Smooth 3D spline

Question

REF: http://stackoverflow.com/questions/588438/curve-fitting-3d-data-set

Does anyone know how to construct a smooth 3D spline with 3D control points?

If you look at the reference provided above, the red points will serve as the control points for the spline (which is supposed to be a best-fit representation of the 3D point cloud).

Answer 1

You could deconstruct it into 2 2D problems:

1. Split the data along the X and Y axes.
2. Form the full 3D equations of the splines with all of the unknown coefficients.
3. Imagine your data projected onto the YZ and XZ planes.
4. In the XZ plane, solve the equations for half of the coefficients.
5. Then, in the YZ plane, solve for the other half.