Implement Mat3x3 Determinant, Inverse, Transpose methods

src/J3ML/LinearAlgebra/Matrix3x3.cpp

@@ -100,5 +100,64 @@ namespace LinearAlgebra {
 
     }
 
+    float Matrix3x3::Determinant() const {
+        const float a = elems[0][0];
+        const float b = elems[0][1];
+        const float c = elems[0][2];
+        const float d = elems[1][0];
+        const float e = elems[1][1];
+        const float f = elems[1][2];
+        const float g = elems[2][0];
+        const float h = elems[2][1];
+        const float i = elems[2][2];
+
+        // Aight, what the fuck?
+        return a*(e*i - f*h) + b*(f*g - d*i) + c*(d*h - e*g);
+    }
+
+    Matrix3x3 Matrix3x3::Inverse() const {
+        // Compute the inverse directly using Cramer's rule
+        // Warning: This method is numerically very unstable!
+        float d = Determinant();
+
+        d = 1.f / d;
+
+        Matrix3x3 i = {
+                d * (At(1, 1) * At(2, 2) - At(1, 2) * At(2, 1)),
+                d * (At(0, 2) * At(2, 1) - At(0, 1) * At(2, 2)),
+                d * (At(0, 1) * At(1, 2) - At(0, 2) * At(1, 1)),
+
+                d * (At(1, 2) * At(2, 0) - At(1, 0) * At(2, 2)),
+                d * (At(0, 0) * At(2, 2) - At(0, 2) * At(2, 0)),
+                d * (At(0, 2) * At(1, 0) - At(0, 0) * At(1, 2)),
+
+                d * (At(1, 0) * At(2, 1) - At(1, 1) * At(2, 0)),
+                d * (At(2, 0) * At(0, 1) - At(0, 0) * At(2,1)),
+                d * (At(0,0) * At(1, 1) - At(0, 1) * At(1, 0))
+        };
+
+        return i;
+    }
+
+    Matrix3x3 Matrix3x3::Transpose() const {
+        auto m00 = this->elems[0][0];
+        auto m01 = this->elems[0][1];
+        auto m02 = this->elems[0][2];
+
+        auto m10 = this->elems[1][0];
+        auto m11 = this->elems[1][1];
+        auto m12 = this->elems[1][2];
+
+        auto m20 = this->elems[2][0];
+        auto m21 = this->elems[2][1];
+        auto m22 = this->elems[2][2];
+
+        return {
+                m00, m10, m20,
+                m01, m11, m21,
+                m02, m12, m22
+        }
+    }
+
 }