Matrix3D.as - papervision3d - Open Source realtime 3D engine for Flash

Source path: svn/ trunk/ as3/ trunk/ src/ org/ papervision3d/ core/ math/ Matrix3D.as

‹r708

r942

package org.papervision3d.core.math
{
	import org.papervision3d.Papervision3D;
	
	/**
	 * The Matrix3D class lets you create and manipulate 4x3 3D transformation matrices.
	 */

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;

	// temp objects to save constant instantiation of objects. 

	static private var temp : Matrix3D = Matrix3D.IDENTITY; 
	
	static private var n3Di : Number3D = Number3D.ZERO; 
	static private var n3Dj : Number3D = Number3D.ZERO; 
	static private var n3Dk : Number3D = Number3D.ZERO; 
	
	// _________________________________________________________________________________ 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 )
	{
		 
		reset(args); 
		//trace("new matrix");
	}
	
	// sets the properties of the Matrix without creating a new one. 
	public function reset( args:Array = null) : void
	{
		
		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];
			} 
			else
			{
				n41 = n42 = n43 = 0;
				n44 = 1;
			}
		}		
	}

	// _________________________________________________________________________________ IDENTITY

	public static function get IDENTITY():Matrix3D
	{
		//trace("Matrix.IDENTITY"); 
		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
	{
		//trace("matrix.multiply"); 
		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 function calculateSkewSymmetric( a:Number3D ) : void
	{
		this.n11 = 0;		this.n12 = -a.z;		this.n13 = a.y;
		this.n21 = a.z;		this.n22 = 0;			this.n23 = -a.x;
		this.n31 = -a.y;	this.n32 = a.x;			this.n33 = 0;	
	}
		
	public static function multiply3x3( a:Matrix3D, b:Matrix3D ):Matrix3D
	{
		//trace("Multiply3x3"); 
		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
	{
		//trace("matrix.add"); 
		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 function calculateTranspose():void
	{
		var n11	:Number = this.n11;
		var n12	:Number = this.n21;
		var n13	:Number = this.n31;
		var n14	:Number = this.n41;
		
		var n21	:Number = this.n12;
		var n22	:Number = this.n22;
		var n23	:Number = this.n32;
		var n24	:Number = this.n42;
		
		var n31	:Number = this.n13;
		var n32	:Number = this.n23;
		var n33	:Number = this.n33;
		var n34	:Number = this.n43;
		
		var n41	:Number = this.n14;
		var n42	:Number = this.n24;
		var n43	:Number = this.n34;
		var n44	:Number = this.n44;
		
		this.n11 = n11;		this.n12 = n12; 	this.n13 = n13; 	this.n14 = n14;
		this.n21 = n21;		this.n22 = n22; 	this.n23 = n23; 	this.n24 = n24;
		this.n31 = n31;		this.n32 = n32; 	this.n33 = n33; 	this.n34 = n34;
		this.n41 = n41;		this.n42 = n42; 	this.n43 = n43; 	this.n44 = n44;
	}
	
	public static function inverse( m:Matrix3D ):Matrix3D
	{
		var inv:Matrix3D = new Matrix3D();
		inv.calculateInverse( m );
		return inv;
	}
	
	public function invert() : void
	{
		temp.copy(this); 	
		calculateInverse(temp); 
		
	}

	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
	{
		this.n11 = m.n11;	this.n12 = m.n12;
		this.n13 = m.n13;	this.n14 = m.n14;

		this.n21 = m.n21;	this.n22 = m.n22;
		this.n23 = m.n23;	this.n24 = m.n24;

		this.n31 = m.n31;	this.n32 = m.n32;
		this.n33 = m.n33;	this.n34 = m.n34;

		return this;
	}


	public function copy3x3( m:Matrix3D ):Matrix3D
	{
		this.n11 = m.n11;   this.n12 = m.n12;   this.n13 = m.n13;
		this.n21 = m.n21;   this.n22 = m.n22;   this.n23 = m.n23;
		this.n31 = m.n31;   this.n32 = m.n32;   this.n33 = m.n33;

		return this;
	}


	public static function clone( m:Matrix3D ):Matrix3D
	{
		//trace("matrix3D.clone"); 
		return new Matrix3D
		(
			[
				m.n11, m.n12, m.n13, m.n14,
				m.n21, m.n22, m.n23, m.n24,
				m.n31, m.n32, m.n33, m.n34
			]
		);
	}

