Vector

Vectors show length and direction

Tuesday, November 18th, 2008 | examples | Comments

Vectors do not have a location. That means you can start them from anywhere and they’ll still travel the same length and direction regardless. The following example demonstrates by using random starting points, but placing planes and lines along the same vector from those different starting points.

View example
source

package {
 
	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.materials.ColorMaterial;
	import org.papervision3d.materials.special.LineMaterial;
	import org.papervision3d.objects.DisplayObject3D;
	import org.papervision3d.objects.primitives.Plane;
	import org.papervision3d.view.BasicView;
 
	[SWF(width="640", height="480", backgroundColor="#000000", frameRate="60")]
	public class VectorsShowLengthAndDirection extends BasicView
	{
		private const NUM_POINTS:int = 50;
		private const NUM_STARTING_POINTS:int = 20;
 
		public function VectorsShowLengthAndDirection()
		{
			var pointA:Number3D = new Number3D(-1000, -800, 500);
			var pointB:Number3D = new Number3D(12000, 8000, 20000);
 
			var vector:Number3D = Number3D.sub(pointB, pointA);
			var vectorCopy:Number3D = new Number3D();
 
			for(var i:int = 0; i < NUM_STARTING_POINTS; i++)
			{
				//create a random starting point
				var startingPoint:Number3D = new Number3D(Math.random() * 2000 - 1000, Math.random() * 2000 - 1000, Math.random() * 2000 );
				var randColor:Number = Math.random() * 0xffffff;
				var lines:Lines3D = new Lines3D();
				var lineMaterial:LineMaterial = new LineMaterial(randColor);
				for(var j:int = 0; j < NUM_POINTS; j++)
				{
					vectorCopy.copyFrom(vector);
					var pointAlongVector:DisplayObject3D = new Plane(new ColorMaterial(randColor), 100, 100);
					vectorCopy.multiplyEq(j/NUM_POINTS);
					//use the startingPoint as the first position
					pointAlongVector.position = Number3D.add(startingPoint, vectorCopy);
					scene.addChild(pointAlongVector);
				}	
				var line:Line3D = new Line3D(lines, lineMaterial, 5, 
					new Vertex3D(startingPoint.x, startingPoint.y, startingPoint.z),
					new Vertex3D(pointAlongVector.x, pointAlongVector.y, pointAlongVector.z));
 
				lines.addLine(line);
				scene.addChild(lines);
			}
 
			singleRender();
		}
	}
}

Tags: line, math, vector

Points along a displacement vector – Part 2

Tuesday, November 18th, 2008 | snippets | Comments

While the last example was supposed to be simple to read and understand, this shows how to do the same thing with much less code by using the built-in vector methods:

Number3D.add(vectorA, vectorB); //adds two vectors
//which is much faster than writing
vector = vectorA.x + vectorB.x;
vector = vectorA.y + vectorB.y;
vector = vectorA.z + vectorB.z;
 
Number3D.sub(vectorA, vectorB); //subtracts two vectors
 
vector.multiplyEq(number); //multiplies the x, y, and z by the given number

Look at the following code and compare it to the first example to try and match up what’s happening.

private const NUM_POINTS:int = 150;
 
public function PointsAlongAVector()
{
	var pointA:Number3D = new Number3D(-1000, -800, 500);
	var pointB:Number3D = new Number3D(12000, 8000, 20000);
 
	var vector:Number3D = Number3D.sub(pointB, pointA);
	var vectorCopy:Number3D = new Number3D();
 
	for(var i:int = 0; i < NUM_POINTS; i++)
	{
		vectorCopy.copyFrom(vector);
		var pointAlongVector:DisplayObject3D = new Plane(null, 10, 10);
		vectorCopy.multiplyEq(i/NUM_POINTS);
		pointAlongVector.position = Number3D.add(pointA, vectorCopy);
 
		scene.addChild(pointAlongVector);
	}
 
	singleRender();
}

*note – you will need the latest version of Papervision3D to be able to use the “position” property of a DisplayObject3D.

Tags: line, math, vector

Points along a displacement vector – Part 1

Tuesday, November 18th, 2008 | examples | Comments

I thought it might be helpful to teach a bit about vectors.

In this example, you’ll see a starting point (the green sphere) and an ending point (the red sphere). The displacement vector between the sphere is going from the starting point to the ending point.

You find the displacement vector by subtracting the ending point’s x, y, and z from the starting point’s x, y, and z. Then you can easily add points along the vector in a loop as demonstrated in the code:

View example
source

package {
 
	import org.papervision3d.core.math.Number3D;
	import org.papervision3d.materials.WireframeMaterial;
	import org.papervision3d.objects.primitives.Sphere;
	import org.papervision3d.view.BasicView;
 
	[SWF(width="640", height="480", backgroundColor="#000000", frameRate="60")]
	public class PointsAlongAVector extends BasicView
	{
 
		private const NUM_POINTS:int = 10;
		public function PointsAlongAVector()
		{
			var pointA:Sphere = new Sphere(new WireframeMaterial(0x00cc00), 500);
			pointA.x = -1000;
			pointA.y = -800;
			pointA.z = 500;
 
			var pointB:Sphere = new Sphere(new WireframeMaterial(0xcc0000), 500);
			pointB.x = 12000;
			pointB.y = 8000;
			pointB.z = 20000;
 
			scene.addChild(pointA);
			scene.addChild(pointB);
 
			//we're going from A to B
			//so subtract A from B
			var vector:Number3D = 
			new Number3D
			(
				pointB.x - pointA.x,
				pointB.y - pointA.y,
				pointB.z - pointA.z
			);	
 
			for(var i:int = 0; i < NUM_POINTS; i++)
			{
				var pointAlongVector:Sphere = new Sphere(null, 50, 4, 4);
				//take the starting point (pointA) 
				//add the vector and multiply it by
				//the proportion of the current time through the loop (i)
				//over the total number of times through the loop (NUM_POINTS)
				pointAlongVector.x = pointA.x + (vector.x * i / NUM_POINTS);
				pointAlongVector.y = pointA.y + (vector.y * i / NUM_POINTS);
				pointAlongVector.z = pointA.z + (vector.z * i / NUM_POINTS);
 
				scene.addChild(pointAlongVector);
			}			
 
			//nothing's moving, so we only render once
			singleRender();
		}
	}
}