lights.PointLight3D;
	import org.papervision3d.materials.shadematerials.FlatShadeMaterial;
	import org.papervision3d.materials.special.LineMaterial;
	import org.papervision3d.objects.primitives.Sphere;
	import org.papervision3d.view.BasicView;
 
	[SWF(width="640", height="480", backgroundColor="#000000", frameRate="60")]
	public class DragAndRelease extends BasicView
	{
		private var sphere:Sphere;
		private var line:Line3D;
		private const LENGTH:Number = 2000;
 
		private var isSpherePressed:Boolean = false;
 
		public function DragAndRelease()
		{
			viewport.interactive = true;
			camera.fov = 110;
			var light:PointLight3D = new PointLight3D();
			light.x = -1000, light.y = 1000;
 
 
			var material:FlatShadeMaterial = new FlatShadeMaterial(light, 0xcc0000);
			material.interactive = true;
			sphere = new Sphere(material, 200, 12, 12);
 
			sphere.addEventListener(InteractiveScene3DEvent.OBJECT_PRESS, objectPressHandler);
			sphere.z = LENGTH + camera.z;
			stage.addEventListener(MouseEvent.MOUSE_UP, mouseUpHandler);
 
			var lineMaterial:LineMaterial = new LineMaterial(0x00cc00);
			var lines:Lines3D = new Lines3D();
			line = new Line3D(lines, lineMaterial, 1, new Vertex3D(1000,1000,1000), new Vertex3D(-1000,0,0));
			lines.addLine(line);
 
			scene.addChild(lines);
			scene.addChild(sphere);
 
			startRendering();
		}
 
		override protected function onRenderTick(event:Event=null):void
		{
			var ray:Number3D = camera.unproject(viewport.containerSprite.mouseX, viewport.containerSprite.mouseY);
			line.v0.x = ray.x, line.v0.y = ray.y, line.v0.z = ray.z;
			line.v1.x = sphere.x, line.v1.y = sphere.y, line.v1.z = sphere.z;
 
			ray.normalize();
			ray.multiplyEq(LENGTH);
			ray = Number3D.add(ray, new Number3D(camera.x, camera.y, camera.z));
 
			if(isSpherePressed)
			{
				sphere.position = ray;
			}
 
			renderer.renderScene(scene, camera, viewport);
		}
 
		private function objectPressHandler(event:InteractiveScene3DEvent):void
		{
			TweenMax.killTweensOf(sphere);
			isSpherePressed = true;
		}
 
		private function mouseUpHandler(event:MouseEvent):void
		{
			isSpherePressed = false;
			TweenMax.to(sphere, 1, {x:0, y:0, z:LENGTH + camera.z, ease:Elastic.easeOut});
		}
	}
}