Modeling surfaces of arbitrary topology using manifolds

Cindy M. Grimm, John F. Hughes
1995 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques - SIGGRAPH '95  
We describe an extension of B-splines to surfaces of arbitrary topology, including arbitrary boundaries. The technique inherits many of the properties of B-splines: local control, a compact representation, and guaranteed continuity of arbitrary degree. The surface is specified using a polyhedral control mesh instead of a rectangular one; the resulting surface approximates the polyhedral mesh much as a B-spline approximates its rectangular control mesh. Like a Bspline, the surface is a single,
more » ... ntinuous object. This is achieved by modeling the domain of the surface with a manifold whose topology matches that of the polyhedral mesh, then embedding this domain into 3-space using a basis-function/control-point formulation. We provide a constructive approach to building a manifold.
doi:10.1145/218380.218475 dblp:conf/siggraph/GrimmH95 fatcat:owxwqr33rrabfcigw5odlyeqsy