chapter  8
Subdivision for Graphics and Visualization
Pages 52

Tensor product B-spline surfaces restrict the defining control mesh to a rectangular topology. Such a restriction tremendously limits the complexity of shapes that can be represented. This limitation motivated the search for a general solution that can handle arbitrary topology, yet still produce regular B-spline surfaces in the normal way. The concept of subdivision surfaces was initiated by two papers that appeared in the same journal in 1978. They were both extensions of B-spline surfaces over such a topology. The first paper presented the Doo-Sabin [Doo78] subdivision algorithm that produces standard quadratic B-splines and the second paper introduced the Catmull-Clark algorithm [Catm78] that produces cubic Bsplines. Following these results, subdivision surfaces became a central issue for the graphics and geometric modeling community.