Matrix4: Optimize invert() calculation (#32657)

src/math/Matrix4.js

@@ -707,7 +707,7 @@ class Matrix4 {
 	 */
 	invert() {
 
-		// based on http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm
+		// based on https://github.com/toji/gl-matrix
 		const te = this.elements,
 
 			n11 = te[ 0 ], n21 = te[ 1 ], n31 = te[ 2 ], n41 = te[ 3 ],
@@ -715,36 +715,44 @@ class Matrix4 {
 			n13 = te[ 8 ], n23 = te[ 9 ], n33 = te[ 10 ], n43 = te[ 11 ],
 			n14 = te[ 12 ], n24 = te[ 13 ], n34 = te[ 14 ], n44 = te[ 15 ],
 
-			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;
-
-		const det = n11 * t11 + n21 * t12 + n31 * t13 + n41 * t14;
+			t1 = n11 * n22 - n21 * n12,
+			t2 = n11 * n32 - n31 * n12,
+			t3 = n11 * n42 - n41 * n12,
+			t4 = n21 * n32 - n31 * n22,
+			t5 = n21 * n42 - n41 * n22,
+			t6 = n31 * n42 - n41 * n32,
+			t7 = n13 * n24 - n23 * n14,
+			t8 = n13 * n34 - n33 * n14,
+			t9 = n13 * n44 - n43 * n14,
+			t10 = n23 * n34 - n33 * n24,
+			t11 = n23 * n44 - n43 * n24,
+			t12 = n33 * n44 - n43 * n34;
+
+		const det = t1 * t12 - t2 * t11 + t3 * t10 + t4 * t9 - t5 * t8 + t6 * t7;
 
 		if ( det === 0 ) return this.set( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 );
 
 		const detInv = 1 / det;
 
-		te[ 0 ] = t11 * detInv;
-		te[ 1 ] = ( n24 * n33 * n41 - n23 * n34 * n41 - n24 * n31 * n43 + n21 * n34 * n43 + n23 * n31 * n44 - n21 * n33 * n44 ) * detInv;
-		te[ 2 ] = ( n22 * n34 * n41 - n24 * n32 * n41 + n24 * n31 * n42 - n21 * n34 * n42 - n22 * n31 * n44 + n21 * n32 * n44 ) * detInv;
-		te[ 3 ] = ( n23 * n32 * n41 - n22 * n33 * n41 - n23 * n31 * n42 + n21 * n33 * n42 + n22 * n31 * n43 - n21 * n32 * n43 ) * detInv;
-
-		te[ 4 ] = t12 * detInv;
-		te[ 5 ] = ( n13 * n34 * n41 - n14 * n33 * n41 + n14 * n31 * n43 - n11 * n34 * n43 - n13 * n31 * n44 + n11 * n33 * n44 ) * detInv;
-		te[ 6 ] = ( n14 * n32 * n41 - n12 * n34 * n41 - n14 * n31 * n42 + n11 * n34 * n42 + n12 * n31 * n44 - n11 * n32 * n44 ) * detInv;
-		te[ 7 ] = ( n12 * n33 * n41 - n13 * n32 * n41 + n13 * n31 * n42 - n11 * n33 * n42 - n12 * n31 * n43 + n11 * n32 * n43 ) * detInv;
-
-		te[ 8 ] = t13 * detInv;
-		te[ 9 ] = ( n14 * n23 * n41 - n13 * n24 * n41 - n14 * n21 * n43 + n11 * n24 * n43 + n13 * n21 * n44 - n11 * n23 * n44 ) * detInv;
-		te[ 10 ] = ( n12 * n24 * n41 - n14 * n22 * n41 + n14 * n21 * n42 - n11 * n24 * n42 - n12 * n21 * n44 + n11 * n22 * n44 ) * detInv;
-		te[ 11 ] = ( n13 * n22 * n41 - n12 * n23 * n41 - n13 * n21 * n42 + n11 * n23 * n42 + n12 * n21 * n43 - n11 * n22 * n43 ) * detInv;
-
-		te[ 12 ] = t14 * detInv;
-		te[ 13 ] = ( n13 * n24 * n31 - n14 * n23 * n31 + n14 * n21 * n33 - n11 * n24 * n33 - n13 * n21 * n34 + n11 * n23 * n34 ) * detInv;
-		te[ 14 ] = ( n14 * n22 * n31 - n12 * n24 * n31 - n14 * n21 * n32 + n11 * n24 * n32 + n12 * n21 * n34 - n11 * n22 * n34 ) * detInv;
-		te[ 15 ] = ( n12 * n23 * n31 - n13 * n22 * n31 + n13 * n21 * n32 - n11 * n23 * n32 - n12 * n21 * n33 + n11 * n22 * n33 ) * detInv;
+		te[ 0 ] = ( n22 * t12 - n32 * t11 + n42 * t10 ) * detInv;
+		te[ 1 ] = ( n31 * t11 - n21 * t12 - n41 * t10 ) * detInv;
+		te[ 2 ] = ( n24 * t6 - n34 * t5 + n44 * t4 ) * detInv;
+		te[ 3 ] = ( n33 * t5 - n23 * t6 - n43 * t4 ) * detInv;
+
+		te[ 4 ] = ( n32 * t9 - n12 * t12 - n42 * t8 ) * detInv;
+		te[ 5 ] = ( n11 * t12 - n31 * t9 + n41 * t8 ) * detInv;
+		te[ 6 ] = ( n34 * t3 - n14 * t6 - n44 * t2 ) * detInv;
+		te[ 7 ] = ( n13 * t6 - n33 * t3 + n43 * t2 ) * detInv;
+
+		te[ 8 ] = ( n12 * t11 - n22 * t9 + n42 * t7 ) * detInv;
+		te[ 9 ] = ( n21 * t9 - n11 * t11 - n41 * t7 ) * detInv;
+		te[ 10 ] = ( n14 * t5 - n24 * t3 + n44 * t1 ) * detInv;
+		te[ 11 ] = ( n23 * t3 - n13 * t5 - n43 * t1 ) * detInv;
+
+		te[ 12 ] = ( n22 * t8 - n12 * t10 - n32 * t7 ) * detInv;
+		te[ 13 ] = ( n11 * t10 - n21 * t8 + n31 * t7 ) * detInv;
+		te[ 14 ] = ( n24 * t2 - n14 * t4 - n34 * t1 ) * detInv;
+		te[ 15 ] = ( n13 * t4 - n23 * t2 + n33 * t1 ) * detInv;
 
 		return this;