Name
Abstract | ||
|---|---|---|
A well-documented problem of Catmull and Clark subdivision surfaces is that, in the neighborhood of extraordinary points, the curvature is unbounded and fluctuates. In fact, since one of the eigenvalues that determines elliptic shape is too small, the limit surface can have a saddle point when the designer's input mesh suggests a convex shape. Here, we replace, near the extraordinary point, Catmull-Clark subdivision by another set of rules based on refining each bi-cubic B-spline into nine. This provides many localized degrees of freedom for special rules that need not reach out to neighbor vertices in order to tune the behavior. In this paper, we provide a strategy for setting such degrees of freedom and exhibit tuned ternary quad subdivision that yields surfaces with bounded curvature, nonnegative weights and full contribution of elliptic and hyperbolic shape components. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1016/j.cagd.2007.03.009 | Computer Aided Geometric Design |
Keywords | Field | DocType |
subdivision,convex hull,bi-cubic b-spline,ternary subdivision,extraordinary point,hyperbolic shape component,bounded curvature,elliptic shape,quadrilateral mesh,ternary quad subdivision,full contribution,convex shape,catmull-clark subdivision,saddle point,ternary,degree of freedom,rule based,eigenvalues | Topology,Curvature,Saddle point,Vertex (geometry),Convex hull,Regular polygon,Finite subdivision rule,Subdivision surface,Subdivision,Mathematics | Journal |
Volume | Issue | ISSN |
24 | 6 | Computer Aided Geometric Design |
Citations | PageRank | References |
4 | 0.45 | 6 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Tianyun Ni | 1 | 82 | 5.77 |
| Ahmad H. Nasri | 2 | 430 | 121.97 |
| Jörg Peters | 3 | 267 | 33.10 |