invert method
Implementation
Matrix4 invert() {
// based on http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm
var te = elements;
final double n11 = te[0],
n21 = te[1],
n31 = te[2],
n41 = te[3],
n12 = te[4],
n22 = te[5],
n32 = te[6],
n42 = te[7],
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;
final det = n11 * t11 + n21 * t12 + n31 * t13 + n41 * t14;
if (det == 0) return set(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
var 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;
return this;
}
