11. Constructing C1 Surfaces of Arbitrary Topology Using Biquadratic and Bicubic Splines

Given a bivariate mesh of points, a C 1 surface of corresponding genus and connectedness is constructed. Most of the surface is parametrized by a biquadratic spline whose control points are obtained by refining the input mesh via corner cutting. The remaining mesh regions are parametrized by bicubic patches in Bernstein-Bezier form. The construction can be extended to rational patches and to interpolate at the vertices of the input mesh. t Department of Computer Science, Purdue University, W-Lafayette IN 47907 Supported by NSF grant CCR-9211322

[1]  Nira Dyn,et al.  Interpolatory convexity-preserving subdivision schemes for curves and surfaces , 1992, Comput. Aided Des..

[2]  Charles T. Loop,et al.  Smooth Subdivision Surfaces Based on Triangles , 1987 .

[3]  Jarke J. van Wijk,et al.  Bicubic patches for approximating non-rectangular control-point meshes , 1986, Comput. Aided Geom. Des..

[4]  M. A. Sabin.  Non-Rectangular Surface Patches Suitable for Inclusion in a B-Spline Surface , 1983, Eurographics.

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

[6]  J. Hahn,et al.  Filling polygonal holes with rectangular patches , 1989 .

[7]  Tony DeRose,et al.  Generalized B-spline surfaces of arbitrary topology , 1990, SIGGRAPH.

[8]  A. A. Ball,et al.  A matrix approach to the analysis of recursively generated B-spline surfaces , 1986 .

[9]  Ramon F. Sarraga,et al.  G1 interpolation of generally unrestricted cubic Bézier curves , 1987, Comput. Aided Geom. Des..

[10]  A. A. Ball,et al.  Conditions for tangent plane continuity over recursively generated B-spline surfaces , 1988, TOGS.

[11]  Klaus Höllig,et al.  G-splines , 1990, Comput. Aided Geom. Des..

[12]  John A. Gregory,et al.  Filling polygonal holes with bicubic patches , 1994, Comput. Aided Geom. Des..

[13]  John A. Gregory,et al.  Smooth Parametric Surfaces and n-Sided Patches , 1990 .

[14]  J. A. Gregory.  Smooth interpolation without twist constraints , 1974 .

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

[16]  Tim N. T. Goodman,et al.  Closed surfaces defined from biquadratic splines , 1991 .