Point Sequence Interpolation

Question

Given an arbitrary sequence of points in space, how would you produce a smooth continuous interpolation between them?

2D and 3D solutions are welcome. Solutions tha

Answer 1

You should take a look at B-splines. Their advantage over Bezier curves is that each part is only dependent on local points. So moving a point has no effect on parts of the curve that are far away, where "far away" is determined by a parameter of the spline.

The problem with the Langrange polynomial is that adding a point can have extreme effects on seemingly arbitrary parts of the curve; there's no "localness" like described above.