Name
Abstract | ||
|---|---|---|
For a stationary, affine invariant, symmetric, linear and local subdivision scheme that is C^2 apart from the extraordinary point the curvature is bounded if the square of the subdominant eigenvalue equals the subsubdominant eigenvalue. This paper gives a technique for quickly establishing an interval to which the curvature is confined at the extraordinary point. The approach factors the work into precomputed intervals that depend only on the scheme and a mesh-specific component. When the intervals are tight enough they can be used as a test of shape-faithfulness of the given subdivision scheme; i.e., if the limit surface in the neighborhood of the extraordinary point of the subdivision scheme is consistent with the geometry implied by the input mesh. |
Year | DOI | Venue |
|---|---|---|
2001 | 10.1016/S0167-8396(01)00041-3 | Computer Aided Geometric Design |
Keywords | Field | DocType |
bounded curvature subdivision,approach factor,subdominant eigenvalue,local subdivision scheme,limit surface,affine invariant,extraordinary point,input mesh,mesh-specific component,computing curvature bound,subsubdominant eigenvalue,subdivision scheme,eigenvalues | Affine transformation,Topology,Curvature,Center of curvature,Subdivision,Invariant (mathematics),Eigenvalues and eigenvectors,Mesh generation,Mathematics,Bounded function | Journal |
Volume | Issue | ISSN |
18 | 5 | 0167-8396 |
Citations | PageRank | References |
8 | 0.85 | 5 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jörg Peters | 1 | 47 | 3.96 |
| Georg Umlauf | 2 | 134 | 16.86 |