matrix3d.as

一个2D基于verlet的Flash物理引擎。它用AS3编写而成。Fisix的目标是应用到游戏等计算量很大的实时应用中。尽管flash比c/c++要慢,很棒的物理引擎

/*
 *  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.
 */

// ______________________________________________________________________ Matrix3D

package org.papervision3d.core.math
{


/**
* The Matrix3D class lets you create and manipulate 4x3 3D transformation matrices.
*/

/*
 Acknowledgements and references:

 > Industrial Light & Magic, a division of Lucas Digital Ltd. LLC
 > DAVID H. EBERLY3D: Game Engine Design
 > TOMAS AKENINE-MöLLER AND ERIC HAINES: Real-Time Rendering
 > THOMAS PFEIFFER: Sandy3D - www.flashsandy.org
 > The Matrix and Quaternion FAQ - http://www.j3d.org/matrix_faq/matrfaq_latest.html

*/

public class Matrix3D
{
	/**
	 * X O O O
	 * O O O O
	 * O O O O
	*/
	public var n11 :Number;

	/**
	 * O X O O
	 * O O O O
	 * O O O O
	*/
	public var n12 :Number;

	/**
	 * O O X O
	 * O O O O
	 * O O O O
	*/
	public var n13 :Number;

	/**
	 * O O O X
	 * O O O O
	 * O O O O
	*/
	public var n14 :Number;


	/**
	 * O O O O
	 * X O O O
	 * O O O O
	*/
	public var n21 :Number;

	/**
	 * O O O O
	 * O X O O
	 * O O O O
	*/
	public var n22 :Number;

	/**
	 * O O O O
	 * O O X O
	 * O O O O
	*/
	public var n23 :Number;

	/**
	 * O O O O
	 * O O O X
	 * O O O O
	*/
	public var n24 :Number;


	/**
	 * O O O O
	 * O O O O
	 * X O O O
	*/
	public var n31 :Number;

	/**
	 * O O O O
	 * O O O O
	 * O X O O
	*/
	public var n32 :Number;

	/**
	 * O O O O
	 * O O O O
	 * O O X O
	*/
	public var n33 :Number;

	/**
	 * O O O O
	 * O O O O
	 * O O O X
	*/
	public var n34 :Number;

	/**
	 * O O O O
	 * O O O O
	 * O O O O
	 * X O O O
	*/
	public var n41 :Number;

	/**
	 * O O O O
	 * O O O O
	 * O O O O
	 * O X O O
	*/
	public var n42 :Number;

	/**
	 * O O O O
	 * O O O O
	 * O O O O
	 * O O X O
	*/
	public var n43 :Number;

	/**
	 * O O O O
	 * O O O O
	 * O O O O
	 * O O O X
	*/
	public var n44 :Number;
	
	public var sid:String;
	public var type:String = "";
	
	// _________________________________________________________________________________ Matrix3D

	/**
	* The Matrix3D constructor lets you create Matrix3D objects.
	*
	* @param	args	The values to populate the matrix with. Identity matrix is returned by default.
	*/

	public function Matrix3D( args:Array=null )
	{
		if( ! args || args.length < 12 )
		{
			n11 = n22 = n33 = n44 = 1;
			n12 = n13 = n14 = n21 = n23 = n24 = n31 = n32 = n34 = n41 = n42 = n43 = 0;
		}
		else
		{
			n11 = args[0];  n12 = args[1];  n13 = args[2];  n14 = args[3];
			n21 = args[4];  n22 = args[5];  n23 = args[6];  n24 = args[7];
			n31 = args[8];  n32 = args[9];  n33 = args[10]; n34 = args[11];
			
			if( args.length == 16 )
			{
				n41 = args[12];	 n42 = args[13]; n43 = args[14]; n44 = args[15];
			}	
		}
	}

	// _________________________________________________________________________________ IDENTITY

	public static function get IDENTITY():Matrix3D
	{
		return new Matrix3D
		(
			[
				1, 0, 0, 0,
				0, 1, 0, 0,
				0, 0, 1, 0,
				0, 0, 0, 1
			]
		);
	}

	// _________________________________________________________________________________ trace

	public function toString():String
	{
		var s:String = "";

		s += int(n11*1000)/1000 + "\t\t" + int(n12*1000)/1000 + "\t\t" + int(n13*1000)/1000 + "\t\t" + int(n14*1000)/1000 +"\n";
		s += int(n21*1000)/1000 + "\t\t" + int(n22*1000)/1000 + "\t\t" + int(n23*1000)/1000 + "\t\t" + int(n24*1000)/1000 + "\n";
		s += int(n31*1000)/1000 + "\t\t" + int(n32*1000)/1000 + "\t\t" + int(n33*1000)/1000 + "\t\t" + int(n34*1000)/1000 + "\n";
		s += int(n41*1000)/1000 + "\t\t" + int(n42*1000)/1000 + "\t\t" + int(n43*1000)/1000 + "\t\t" + int(n44*1000)/1000 + "\n";

