Name
Abstract | ||
|---|---|---|
Barycentric coordinates are unique for triangles, but there are many possible generalizations to con- vex polygons. In this paper we derive sharp upper and lower bounds on all barycentric coordinates over convex polygons and use them to show that all such coordinates have the same continuous extension to the boundary. We then present a general approach for constructing such coordinates and use it to show that the Wachspress, mean value, and discrete harmonic coordinates all belong to a unifying one-parameter family of smooth three-point coordinates. We show that the only members of this family that are positive, and therefore barycentric, are the Wachspress and mean value ones. However, our general approach allows us to construct several sets of smooth five-point coordinates, which are positive and therefore barycentric. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1007/s10444-004-7611-6 | Adv. Comput. Math. |
Keywords | Field | DocType |
barycentric coordinates,convex polygons,rational polynomials | Mathematical optimization,Log-polar coordinates,Bipolar coordinates,Circumscribed circle,Action-angle coordinates,Orthogonal coordinates,Generalized coordinates,Trilinear coordinates,Mathematics,Barycentric coordinate system | Journal |
Volume | Issue | ISSN |
24 | 1-4 | 1019-7168 |
Citations | PageRank | References |
75 | 5.54 | 12 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Michael S. Floater | 1 | 1333 | 117.22 |
| Kai Hormann | 2 | 726 | 53.94 |
| G. Kos | 3 | 287 | 19.43 |