Multilevel B-Spline Interpolation

Multilevel B-Spline Interpolation

I took a grad course in splines at Waterloo, and my final project was on scattered data interpolation. Scattered data interpolation is about finding a smooth function which has a specified value at specified points, where the specified points do not have any structure.

It is an interesting problem, and a really good solution would have immediate application. In computer graphics, you often know the value of something in certain locations, and everywhere else, you don’t care, but you’d like it to be smooth. Multilevel B-Splines are a beautiful solution, and would give great visual results in a variety of situations, but are too slow to use all over the place. I was playing around with a wavelet alternative, but never got anywhere close to the quality of the spline approach. At some point I might get back to playing with wavelets, or find a fun application for Multilevel B-Splines.

The project summary is here:

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