Abstract
A new n-sided surface scheme is presented, that generalizes tensor product Bézier patches. Boundaries and corresponding cross-derivatives are specified as conventional Bézier surfaces of arbitrary degrees. The surface is defined over a convex polygonal domain; local coordinates are computed from generalized barycentric coordinates; control points are multiplied by weighted, biparametric Bernstein functions. A method for interpolating a middle point is also presented. This Generalized Bézier (GB) patch is based on a new displacement scheme that builds up multi-sided patches as a combination of a base patch, n displacement patches and an interior patch; this is considered to be an alternative to the Boolean sum concept. The input ribbons may have different degrees, but the final patch representation has a uniform degree. Interior control points - other than those specified by the user - are placed automatically by a special degree elevation algorithm. GB patches connect to adjacent Bézier surfaces with G1continuity. The control structure is simple and intuitive; the number of control points is proportional to those of quadrilateral control grids. The scheme is introduced through simple examples; suggestions for future work are also discussed.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 307-317 |
| Number of pages | 11 |
| Journal | Computer Graphics Forum |
| Volume | 35 |
| Issue number | 2 |
| DOIs | |
| State | Published - May 27 2016 |
| Externally published | Yes |
ASJC Scopus subject areas
- Computer Networks and Communications