		return s;
	}

	// _________________________________________________________________________________ OPERATIONS

	public function calculateMultiply( a:Matrix3D, b:Matrix3D ):void
	{
		var a11:Number = a.n11; var b11:Number = b.n11;
		var a21:Number = a.n21; var b21:Number = b.n21;
		var a31:Number = a.n31; var b31:Number = b.n31;
		var a12:Number = a.n12; var b12:Number = b.n12;
		var a22:Number = a.n22; var b22:Number = b.n22;
		var a32:Number = a.n32; var b32:Number = b.n32;
		var a13:Number = a.n13; var b13:Number = b.n13;
		var a23:Number = a.n23; var b23:Number = b.n23;
		var a33:Number = a.n33; var b33:Number = b.n33;
		var a14:Number = a.n14; var b14:Number = b.n14;
		var a24:Number = a.n24; var b24:Number = b.n24;
		var a34:Number = a.n34; var b34:Number = b.n34;

		this.n11 = a11 * b11 + a12 * b21 + a13 * b31;
		this.n12 = a11 * b12 + a12 * b22 + a13 * b32;
		this.n13 = a11 * b13 + a12 * b23 + a13 * b33;
		this.n14 = a11 * b14 + a12 * b24 + a13 * b34 + a14;

		this.n21 = a21 * b11 + a22 * b21 + a23 * b31;
		this.n22 = a21 * b12 + a22 * b22 + a23 * b32;
		this.n23 = a21 * b13 + a22 * b23 + a23 * b33;
		this.n24 = a21 * b14 + a22 * b24 + a23 * b34 + a24;

		this.n31 = a31 * b11 + a32 * b21 + a33 * b31;
		this.n32 = a31 * b12 + a32 * b22 + a33 * b32;
		this.n33 = a31 * b13 + a32 * b23 + a33 * b33;
		this.n34 = a31 * b14 + a32 * b24 + a33 * b34 + a34;
	}

	public static function multiply( a:Matrix3D, b:Matrix3D ):Matrix3D
	{
		var m:Matrix3D = new Matrix3D();
		
		m.calculateMultiply( a, b );
		
		return m;
	}


	public function calculateMultiply3x3( a:Matrix3D, b:Matrix3D ):void
	{
		var a11:Number = a.n11; var b11:Number = b.n11;
		var a21:Number = a.n21; var b21:Number = b.n21;
		var a31:Number = a.n31; var b31:Number = b.n31;
		var a12:Number = a.n12; var b12:Number = b.n12;
		var a22:Number = a.n22; var b22:Number = b.n22;
		var a32:Number = a.n32; var b32:Number = b.n32;
		var a13:Number = a.n13; var b13:Number = b.n13;
		var a23:Number = a.n23; var b23:Number = b.n23;
		var a33:Number = a.n33; var b33:Number = b.n33;

		this.n11 = a11 * b11 + a12 * b21 + a13 * b31;
		this.n12 = a11 * b12 + a12 * b22 + a13 * b32;
		this.n13 = a11 * b13 + a12 * b23 + a13 * b33;

		this.n21 = a21 * b11 + a22 * b21 + a23 * b31;
		this.n22 = a21 * b12 + a22 * b22 + a23 * b32;
		this.n23 = a21 * b13 + a22 * b23 + a23 * b33;

		this.n31 = a31 * b11 + a32 * b21 + a33 * b31;
		this.n32 = a31 * b12 + a32 * b22 + a33 * b32;
		this.n33 = a31 * b13 + a32 * b23 + a33 * b33;
	}

	public function calculateMultiply4x4( a:Matrix3D, b:Matrix3D ):void
	{
		var a11:Number = a.n11; var b11:Number = b.n11;
		var a21:Number = a.n21; var b21:Number = b.n21;
		var a31:Number = a.n31; var b31:Number = b.n31;
		var a41:Number = a.n41; var b41:Number = b.n41;
		
		var a12:Number = a.n12; var b12:Number = b.n12;
		var a22:Number = a.n22; var b22:Number = b.n22;
		var a32:Number = a.n32; var b32:Number = b.n32;
		var a42:Number = a.n42; var b42:Number = b.n42;
		
		var a13:Number = a.n13; var b13:Number = b.n13;
		var a23:Number = a.n23; var b23:Number = b.n23;
		var a33:Number = a.n33; var b33:Number = b.n33;
		var a43:Number = a.n43; var b43:Number = b.n43;
		
		var a14:Number = a.n14; var b14:Number = b.n14;
		var a24:Number = a.n24; var b24:Number = b.n24;
		var a34:Number = a.n34; var b34:Number = b.n34;
		var a44:Number = a.n44; var b44:Number = b.n44;

