On subdivision schemes generalizing uniform B-spline surfaces of arbitrarydegree

We introduce a new class of subdivision surfaces which generalize uniform t enser product B-spline surfaces of any bi-degree to meshes of arbitrary top ology. 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 s pecial case when m = 1. Our new schemes should be of interest to the high-e nd design market where surfaces of bi-degree up to 7 are common. (C) 2001 E lsevier Science B.V. All rights reserved.