+void multiply_3x3_matrices(const Matrix3x3 a, const Matrix3x3 b, Matrix3x3 result)
+{
+ result[0] = a[0] * b[0] + a[3] * b[1] + a[6] * b[2];
+ result[1] = a[1] * b[0] + a[4] * b[1] + a[7] * b[2];
+ result[2] = a[2] * b[0] + a[5] * b[1] + a[8] * b[2];
+
+ result[3] = a[0] * b[3] + a[3] * b[4] + a[6] * b[5];
+ result[4] = a[1] * b[3] + a[4] * b[4] + a[7] * b[5];
+ result[5] = a[2] * b[3] + a[5] * b[4] + a[8] * b[5];
+
+ result[6] = a[0] * b[6] + a[3] * b[7] + a[6] * b[8];
+ result[7] = a[1] * b[6] + a[4] * b[7] + a[7] * b[8];
+ result[8] = a[2] * b[6] + a[5] * b[7] + a[8] * b[8];
+}
+
+void invert_3x3_matrix(const Matrix3x3 m, Matrix3x3 result)
+{
+ double inv_det = 1.0 / (
+ m[6] * m[1] * m[5] - m[6] * m[2] * m[4] -
+ m[3] * m[1] * m[8] + m[3] * m[2] * m[7] +
+ m[0] * m[4] * m[8] - m[0] * m[5] * m[7]);
+
+ result[0] = inv_det * (m[4] * m[8] - m[5] * m[7]);
+ result[1] = inv_det * (m[2] * m[7] - m[1] * m[8]);
+ result[2] = inv_det * (m[1] * m[5] - m[2] * m[4]);
+
+ result[3] = inv_det * (m[6] * m[5] - m[3] * m[8]);
+ result[4] = inv_det * (m[0] * m[8] - m[6] * m[2]);
+ result[5] = inv_det * (m[3] * m[2] - m[0] * m[5]);
+
+ result[6] = inv_det * (m[3] * m[7] - m[6] * m[4]);
+ result[7] = inv_det * (m[6] * m[1] - m[0] * m[7]);
+ result[8] = inv_det * (m[0] * m[4] - m[3] * m[1]);
+}
+
+void print_3x3_matrix(const Matrix3x3 m)
+{
+ printf("%6.4f %6.4f %6.4f\n", m[0], m[3], m[6]);
+ printf("%6.4f %6.4f %6.4f\n", m[1], m[4], m[7]);
+ printf("%6.4f %6.4f %6.4f\n", m[2], m[5], m[8]);
+ printf("\n");
+}