In this study,a systematic refinement method was developed for non-uniform Catmull-Clark subdivision surfaces to improve the quality of the surface at extraordinary points(EPs).The developed method modifies the eigenp...In this study,a systematic refinement method was developed for non-uniform Catmull-Clark subdivision surfaces to improve the quality of the surface at extraordinary points(EPs).The developed method modifies the eigenpolyhedron by designing the angles between two adjacent edges that contain an EP.Refinement rules are then formulated with the help of the modified eigenpolyhedron.Numerical experiments show that the method significantly improves the performance of the subdivision surface for non-uniform parameterization.展开更多
Since Doo-Sabin and Catmull-Clark surfaces were proposed in 1978, eigenstructure, convergence and continuity analyses of stationary subdivision have been performed very well, but it has been very difficult to prove th...Since Doo-Sabin and Catmull-Clark surfaces were proposed in 1978, eigenstructure, convergence and continuity analyses of stationary subdivision have been performed very well, but it has been very difficult to prove the convergence and continuity of non-uniform recursive subdivision surfaces (NURSSes, for short) of arbitrary topology. In fact, so far a problem whether or not there exists the limit surface as well as G1 continuity of a non-uniform Catmull-Clark subdivision has not been solved yet. Here the concept of equivalent knot spacing is introduced. A new technique for eigenanaly-sis, convergence and continuity analyses of non-uniform Catmull-Clark surfaces is proposed such that the convergence and G1 continuity of NURSSes at extraordinary points are proved. In addition, slightly improved rules for NURSSes are developed. This offers us one more alternative for modeling free-form surfaces of arbitrary topologies with geometric features such as cusps, sharp edges, creases and darts, while elsewhere maintaining the same order of continuity as B-spline surfaces.展开更多
This paper constructs a new non-uniform Doo-Sabin subdivision scheme via eigen polygon.The authors proved that the limit surface is always convergent and is G1 continuous for any valence and any positive knot interval...This paper constructs a new non-uniform Doo-Sabin subdivision scheme via eigen polygon.The authors proved that the limit surface is always convergent and is G1 continuous for any valence and any positive knot intervals under a minor assumption, that λ is the second and third eigenvalues of the subdivision matrix. And then, a million of numerical experiments are tested with randomly selecting positive knot intervals, which verify that our new subdivision scheme satisfies the assumption.However this is not true for the other two existing non-uniform Doo-Sabin schemes in Sederberg, et al.(1998), Huang and Wang(2013). In additional, numerical experiments indicate that the quality of the new limit surface can be improved.展开更多
基金This work was supported by the National Key R&D Program of China,No.2020YFB1708900Natural Science Foundation of China,Nos.61872328 and 11801126.
文摘In this study,a systematic refinement method was developed for non-uniform Catmull-Clark subdivision surfaces to improve the quality of the surface at extraordinary points(EPs).The developed method modifies the eigenpolyhedron by designing the angles between two adjacent edges that contain an EP.Refinement rules are then formulated with the help of the modified eigenpolyhedron.Numerical experiments show that the method significantly improves the performance of the subdivision surface for non-uniform parameterization.
文摘Since Doo-Sabin and Catmull-Clark surfaces were proposed in 1978, eigenstructure, convergence and continuity analyses of stationary subdivision have been performed very well, but it has been very difficult to prove the convergence and continuity of non-uniform recursive subdivision surfaces (NURSSes, for short) of arbitrary topology. In fact, so far a problem whether or not there exists the limit surface as well as G1 continuity of a non-uniform Catmull-Clark subdivision has not been solved yet. Here the concept of equivalent knot spacing is introduced. A new technique for eigenanaly-sis, convergence and continuity analyses of non-uniform Catmull-Clark surfaces is proposed such that the convergence and G1 continuity of NURSSes at extraordinary points are proved. In addition, slightly improved rules for NURSSes are developed. This offers us one more alternative for modeling free-form surfaces of arbitrary topologies with geometric features such as cusps, sharp edges, creases and darts, while elsewhere maintaining the same order of continuity as B-spline surfaces.
基金supported by the National Natural Science Foundation of China under Grant No.61872328SRF for ROCS SE+1 种基金the Youth Innovation Promotion Association CASCAS-TWAS president’s fellowship program。
文摘This paper constructs a new non-uniform Doo-Sabin subdivision scheme via eigen polygon.The authors proved that the limit surface is always convergent and is G1 continuous for any valence and any positive knot intervals under a minor assumption, that λ is the second and third eigenvalues of the subdivision matrix. And then, a million of numerical experiments are tested with randomly selecting positive knot intervals, which verify that our new subdivision scheme satisfies the assumption.However this is not true for the other two existing non-uniform Doo-Sabin schemes in Sederberg, et al.(1998), Huang and Wang(2013). In additional, numerical experiments indicate that the quality of the new limit surface can be improved.