	// _________________________________________________________________________________ VECTOR

	public static function multiplyVector( m:Matrix3D, v:Number3D ):void
	{
		var vx:Number = v.x;
		var vy:Number = v.y;
		var vz:Number = v.z;

		v.x = vx * m.n11 + vy * m.n12 + vz * m.n13 + m.n14;
		v.y = vx * m.n21 + vy * m.n22 + vz * m.n23 + m.n24;
		v.z = vx * m.n31 + vy * m.n32 + vz * m.n33 + m.n34;
	}


	public static function multiplyVector3x3( m:Matrix3D, v:Number3D ):void
	{
		var vx:Number = v.x;
		var vy:Number = v.y;
		var vz:Number = v.z;

		v.x = vx * m.n11 + vy * m.n12 + vz * m.n13;
		v.y = vx * m.n21 + vy * m.n22 + vz * m.n23;
		v.z = vx * m.n31 + vy * m.n32 + vz * m.n33;
	}

	public static function multiplyVector4x4( m:Matrix3D, v:Number3D ):void
	{
		var vx:Number = v.x;
		var vy:Number = v.y;
		var vz:Number = v.z;
		var vw:Number = 1.0 / (vx * m.n41 + vy * m.n42 + vz * m.n43 + m.n44);
		
		v.x = vx * m.n11 + vy * m.n12 + vz * m.n13 + m.n14;
		v.y = vx * m.n21 + vy * m.n22 + vz * m.n23 + m.n24;
		v.z = vx * m.n31 + vy * m.n32 + vz * m.n33 + m.n34;
		
		v.x *= vw;
		v.y *= vw;
		v.z *= vw;
	}
	
	public static function rotateAxis( m:Matrix3D, v:Number3D ):void
	{
		var vx:Number = v.x;
		var vy:Number = v.y;
		var vz:Number = v.z;

		v.x = vx * m.n11 + vy * m.n12 + vz * m.n13;
		v.y = vx * m.n21 + vy * m.n22 + vz * m.n23;
		v.z = vx * m.n31 + vy * m.n32 + vz * m.n33;

		v.normalize();
	}

/*
	public static function projectVector( m:Matrix3D, v:Number3D ):void
	{
		var c:Number = 1 / ( v.x * m.n41 + v.y * m.n42 + v.z * m.n43 + 1 );

		multiplyVector( m, v );

		v.x = v.x * c;
		v.y = v.y * c;
		v.z = 0;
	}
*/

	// _________________________________________________________________________________ EULER

/*
	public static function matrix2eulerOLD( m:Matrix3D ):Number3D
	{
		var angle:Number3D = new Number3D();

		var d :Number = -Math.asin( Math.max( -1, Math.min( 1, m.n13 ) ) ); // Calculate Y-axis angle
		var c :Number =  Math.cos( d );

		angle.y = d * toDEGREES;

		var trX:Number, trY:Number;

		if( Math.abs( c ) > 0.005 )  // Gimball lock?
		{
			trX =  m.n33 / c;  // No, so get X-axis angle
			trY = -m.n23 / c;

			angle.x = Math.atan2( trY, trX ) * toDEGREES;

			trX =  m.n11 / c;  // Get Z-axis angle
			trY = -m.n12 / c;

			angle.z = Math.atan2( trY, trX ) * toDEGREES;
		}
		else  // Gimball lock has occurred
		{
			angle.x = 0;  // Set X-axis angle to zero

			trX = m.n22;  // And calculate Z-axis angle
			trY = m.n21;

			angle.z = Math.atan2( trY, trX ) * toDEGREES;
		}

		// TODO: Clamp all angles to range

		return angle;
	}
	
	public static function matrix2euler2( t:Matrix3D, rot:Number3D = null, scale:Number3D=null):Number3D
	{
		if(!rot) rot = Number3D.ZERO; 

		// Normalize the local x, y and z axes to remove scaling.
		n3Di.reset( t.n11, t.n21, t.n31 );
		n3Dj.reset( t.n12, t.n22, t.n32 );
		n3Dk.reset( t.n13, t.n23, t.n33 );

		n3Di.normalize();
		n3Dj.normalize();
		n3Dk.normalize();

		temp.reset([
			n3Di.x, n3Dj.x, n3Dk.x, 0,
			n3Di.y, n3Dj.y, n3Dk.y, 0,
			n3Di.z, n3Dj.z, n3Dk.z, 0
		]);

		var m:Matrix3D = temp;

