A butterfly subdivision scheme for surface interpolation with tension control

A new interpolatory subdivision scheme for surface design is presented. The new scheme is designed for a general triangulation of control points and has a tension parameter that provides design flexibility. The resulting limit surface is C1 for a specified range of the tension parameter, with a few exceptions. Application of the butterfly scheme and the role of the tension parameter are demonstrated by several examples.

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

[2]  Tom Lyche,et al.  Discrete B-splines and subdivision techniques in computer-aided geometric design and computer graphics , 1980 .

[3]  Nira Dyn,et al.  Analysis of uniform binary subdivision schemes for curve design , 1991 .

[4]  Wolfgang Böhm,et al.  Triangular spline algorithms , 1985, Comput. Aided Geom. Des..

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

[6]  Richard F. Riesenfeld,et al.  Discrete box splines and refinement algorithms , 1984, Comput. Aided Geom. Des..

[7]  George Merrill Chaikin,et al.  An algorithm for high-speed curve generation , 1974, Comput. Graph. Image Process..

[8]  Nira Dyn,et al.  Using parameters to increase smoothness of curves and surfaces generated by subdivision , 1990, Comput. Aided Geom. Des..

[9]  Charles A. Micchelli,et al.  Computing curves invariant under halving , 1987, Comput. Aided Geom. Des..

[10]  Nira Dyn,et al.  A 4-point interpolatory subdivision scheme for curve design , 1987, Comput. Aided Geom. Des..

[11]  Wolfgang Böhm.  Sudividing multivariate splines , 1983 .

[12]  Richard F. Riesenfeld,et al.  A Theoretical Development for the Computer Generation and Display of Piecewise Polynomial Surfaces , 1980, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[13]  Charles A. Micchelli,et al.  Computing surfaces invariant under subdivision , 1987, Comput. Aided Geom. Des..

[14]  C. Micchelli,et al.  Uniform refinement of curves , 1989 .

[15]  Wolfgang Böhm,et al.  A survey of curve and surface methods in CAGD , 1984, Comput. Aided Geom. Des..

[16]  Ahmad H. Nasri,et al.  Polyhedral subdivision methods for free-form surfaces , 1987, TOGS.