		this.n11 = a11 * b11 + a12 * b21 + a13 * b31;
		this.n12 = a11 * b12 + a12 * b22 + a13 * b32;
		this.n13 = a11 * b13 + a12 * b23 + a13 * b33;
		this.n14 = a11 * b14 + a12 * b24 + a13 * b34 + a14;

		this.n21 = a21 * b11 + a22 * b21 + a23 * b31;
		this.n22 = a21 * b12 + a22 * b22 + a23 * b32;
		this.n23 = a21 * b13 + a22 * b23 + a23 * b33;
		this.n24 = a21 * b14 + a22 * b24 + a23 * b34 + a24;

		this.n31 = a31 * b11 + a32 * b21 + a33 * b31;
		this.n32 = a31 * b12 + a32 * b22 + a33 * b32;
		this.n33 = a31 * b13 + a32 * b23 + a33 * b33;
		this.n34 = a31 * b14 + a32 * b24 + a33 * b34 + a34;
		
		this.n41 = a41 * b11 + a42 * b21 + a43 * b31;
		this.n42 = a41 * b12 + a42 * b22 + a43 * b32;
		this.n43 = a41 * b13 + a42 * b23 + a43 * b33;
		this.n44 = a41 * b14 + a42 * b24 + a43 * b34 + a44;
	}
	
	public static function multiply3x3( a:Matrix3D, b:Matrix3D ):Matrix3D
	{
		var m:Matrix3D = new Matrix3D();
		
		m.calculateMultiply3x3( a, b );
		
		return m;
	}


	public function calculateAdd( a:Matrix3D, b:Matrix3D ):void
	{
		this.n11 = a.n11 + b.n11;
		this.n12 = a.n12 + b.n12;
		this.n13 = a.n13 + b.n13;
		this.n14 = a.n14 + b.n14;

		this.n21 = a.n21 + b.n21;
		this.n22 = a.n22 + b.n22;
		this.n23 = a.n23 + b.n23;
		this.n24 = a.n24 + b.n24;

		this.n31 = a.n31 + b.n31;
		this.n32 = a.n32 + b.n32;
		this.n33 = a.n33 + b.n33;
		this.n34 = a.n34 + b.n34;
	}

	public static function add( a:Matrix3D, b:Matrix3D ):Matrix3D
	{
		var m:Matrix3D = new Matrix3D();
		
		m.calculateAdd( a, b );
		
		return m;
	}


	public function calculateInverse( m:Matrix3D ):void
	{
		var d:Number = m.det;

		if( Math.abs(d) > 0.001 )
		{
			d = 1/d;
	
			var m11:Number = m.n11; var m21:Number = m.n21; var m31:Number = m.n31;
			var m12:Number = m.n12; var m22:Number = m.n22; var m32:Number = m.n32;
			var m13:Number = m.n13; var m23:Number = m.n23; var m33:Number = m.n33;
			var m14:Number = m.n14; var m24:Number = m.n24; var m34:Number = m.n34;
	
			this.n11 =	 d * ( m22 * m33 - m32 * m23 );
			this.n12 =	-d * ( m12 * m33 - m32 * m13 );
			this.n13 =	 d * ( m12 * m23 - m22 * m13 );
			this.n14 =	-d * ( m12 * (m23*m34 - m33*m24) - m22 * (m13*m34 - m33*m14) + m32 * (m13*m24 - m23*m14) );
	
			this.n21 =	-d * ( m21 * m33 - m31 * m23 );
			this.n22 =	 d * ( m11 * m33 - m31 * m13 );
			this.n23 =	-d* ( m11 * m23 - m21 * m13 );
			this.n24 =	 d * ( m11 * (m23*m34 - m33*m24) - m21 * (m13*m34 - m33*m14) + m31 * (m13*m24 - m23*m14) );
	
			this.n31 =	 d * ( m21 * m32 - m31 * m22 );
			this.n32 =	-d* ( m11 * m32 - m31 * m12 );
			this.n33 =	 d * ( m11 * m22 - m21 * m12 );
			this.n34 =	-d* ( m11 * (m22*m34 - m32*m24) - m21 * (m12*m34 - m32*m14) + m31 * (m12*m24 - m22*m14) );
		}
	}

	public static function inverse( m:Matrix3D ):Matrix3D
	{
		var inv:Matrix3D = new Matrix3D();
		
		inv.calculateInverse( m );
		
		return inv;
	}


	public function get det():Number
	{
		return	(this.n11 * this.n22 - this.n21 * this.n12) * this.n33 - (this.n11 * this.n32 - this.n31 * this.n12) * this.n23 +
				(this.n21 * this.n32 - this.n31 * this.n22) * this.n13;
	}


	public function get trace():Number
	{
		return this.n11 + this.n22 + this.n33 + 1;
	}

	// _________________________________________________________________________________ COPY

	public function copy( m:Matrix3D ):Matrix3D