public double [,] generate_rotation_matrix(Vector3 [] new_positions)
{
//3x3 matrix of zeros used for summation
apq = new double [, ] {
{ 0, 0, 0 }, { 0, 0, 0 }, { 0, 0, 0 }
};
for (int i = 0; i < original_positions.Length; i++)
{
MatrixFunctions.matrix_add_3x3(ref apq, MatrixFunctions.vector3_covariance(new_positions[i], original_positions[i]));
//CHECKED: new positions are different from old ones, seem consitent
}
//CHECKED THROUGH THIS POINT
s = MatrixFunctions.matrixMultiply3x3(MatrixFunctions.transpose3x3(apq), apq);
MatrixFunctions.matrixInverseSquareRoot(ref s);
double [,] r = MatrixFunctions.matrixMultiply3x3(apq, s);
return(r);
}