Name
Abstract | ||
|---|---|---|
In this paper a method is presented to fair the limit surface of a subdivision algorithm locally around an extraordinary point. The dominant six eigenvalues of the subdivision matrix have to satisfy linear and quadratic equality- and inequality-constraints in order to guarantee normal-continuity and bounded curvature at the extraordinary point. All other eigenvalues can be chosen arbitrarily within certain intervals and therefore can be used to optimize the shape of the subdivision surface by minimizing quadratic energy functionals. Additionally, if the sub- and subsub-dominant eigenvalues vary within predefined intervals, C^1-regularity of the surface and locality of the stencils can be guaranteed, although eigenvectors are changed. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1016/j.cagd.2007.08.003 | Computer Aided Geometric Design |
Keywords | Field | DocType |
algorithm of catmull-clark,subsub-dominant eigenvalues,subdivision matrix,local energy-optimizing subdivision algorithm,algorithm of loop,quadratic equality,quadratic energy functionals,extraordinary point,constrained optimization,bounded curvature,certain interval,algorithm of catmull–clark,eigenvalues,thin-plate energy,subdivision surface,subdivision algorithms,subdivision algorithm,limit surface,eigenvectors,energy optimization,satisfiability | Topology,Mathematical optimization,Locality,Curvature,Matrix (mathematics),Quadratic equation,Subdivision surface,Subdivision,Eigenvalues and eigenvectors,Mathematics,Constrained optimization | Journal |
Volume | Issue | ISSN |
25 | 3 | Computer Aided Geometric Design |
Citations | PageRank | References |
3 | 0.45 | 17 |
Authors | ||
2 | ||