	    // Extract the first angle, rot.x
		rot.x = Math.atan2( m.n23, m.n33 ); // rot.x = Math<T>::atan2 (M[1][2], M[2][2]);
	
		// Remove the rot.x rotation from M, so that the remaining
		// rotation, N, is only around two axes, and gimbal lock
		// cannot occur.
		var rx:Matrix3D = Matrix3D.rotationX( -rot.x );
		var n:Matrix3D = Matrix3D.multiply( rx, m );

		// Extract the other two angles, rot.y and rot.z, from N.
		var cy:Number = Math.sqrt( n.n11 * n.n11 + n.n21 * n.n21); // T cy = Math<T>::sqrt (N[0][0]*N[0][0] + N[0][1]*N[0][1]);
		rot.y = Math.atan2( -n.n31, cy ); // rot.y = Math<T>::atan2 (-N[0][2], cy);
		rot.z = Math.atan2( -n.n12, n.n11 ); //rot.z = Math<T>::atan2 (-N[1][0], N[1][1]);

		// Fix angles
		if( rot.x == Math.PI )
		{
			if( rot.y > 0 )
				rot.y -= Math.PI;
			else
				rot.y += Math.PI;

			rot.x = 0;
			rot.z += Math.PI;
		}

		// Convert to degrees if needed 
		// Shouldn't this have a check for Papervision3D.useDEGREES? 
		
		rot.x *= toDEGREES;
		rot.y *= toDEGREES;
		rot.z *= toDEGREES;
		
		return rot;
	}
	*/	
	
	public static function matrix2euler( m :Matrix3D, euler:Number3D=null, scale:Number3D=null ) : Number3D
	{
		euler = euler || new Number3D();
		
		// need to get rid of scale
		// TODO: whene scale is uniform, we can save some cycles. s = 3x3 determinant i beleive
		var sx		:Number = (scale && scale.x == 1) ? 1 : Math.sqrt(m.n11 * m.n11 + m.n21 * m.n21 + m.n31 * m.n31);
		var sy		:Number = (scale && scale.y == 1) ? 1 : Math.sqrt(m.n12 * m.n12 + m.n22 * m.n22 + m.n32 * m.n32);
		var sz		:Number = (scale && scale.z == 1) ? 1 : Math.sqrt(m.n13 * m.n13 + m.n23 * m.n23 + m.n33 * m.n33);
		
		var n11		:Number = m.n11 / sx;
		var n21		:Number = m.n21 / sy;
		var n31		:Number = m.n31 / sz;
		var n32		:Number = m.n32 / sz;
		var n33		:Number = m.n33 / sz;
		
		n31 = n31 > 1 ? 1 : n31;
		n31 = n31 < -1 ? -1 : n31;
		
		// zyx
		euler.y = Math.asin(-n31);
		euler.z = Math.atan2(n21, n11);
		euler.x = Math.atan2(n32, n33);

		// TODO: fix singularities
		
		// yzx
		//euler.z = Math.asin(-m.n21);
		//euler.y = Math.atan2(m.n31, m.n11);
		//euler.x = Math.atan2(-m.n23, m.n22);
		
		// zxy
		//euler.x = Math.asin(-m.n32);
		//euler.z = Math.atan2(-m.n12, m.n22);
		//euler.y = Math.atan2(-m.n31, m.n33);
		
		if(Papervision3D.useDEGREES)
		{
			euler.x *= toDEGREES;
			euler.y *= toDEGREES;
			euler.z *= toDEGREES;
		}
		
		//  Clamp values
       // euler.x = euler.x < 0 ? euler.x + 360 : euler.x;
       // euler.y = euler.y < 0 ? euler.y + 360 : euler.y;
       // euler.z = euler.z < 0 ? euler.z + 360 : euler.z;
        
		return euler;
	}
	
	public static function euler2matrix( deg:Number3D ):Matrix3D
	{
		//trace("euler2matrix"); 
		
		temp.reset();
		var m:Matrix3D = temp;
		 
		m = temp; 

		var ax:Number = deg.x * toRADIANS;
		var ay:Number = deg.y * toRADIANS;
		var az:Number = deg.z * toRADIANS;

		var a:Number = Math.cos( ax );
		var b:Number = Math.sin( ax );
		var c:Number = Math.cos( ay );
		var d:Number = Math.sin( ay );
		var e:Number = Math.cos( az );
		var f:Number = Math.sin( az );

