Merge pull request #8228 from tschw/MatrixInversion

Matrix inversion

src/math/Matrix3.js

@@ -2,6 +2,7 @@
  * @author alteredq / http://alteredqualia.com/
  * @author WestLangley / http://github.com/WestLangley
  * @author bhouston / http://clara.io
+ * @author tschw
  */
 
 THREE.Matrix3 = function () {
@@ -30,9 +31,9 @@ THREE.Matrix3.prototype = {
 
 		var te = this.elements;
 
-		te[ 0 ] = n11; te[ 3 ] = n12; te[ 6 ] = n13;
-		te[ 1 ] = n21; te[ 4 ] = n22; te[ 7 ] = n23;
-		te[ 2 ] = n31; te[ 5 ] = n32; te[ 8 ] = n33;
+		te[ 0 ] = n11; te[ 1 ] = n21; te[ 2 ] = n31;
+		te[ 3 ] = n12; te[ 4 ] = n22; te[ 5 ] = n32;
+		te[ 6 ] = n13; te[ 7 ] = n23; te[ 8 ] = n33;
 
 		return this;
 
@@ -74,6 +75,22 @@ THREE.Matrix3.prototype = {
 
 	},
 
+	setFromMatrix4: function( m ) {
+
+		var me = m.elements;
+
+		this.set(
+
+			me[ 0 ], me[ 4 ], me[  8 ],
+			me[ 1 ], me[ 5 ], me[  9 ],
+			me[ 2 ], me[ 6 ], me[ 10 ]
+
+		);
+
+		return this;
+
+	},
+
 	applyToVector3Array: function () {
 
 		var v1;
@@ -152,25 +169,24 @@ THREE.Matrix3.prototype = {
 
 	getInverse: function ( matrix, throwOnDegenerate ) {
 
-		// input: THREE.Matrix4
-		// ( based on http://code.google.com/p/webgl-mjs/ )
+		if ( matrix instanceof THREE.Matrix4 ) {
 
-		var me = matrix.elements;
-		var te = this.elements;
+			console.warn( "THREE.Matrix3.getInverse no longer takes a Matrix4 argument." );
+
+		}
+
+		var me = matrix.elements,
+			te = this.elements,
 
-		te[ 0 ] =   me[ 10 ] * me[ 5 ] - me[ 6 ] * me[ 9 ];
-		te[ 1 ] = - me[ 10 ] * me[ 1 ] + me[ 2 ] * me[ 9 ];
-		te[ 2 ] =   me[ 6 ] * me[ 1 ] - me[ 2 ] * me[ 5 ];
-		te[ 3 ] = - me[ 10 ] * me[ 4 ] + me[ 6 ] * me[ 8 ];
-		te[ 4 ] =   me[ 10 ] * me[ 0 ] - me[ 2 ] * me[ 8 ];
-		te[ 5 ] = - me[ 6 ] * me[ 0 ] + me[ 2 ] * me[ 4 ];
-		te[ 6 ] =   me[ 9 ] * me[ 4 ] - me[ 5 ] * me[ 8 ];
-		te[ 7 ] = - me[ 9 ] * me[ 0 ] + me[ 1 ] * me[ 8 ];
-		te[ 8 ] =   me[ 5 ] * me[ 0 ] - me[ 1 ] * me[ 4 ];
+			n11 = me[ 0 ], n21 = me[ 1 ], n31 = me[ 2 ],
+			n12 = me[ 3 ], n22 = me[ 4 ], n32 = me[ 5 ],
+			n13 = me[ 6 ], n23 = me[ 7 ], n33 = me[ 8 ],
 
-		var det = me[ 0 ] * te[ 0 ] + me[ 1 ] * te[ 3 ] + me[ 2 ] * te[ 6 ];
+			t11 = n33 * n22 - n32 * n23,
+			t12 = n32 * n13 - n33 * n12,
+			t13 = n23 * n12 - n22 * n13,
 
-		// no inverse
+			det = n11 * t11 + n21 * t12 + n31 * t13;
 
 		if ( det === 0 ) {
 
@@ -186,15 +202,22 @@ THREE.Matrix3.prototype = {
 
 			}
 
-			this.identity();
+			return this.identity();
+		}
 
-			return this;
+		te[ 0 ] = t11;
+		te[ 1 ] = n31 * n23 - n33 * n21;
+		te[ 2 ] = n32 * n21 - n31 * n22;
 
-		}
+		te[ 3 ] = t12;
+		te[ 4 ] = n33 * n11 - n31 * n13;
+		te[ 5 ] = n31 * n12 - n32 * n11;
 
-		this.multiplyScalar( 1.0 / det );
+		te[ 6 ] = t13;
+		te[ 7 ] = n21 * n13 - n23 * n11;
+		te[ 8 ] = n22 * n11 - n21 * n12;
 
