Surface Compression with Hierarchical Powell-Sabin B-splines

We show how to construct a stable hierarchical basis for piecewise quadratic C continuous splines defined on Powell–Sabin triangulations. We prove that this hierarchical basis is well suited for compressing surfaces. Our compression method does not require the construction of wavelets which are usually expensive to compute, but instead we construct a stable quasi-interpolation scheme for our spline space which achieves optimal approximation order. Numerical experiments demonstrate the high compression rate of the algorithm.