On subdivision schemes generalizing uniform B-spline surfaces of arbitrary degree

We introduce a new class of subdivision surfaces which generalize uniform tensor product B-spline surfaces of any bi-degree to meshes of arbitrary topology. Surprisingly , this can be done using subdivision rules that involve direct neighbors only. Consequently, our schemes are very easy to implement, regardless of degree. The famous Catmull-Clark scheme is a special case. Similarly we show that triangular box splines of total degree 3m + 1 can be generalized to arbitrary triangulations. Loop subdivision surfaces are a special case when m = 1. Our new schemes should be of interest to the high-end design market where surfaces of bi-degree up to 7 are common.