-		return this;
+		return this.multiplyScalar( 1 / det );
 
 	},
 
@@ -230,13 +253,9 @@ THREE.Matrix3.prototype = {
 
 	},
 
-	getNormalMatrix: function ( m ) {
-
-		// input: THREE.Matrix4
+	getNormalMatrix: function ( matrix4 ) {
 
-		this.getInverse( m ).transpose();
-
-		return this;
+		return this.setFromMatrix4( matrix4 ).getInverse( this ).transpose();
 
 	},
 

src/math/Matrix4.js

@@ -610,41 +610,29 @@ THREE.Matrix4.prototype = {
 
 	},
 
-	getInverse: function ( m, throwOnInvertible ) {
+	getInverse: function ( m, throwOnDegenerate ) {
 
 		// based on http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm
-		var te = this.elements;
-		var me = m.elements;
+		var te = this.elements,
+			me = m.elements,
 
-		var n11 = me[ 0 ], n12 = me[ 4 ], n13 = me[ 8 ], n14 = me[ 12 ];
-		var n21 = me[ 1 ], n22 = me[ 5 ], n23 = me[ 9 ], n24 = me[ 13 ];
-		var n31 = me[ 2 ], n32 = me[ 6 ], n33 = me[ 10 ], n34 = me[ 14 ];
-		var n41 = me[ 3 ], n42 = me[ 7 ], n43 = me[ 11 ], n44 = me[ 15 ];
+			n11 = me[ 0 ], n21 = me[ 1 ], n31 = me[ 2 ], n41 = me[ 3 ],
+			n12 = me[ 4 ], n22 = me[ 5 ], n32 = me[ 6 ], n42 = me[ 7 ],
+			n13 = me[ 8 ], n23 = me[ 9 ], n33 = me[ 10 ], n43 = me[ 11 ],
+			n14 = me[ 12 ], n24 = me[ 13 ], n34 = me[ 14 ], n44 = me[ 15 ],
 
-		te[ 0 ] = n23 * n34 * n42 - n24 * n33 * n42 + n24 * n32 * n43 - n22 * n34 * n43 - n23 * n32 * n44 + n22 * n33 * n44;
-		te[ 4 ] = n14 * n33 * n42 - n13 * n34 * n42 - n14 * n32 * n43 + n12 * n34 * n43 + n13 * n32 * n44 - n12 * n33 * n44;
-		te[ 8 ] = n13 * n24 * n42 - n14 * n23 * n42 + n14 * n22 * n43 - n12 * n24 * n43 - n13 * n22 * n44 + n12 * n23 * n44;
-		te[ 12 ] = n14 * n23 * n32 - n13 * n24 * n32 - n14 * n22 * n33 + n12 * n24 * n33 + n13 * n22 * n34 - n12 * n23 * n34;
-		te[ 1 ] = n24 * n33 * n41 - n23 * n34 * n41 - n24 * n31 * n43 + n21 * n34 * n43 + n23 * n31 * n44 - n21 * n33 * n44;
-		te[ 5 ] = n13 * n34 * n41 - n14 * n33 * n41 + n14 * n31 * n43 - n11 * n34 * n43 - n13 * n31 * n44 + n11 * n33 * n44;
-		te[ 9 ] = n14 * n23 * n41 - n13 * n24 * n41 - n14 * n21 * n43 + n11 * n24 * n43 + n13 * n21 * n44 - n11 * n23 * n44;
-		te[ 13 ] = n13 * n24 * n31 - n14 * n23 * n31 + n14 * n21 * n33 - n11 * n24 * n33 - n13 * n21 * n34 + n11 * n23 * n34;
-		te[ 2 ] = n22 * n34 * n41 - n24 * n32 * n41 + n24 * n31 * n42 - n21 * n34 * n42 - n22 * n31 * n44 + n21 * n32 * n44;
-		te[ 6 ] = n14 * n32 * n41 - n12 * n34 * n41 - n14 * n31 * n42 + n11 * n34 * n42 + n12 * n31 * n44 - n11 * n32 * n44;
-		te[ 10 ] = n12 * n24 * n41 - n14 * n22 * n41 + n14 * n21 * n42 - n11 * n24 * n42 - n12 * n21 * n44 + n11 * n22 * n44;
-		te[ 14 ] = n14 * n22 * n31 - n12 * n24 * n31 - n14 * n21 * n32 + n11 * n24 * n32 + n12 * n21 * n34 - n11 * n22 * n34;
-		te[ 3 ] = n23 * n32 * n41 - n22 * n33 * n41 - n23 * n31 * n42 + n21 * n33 * n42 + n22 * n31 * n43 - n21 * n32 * n43;
-		te[ 7 ] = n12 * n33 * n41 - n13 * n32 * n41 + n13 * n31 * n42 - n11 * n33 * n42 - n12 * n31 * n43 + n11 * n32 * n43;
-		te[ 11 ] = n13 * n22 * n41 - n12 * n23 * n41 - n13 * n21 * n42 + n11 * n23 * n42 + n12 * n21 * n43 - n11 * n22 * n43;
-		te[ 15 ] = n12 * n23 * n31 - n13 * n22 * n31 + n13 * n21 * n32 - n11 * n23 * n32 - n12 * n21 * n33 + n11 * n22 * n33;
+			t11 = n23 * n34 * n42 - n24 * n33 * n42 + n24 * n32 * n43 - n22 * n34 * n43 - n23 * n32 * n44 + n22 * n33 * n44,
+			t12 = n14 * n33 * n42 - n13 * n34 * n42 - n14 * n32 * n43 + n12 * n34 * n43 + n13 * n32 * n44 - n12 * n33 * n44,
+			t13 = n13 * n24 * n42 - n14 * n23 * n42 + n14 * n22 * n43 - n12 * n24 * n43 - n13 * n22 * n44 + n12 * n23 * n44,
+			t14 = n14 * n23 * n32 - n13 * n24 * n32 - n14 * n22 * n33 + n12 * n24 * n33 + n13 * n22 * n34 - n12 * n23 * n34;
 
