Hierarchical coding of 3-D surfaces using box splines

Optimal mechanisms are determined for the hierarchical decomposition of wire-frame surfaces. A family of box-splines with compact support, suitable for the approximation of wire-frames is defined, generated by arbitrary sampling matrices with integer eigenvalues. Criterion of optimality is the minimization of the variance of the error difference between the original surface and its representation at each resolution level. This is needed so as to ensure that the wire mesh produces at each resolution as close a replica of the original surface as possible.