		var ad:Number = a * d;
		var bd:Number = b * d;

		m.n11 =  c  * e;
		m.n12 = -c  * f;
		m.n13 =  d;
		m.n21 =  bd * e + a * f;
		m.n22 = -bd * f + a * e;
		m.n23 = -b  * c;
		m.n31 = -ad * e + b * f;
		m.n32 =  ad * f + b * e;
		m.n33 =  a  * c;

		return m;
	}

	// _________________________________________________________________________________ ROTATION

	public static function rotationX( rad:Number ):Matrix3D
	{
		//trace("rotationX"); 
		var m :Matrix3D = IDENTITY;
		
		var c :Number   = Math.cos( rad );
		var s :Number   = Math.sin( rad );

		m.n22 =  c;
		m.n23 = -s;
		m.n32 =  s;
		m.n33 =  c;

		return m;
	}

	public static function rotationY( rad:Number ):Matrix3D
	{
		//trace("rotationY"); 
		var m :Matrix3D = IDENTITY;
		var c :Number   = Math.cos( rad );
		var s :Number   = Math.sin( rad );

		m.n11 =  c;
		m.n13 = -s;
		m.n31 =  s;
		m.n33 =  c;

		return m;
	}

	public static function rotationZ( rad:Number ):Matrix3D
	{
		//trace("rotationZ"); 
		var m :Matrix3D = IDENTITY;
		var c :Number   = Math.cos( rad );
		var s :Number   = Math.sin( rad );

		m.n11 =  c;
		m.n12 = -s;
		m.n21 =  s;
		m.n22 =  c;

		return m;
	}

	public static function rotationMatrix( x:Number, y:Number, z:Number, rad:Number, targetmatrix:Matrix3D = null ):Matrix3D
	{
		
		var m:Matrix3D;
		if(!targetmatrix) 
		{
			//trace("rotationmatrix"); 
			m = IDENTITY;
		}
		else m = targetmatrix; 
		
		var nCos:Number	= Math.cos( rad );
		var nSin:Number	= Math.sin( rad );
		var scos:Number	= 1 - nCos;

		var sxy	:Number = x * y * scos;
		var syz	:Number = y * z * scos;
		var sxz	:Number = x * z * scos;
		var sz	:Number = nSin * z;
		var sy	:Number = nSin * y;
		var sx	:Number = nSin * x;

		m.n11 =  nCos + x * x * scos;
		m.n12 = -sz   + sxy;
		m.n13 =  sy   + sxz;
		m.n14 = 0;
		
		m.n21 =  sz   + sxy;
		m.n22 =  nCos + y * y * scos;
		m.n23 = -sx   + syz;
		m.n24 = 0;
		
		m.n31 = -sy   + sxz;
		m.n32 =  sx   + syz;
		m.n33 =  nCos + z * z * scos;
		m.n34 = 0;
		
		return m;
	}

	public static function rotationMatrixWithReference( axis:Number3D, rad:Number, ref:Number3D ):Matrix3D
	{
		var m:Matrix3D = Matrix3D.translationMatrix( ref.x, -ref.y, ref.z );

		m.calculateMultiply( m, Matrix3D.rotationMatrix( axis.x, axis.y, axis.z, rad ) );
		m.calculateMultiply( m, Matrix3D.translationMatrix ( -ref.x, ref.y, -ref.z ) );

		return m;
	}

	// _________________________________________________________________________________ TRANSFORM

	public static function translationMatrix( x:Number, y:Number, z:Number ):Matrix3D
	{
		//trace("translation matrix"); 
		var m:Matrix3D = IDENTITY;

		m.n14 = x;
		m.n24 = y;
		m.n34 = z;

		return m;
	}

	public static function scaleMatrix( x:Number, y:Number, z:Number ):Matrix3D
	{
		//trace("scalematrix"); 
		var m:Matrix3D = IDENTITY;

		m.n11 = x;
		m.n22 = y;
		m.n33 = z;

		return m;
	}

	// _________________________________________________________________________________ QUATERNIONS

	public static function magnitudeQuaternion( q:Object ):Number
    {
		return( Math.sqrt( q.w * q.w + q.x * q.x + q.y * q.y + q.z * q.z ) );
    }


	public static function normalizeQuaternion( q:Object ):Object
	{
		var mag:Number = magnitudeQuaternion( q );

