Interpolating nets of curves by smooth subdivision surfaces

A subdivision algorithm is presented for the computation and representation of a smooth surface of arbitrary topological type interpolating a given net of smooth curves. The algorithm belongs to a new class of subdivision schemes called combined subdivision schemes. These schemes can exactly interpolate a net of curves given in any parametric representation. The surfaces generated by our algorithm are G except at a finite number of points, where the surface is G and has bounded curvature. The algorithm is simple and easy to implement, and is based on a variant of the famous Catmull-Clark subdivision scheme. CR

[1]  Leif Kobbelt,et al.  Interpolatory Subdivision on Open Quadrilateral Nets with Arbitrary Topology , 1996, Comput. Graph. Forum.

[2]  N. Dyn,et al.  A butterfly subdivision scheme for surface interpolation with tension control , 1990, TOGS.

[3]  Peter Schröder,et al.  Interpolating Subdivision for meshes with arbitrary topology , 1996, SIGGRAPH.

[4]  Malcolm A. Sabin,et al.  Behaviour of recursive division surfaces near extraordinary points , 1998 .

[5]  A. A. Ball,et al.  Design of an n-sided surface patch from Hermite boundary data , 1989, Comput. Aided Geom. Des..

[6]  Tony DeRose,et al.  Efficient, fair interpolation using Catmull-Clark surfaces , 1993, SIGGRAPH.

[7]  Tony DeRose,et al.  Subdivision surfaces in character animation , 1998, SIGGRAPH.

[8]  Ahmad H. Nasri,et al.  Curve interpolation in recursively generated B-spline surfaces over arbitrary topology , 1997, Comput. Aided Geom. Des..

[9]  Gabriel Taubin,et al.  A signal processing approach to fair surface design , 1995, SIGGRAPH.

[10]  E. Catmull,et al.  Recursively generated B-spline surfaces on arbitrary topological meshes , 1978 .

[11]  Adi Levin.  Combined subdivision schemes for the design of surfaces satisfying boundary conditions , 1999, Comput. Aided Geom. Des..

[12]  M. A. Sabin,et al.  Cubic Recursive Division With Bounded Curvature , 1991, Curves and Surfaces.

[13]  M. Sabin,et al.  Behaviour of recursive division surfaces near extraordinary points , 1978 .

[14]  Jean Schweitzer,et al.  Analysis and application of subdivision surfaces , 1996 .