-		var det = n11 * te[ 0 ] + n21 * te[ 4 ] + n31 * te[ 8 ] + n41 * te[ 12 ];
+		var det = n11 * t11 + n21 * t12 + n31 * t13 + n41 * t14;
 
 		if ( det === 0 ) {
 
 			var msg = "THREE.Matrix4.getInverse(): can't invert matrix, determinant is 0";
 
-			if ( throwOnInvertible || false ) {
+			if ( throwOnDegenerate || false ) {
 
 				throw new Error( msg );
 
@@ -654,15 +642,31 @@ THREE.Matrix4.prototype = {
 
 			}
 
-			this.identity();
-
-			return this;
+			return this.identity();
 
 		}
 
-		this.multiplyScalar( 1 / det );
+		te[ 0 ] = t11;
+		te[ 1 ] = n24 * n33 * n41 - n23 * n34 * n41 - n24 * n31 * n43 + n21 * n34 * n43 + n23 * n31 * n44 - n21 * n33 * n44;
+		te[ 2 ] = n22 * n34 * n41 - n24 * n32 * n41 + n24 * n31 * n42 - n21 * n34 * n42 - n22 * n31 * n44 + n21 * n32 * n44;
+		te[ 3 ] = n23 * n32 * n41 - n22 * n33 * n41 - n23 * n31 * n42 + n21 * n33 * n42 + n22 * n31 * n43 - n21 * n32 * n43;
 
-		return this;
+		te[ 4 ] = t12;
+		te[ 5 ] = n13 * n34 * n41 - n14 * n33 * n41 + n14 * n31 * n43 - n11 * n34 * n43 - n13 * n31 * n44 + n11 * n33 * n44;
+		te[ 6 ] = n14 * n32 * n41 - n12 * n34 * n41 - n14 * n31 * n42 + n11 * n34 * n42 + n12 * n31 * n44 - n11 * n32 * n44;
+		te[ 7 ] = n12 * n33 * n41 - n13 * n32 * n41 + n13 * n31 * n42 - n11 * n33 * n42 - n12 * n31 * n43 + n11 * n32 * n43;
+
+		te[ 8 ] = t13;
+		te[ 9 ] = n14 * n23 * n41 - n13 * n24 * n41 - n14 * n21 * n43 + n11 * n24 * n43 + n13 * n21 * n44 - n11 * n23 * n44;
+		te[ 10 ] = n12 * n24 * n41 - n14 * n22 * n41 + n14 * n21 * n42 - n11 * n24 * n42 - n12 * n21 * n44 + n11 * n22 * n44;
+		te[ 11 ] = n13 * n22 * n41 - n12 * n23 * n41 - n13 * n21 * n42 + n11 * n23 * n42 + n12 * n21 * n43 - n11 * n22 * n43;
+
+		te[ 12 ] = t14;
+		te[ 13 ] = n13 * n24 * n31 - n14 * n23 * n31 + n14 * n21 * n33 - n11 * n24 * n33 - n13 * n21 * n34 + n11 * n23 * n34;
+		te[ 14 ] = n14 * n22 * n31 - n12 * n24 * n31 - n14 * n21 * n32 + n11 * n24 * n32 + n12 * n21 * n34 - n11 * n22 * n34;
+		te[ 15 ] = n12 * n23 * n31 - n13 * n22 * n31 + n13 * n21 * n32 - n11 * n23 * n32 - n12 * n21 * n33 + n11 * n22 * n33;
+
+		return this.multiplyScalar( 1 / det );
 
 	},