T-spline simplification and local refinement

A typical NURBS surface model has a large percentage of superfluous control points that significantly interfere with the design process. This paper presents an algorithm for eliminating such superfluous control points, producing a T-spline. The algorithm can remove substantially more control points than competing methods such as B-spline wavelet decomposition. The paper also presents a new T-spline local refinement algorithm and answers two fundamental open questions on T-spline theory.

[1]  W. Boehm.  Inserting New Knots into B-spline Curves , 1980 .

[2]  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.

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

[4]  W. Böhm,et al.  Generating the Bézier points of B-spline curves and surfaces , 1981 .

[5]  Tom Lyche,et al.  Knot line refinement algorithms for tensor product B-spline surfaces , 1985, Comput. Aided Geom. Des..

[6]  David Handscomb.  Knot-Elimination; Reversal of the Oslo Algorithm , 1987 .

[7]  Knut Mørken,et al.  Knot removal for parametric B-spline curves and surfaces , 1987, Comput. Aided Geom. Des..

[8]  Gerald E. Farin,et al.  Fairing cubic B-spline curves , 1987, Comput. Aided Geom. Des..

[9]  David R. Forsey,et al.  Hierarchical B-spline refinement , 1988, SIGGRAPH.

[10]  Hans-Peter Seidel,et al.  Knot insertion from a blossoming point of view , 1988, Comput. Aided Geom. Des..

[11]  T. Lyche,et al.  Decomposition of splines , 1992 .

[12]  Tom Lyche,et al.  Knot Insertion and Deletion Algorithms for B-Spline Curves and Surfaces , 1992 .

[13]  Peter Schröder,et al.  Spherical wavelets: efficiently representing functions on the sphere , 1995, SIGGRAPH.

[14]  David R. Forsey,et al.  Multiresolution Surface Reconstruction for Hierarchical B-splines , 1998, Graphics Interface.

[15]  Carlos Gonzalez-Ochoa,et al.  Localized-hierarchy surface splines (LeSS) , 1999, SI3D.

[16]  Tom Lyche,et al.  A Multiresolution Tensor Spline Method for Fitting Functions on the Sphere , 2000, SIAM J. Sci. Comput..

[17]  E. Quak,et al.  Multivariate Approximation and Applications: Theory and algorithms for nonuniform spline wavelets , 2001 .

[18]  Tom Lyche,et al.  Theory and Algorithms for Non-Uniform Spline Wavelets , 2001 .

[19]  Eitan Grinspun,et al.  CHARMS: a simple framework for adaptive simulation , 2002, ACM Trans. Graph..

[20]  Ahmad H. Nasri,et al.  T-splines and T-NURCCs , 2003, ACM Trans. Graph..