		q.x /= mag;
		q.y /= mag;
		q.z /= mag;
		q.w /= mag;

		return q;
	}


	public static function axis2quaternion( x:Number, y:Number, z:Number, angle:Number ):Object
	{
		var sin:Number = Math.sin( angle / 2 );
		var cos:Number = Math.cos( angle / 2 );

		var q:Object = new Object();

		q.x = x * sin;
		q.y = y * sin;
		q.z = z * sin;
		q.w = cos;

		return normalizeQuaternion( q );
	}


	public static function euler2quaternion( ax:Number, ay:Number, az:Number, targetquat:Quaternion = null  ):Quaternion
    {
		var fSinPitch       :Number = Math.sin( ax * 0.5 );
		var fCosPitch       :Number = Math.cos( ax * 0.5 );
		var fSinYaw         :Number = Math.sin( ay * 0.5 );
		var fCosYaw         :Number = Math.cos( ay * 0.5 );
		var fSinRoll        :Number = Math.sin( az * 0.5 );
		var fCosRoll        :Number = Math.cos( az * 0.5 );
		var fCosPitchCosYaw :Number = fCosPitch * fCosYaw;
		var fSinPitchSinYaw :Number = fSinPitch * fSinYaw;

		var q:Quaternion;
		if(!targetquat) q = new Quaternion();
		else q = targetquat; 

		q.x = fSinRoll * fCosPitchCosYaw     - fCosRoll * fSinPitchSinYaw;
		q.y = fCosRoll * fSinPitch * fCosYaw + fSinRoll * fCosPitch * fSinYaw;
		q.z = fCosRoll * fCosPitch * fSinYaw - fSinRoll * fSinPitch * fCosYaw;
		q.w = fCosRoll * fCosPitchCosYaw     + fSinRoll * fSinPitchSinYaw;

		return q;
    }

	// TODO (LOW) rewrite so that this takes an actual Quaternion object

	public static function quaternion2matrix( x:Number, y:Number, z:Number, w:Number, targetmatrix:Matrix3D = null ):Matrix3D
	{
		var xx:Number = x * x;
		var xy:Number = x * y;
		var xz:Number = x * z;
		var xw:Number = x * w;

		var yy:Number = y * y;
		var yz:Number = y * z;
		var yw:Number = y * w;

		var zz:Number = z * z;
		var zw:Number = z * w;
		
		var m:Matrix3D;
		
		if(!targetmatrix) 
		{
			//trace("quat to matrix"); 
			m  = IDENTITY;
		}
		else 
		{
			m = targetmatrix ;
		}
		m.n11 = 1 - 2 * ( yy + zz );
		m.n12 =     2 * ( xy - zw );
		m.n13 =     2 * ( xz + yw );

		m.n21 =     2 * ( xy + zw );
		m.n22 = 1 - 2 * ( xx + zz );
		m.n23 =     2 * ( yz - xw );

		m.n31 =     2 * ( xz - yw );
		m.n32 =     2 * ( yz + xw );
		m.n33 = 1 - 2 * ( xx + yy );

		return m;
	}


	public static function multiplyQuaternion( a:Object, b:Object ):Object
    {
		var ax:Number = a.x;  var ay:Number = a.y;  var az:Number = a.z;  var aw:Number = a.w;
		var bx:Number = b.x;  var by:Number = b.y;  var bz:Number = b.z;  var bw:Number = b.w;

		var q:Object = new Object();

		q.x = aw*bx + ax*bw + ay*bz - az*by;
		q.y = aw*by + ay*bw + az*bx - ax*bz;
		q.z = aw*bz + az*bw + ax*by - ay*bx;
		q.w = aw*bw - ax*bx - ay*by - az*bz;

		return q;
    }


	// _________________________________________________________________________________ TRIG

	static private var toDEGREES :Number = 180/Math.PI;
	static private var toRADIANS :Number = Math.PI/180;
	
	static private var _sin:Function = Math.sin;
	static private var _cos:Function = Math.cos;
		
		
	}
}

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Change log

r852 by tim.knip on Dec 24, 2008 Diff

Matrix3D: added method
calculateSkewSymmetric, used in 3D physics
http://en.wikipedia.org/wiki/Skew-
symmetric_matrix

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r708 by neoriley on Aug 25, 2008 Diff

Updating Trunk to 2.0 Beta

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