/* *  PAPER    ON   ERVIS  NPAPER ISION  PE  IS ON  PERVI IO  APER  SI  PA *  AP  VI  ONPA  RV  IO PA     SI  PA ER  SI NP PE     ON AP  VI ION AP *  PERVI  ON  PE VISIO  APER   IONPA  RV  IO PA  RVIS  NP PE  IS ONPAPE *  ER     NPAPER IS     PE     ON  PE  ISIO  AP     IO PA ER  SI NP PER *  RV     PA  RV SI     ERVISI NP  ER   IO   PE VISIO  AP  VISI  PA  RV3D *  ______________________________________________________________________ *  papervision3d.org ? blog.papervision3d.org ? osflash.org/papervision3d *//* * Copyright 2006 (c) Carlos Ulloa Matesanz, noventaynueve.com. * * Permission is hereby granted, free of charge, to any person * obtaining a copy of this software and associated documentation * files (the "Software"), to deal in the Software without * restriction, including without limitation the rights to use, * copy, modify, merge, publish, distribute, sublicense, and/or sell * copies of the Software, and to permit persons to whom the * Software is furnished to do so, subject to the following * conditions: * * The above copyright notice and this permission notice shall be * included in all copies or substantial portions of the Software. * * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES * OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT * HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR * OTHER DEALINGS IN THE SOFTWARE. */// ______________________________________________________________________//                                                               Plane3Dpackage org.papervision3d.core.math{import org.papervision3d.core.geom.renderables.Vertex3D;/*** The Plane3D class represents a plane in 3D space.* * @author Tim Knip*/public class Plane3D{	/**	* The plane normal (A, B, C).	*/	public var normal: Number3D;	/**	 * D.	 */	public var d: Number;	/**	 * Constructor.	 *	 * @param	normal		The plane normal.	 * @param	ptOnPlane	A point on the plane.	 */	public function Plane3D( normal : Number3D = null, ptOnPlane : Number3D = null ) : void	{		if(normal && ptOnPlane) 		{			this.normal = normal;			this.d = -Number3D.dot(normal, ptOnPlane);		}		else		{			this.normal = new Number3D();			this.d = 0;			}	}		/**	 * Creates a plane from coefficients.	 *	 * @param	a	 * @param	b	 * @param	c	 * @param	d	 *	 * @return	The created plane.	 */	public static function fromCoefficients( a:Number, b:Number, c:Number, d:Number ) : Plane3D	{		var plane:Plane3D = new Plane3D();		plane.setCoefficients(a, b, c, d);		return plane;	}		/**	 * Creates a plane from a normal and a point.	 *	 * @param	normal	 * @param	point	 *	 * @return	The created plane.	 */	public static function fromNormalAndPoint( normal : *, point : * ) : Plane3D 	{		var n : Number3D = normal is Number3D ? normal : new Number3D(normal.x, normal.y, normal.z);		var p : Number3D = point is Number3D ? point : new Number3D(point.x, point.y, point.z);		return new Plane3D(n, p);	}		/**	 * Creates a plane from three points.	 *	 * @param	p0	First point.	 * @param	p1	Second point.	 * @param	p2	Third point.	 *	 * @return	The created plane.	 */	public static function fromThreePoints( p0:*, p1:*, p2:* ):Plane3D	{		var plane:Plane3D = new Plane3D();		var n0 : Number3D = p0 is Number3D ? p0 : new Number3D(p0.x, p0.y, p0.z);		var n1 : Number3D = p1 is Number3D ? p1 : new Number3D(p1.x, p1.y, p1.z);		var n2 : Number3D = p2 is Number3D ? p2 : new Number3D(p2.x, p2.y, p2.z);		plane.setThreePoints(n0, n1, n2);		return plane;	}		/**	 * Get the closest point on the plane.	 *	 * @param	point		The point to 'project'.	 * @param 	ptOnPlane	A known point on the plane.	 */	public function closestPointOnPlane( point : Number3D, ptOnPlane : Number3D ) : Number3D	{		var dist : Number = Number3D.dot(this.normal, Number3D.sub(point, ptOnPlane));		var ret : Number3D = point.clone();		ret.x -= (dist * this.normal.x);		ret.y -= (dist * this.normal.y);		ret.z -= (dist * this.normal.z);		return ret;	}		/**	 * distance of point to plane.	 * 	 * @param	v	 * @return	 */	public function distance( pt:* ):Number	{		var p:Number3D = pt is Vertex3D ? pt.toNumber3D() : pt;		return Number3D.dot(p, normal) + d;	}		/**	 * normalize.	 * 	 * @return	 */	public function normalize():void	{		var n:Number3D = this.normal;				//compute the length of the vector		var len:Number = Math.sqrt(n.x*n.x + n.y*n.y + n.z*n.z);				// normalize		n.x /= len;		n.y /= len;		n.z /= len;		this.d /= len;	}		/**	 * Sets this plane from ABCD coefficients.	 *	 * @param	a	 * @param	b	 * @param	c	 * @param	d	 */	public function setCoefficients( a:Number, b:Number, c:Number, d:Number ):void	{		// set the normal vector		this.normal.x = a;		this.normal.y = b;		this.normal.z = c;		this.d = d;				normalize();	}		/**	 * Sets this plane from a normal and a point.	 *	 * @param	normal	 * @param	pt	 */	public function setNormalAndPoint( normal:Number3D, pt:Number3D ):void	{		this.normal = normal;		this.d = -Number3D.dot(normal, pt);	}		/**	 * Sets this plane from three points.	 *	 * @param	p0	 * @param	p1	 * @param	p2	 */	public function setThreePoints( p0:Number3D, p1:Number3D, p2:Number3D ):void	{						var ab:Number3D = Number3D.sub(p1, p0);		var ac:Number3D = Number3D.sub(p2, p0);		this.normal = Number3D.cross(ab, ac);		this.normal.normalize();		this.d = -Number3D.dot(normal, p0);	}		/**	 * Projects points onto this plane. 	 * <p>Passed points should be in the XY-plane. If the points have Z=0 then the points are	 * projected exactly on the plane. When however Z is greater then zero, the points are	 * moved 'out of the plane' by a distance Z. Negative values for Z move the points 'into the plane'.</p>	 *	 * @param	points	Array of points (any object with x, y, z props).	 * @param	origin	Where to move the points.	 */	public function projectPoints( points : Array, origin : Number3D = null ) : void {		// use other up-vector if angle between plane-normal and up-vector approaches zero.		var dot : Number = Number3D.dot(_yUP, this.normal);				// when the dot-product approaches 1 the angle approaches 0		var up : Number3D = Math.abs(dot) > 0.99 ? _zUP : _yUP;				// get side vector		var side:Number3D = Number3D.cross(up, normal);		side.normalize();		// adjust up vector		up = Number3D.cross(normal, side);		up.normalize();				// create the matrix!		var matrix : Matrix3D = new Matrix3D([			side.x, up.x, normal.x, 0,			side.y, up.y, normal.y, 0,			side.z, up.z, normal.z, 0,			0, 0, 0, 1]);				// translate if wanted			if(origin)			matrix = Matrix3D.multiply(Matrix3D.translationMatrix(origin.x, origin.y, origin.z), matrix);				// project!		var n : Number3D = new Number3D();		for each( var point:* in points ) {			n.x = point["x"];			n.y = point["y"];			n.z = point["z"];						Matrix3D.multiplyVector(matrix, n);						point["x"] = n.x;			point["y"] = n.y;			point["z"] = n.z;		}	}		public function toString():String	{		return "[a:" + normal.x  +" b:" +normal.y + " c:" +normal.z + " d:" + d + "]";	}	private static var _yUP : Number3D = new Number3D(0, 1, 0);		private static var _zUP : Number3D = new Number3D(0, 0, 1);}}