Cubic Spline Interpolation for Large Regular 3D Grid in Cylindrical Coordinate

We present an approach to implement cubic spline interpolation for large regular 3D grid. Our approach is an implementation of cubic spline in three dimensions by using spines in each direction. In large 3D regular grid, we have to take care of computation time of cubic initialization which involved solving a linear system. Therefore, in our method, we solve cubic initialization on all points in one dimension first before using it as pivots for other dimensions. We experiment the interpolation implementation with known functions with various cubic spline interpolation settings. We also compare the precision and accuracy of the implementation with known regular grid interpolations (e.g trilinear, triquadratic interpolation).