Name
Abstract | ||
|---|---|---|
In (Grandine, 1989), it is proved that some types of subdivision do not preserve the convexity of Bézier nets and that for most triangulations, C 1 continuous convex Bernstein-Bézier triangular surface with convex Bézier nets must be linear. In this paper, it is first shown that subdivision always preserves weak convexity of Bézier nets, that is, the weak convexity condition of Bézier nets defined on a base triangle T is preserved on any subtriangles inside T . Then the invariance of weak convexity for elevation B-nets is proved. At last a necessary and sufficient condition characterized by the weak convexity of elevation B-net for the strict convexity of Bernstein-Bézier surface is given. |
Year | DOI | Venue |
|---|---|---|
1994 | 10.1016/0167-8396(94)90026-4 | Computer Aided Geometric Design |
Keywords | Field | DocType |
weak convexity conditions,weak convexity condition,b-net,triangular bernstein-bézier surface,subdivision,invariance | Topology,Mathematical optimization,Convexity,Invariant (physics),Computer Aided Design,Regular polygon,Bézier curve,Subdivision,Computer graphics,Mathematics | Journal |
Volume | Issue | ISSN |
11 | 1 | Computer Aided Geometric Design |
Citations | PageRank | References |
3 | 0.48 | 4 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yu Yu Feng | 1 | 13 | 2.96 |
| Falai Chen | 2 | 403 | 32.47 |
| Hong Ling Zhou | 3 | 3 | 0.48 |