Name
Title | ||
|---|---|---|
Spherical quadratic Bézier triangles with chord length parameterization and tripolar coordinates in space |
Abstract | ||
|---|---|---|
We consider special rational triangular Bezier surfaces of degree two on the sphere in standard form and show that these surfaces are parameterized by chord length. More precisely, it is shown that the ratios of the three distances of a point to the patch vertices and the ratios of the distances of the parameter point to the three vertices of the (suitably chosen) domain triangle are identical. This observation extends an observation of Farin (2006) about rational quadratic curves representing circles to the case of surfaces. In addition, we discuss the relation to tripolar coordinates. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1016/j.cagd.2010.11.001 | Computer Aided Geometric Design |
Keywords | Field | DocType |
domain triangle,patch vertex,chord length parameterization,rational patches on the sphere,rational quadratic,parameter point,standard form,chord length parameterizations,tripolar coordinates,quadratic rational bézier patches,special rational triangular bezier,zier triangle,chord length,spherical quadratic b | Topology,Parametrization,Vertex (geometry),Polynomial interpolation,Algebraic curve,Quadratic equation,Arc length,Bézier curve,Chord (geometry),Geometry,Mathematics | Journal |
Volume | Issue | ISSN |
28 | 2 | Computer Aided Geometric Design |
Citations | PageRank | References |
4 | 0.45 | 8 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Bohumír Bastl | 1 | 136 | 10.49 |
| Bert Jüttler | 2 | 1148 | 96.12 |
| Miroslav LáVičKa | 3 | 158 | 11.36 |
| Josef Schicho | 4 | 121 | 21.43 |
| Zbynk Šír | 5 | 54 | 3.25 |