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Spherical quadratic Bézier triangles with chord length parameterization and tripolar coordinates in space

Citace: [] BASTL, B., JÜTTLER, B. .., LÁVIČKA, M., SCHICHO, J., ŠÍR, Z. Spherical quadratic Bézier triangles with chord length parameterization and tripolar coordinates in space. Computer Aided Geometric Design, 2011, roč. 28, č. 2, s. 127-134. ISSN: 0167-8396
Druh: ČLÁNEK
Jazyk publikace: eng
Anglický název: Spherical quadratic Bézier triangles with chord length parameterization and tripolar coordinates in space
Rok vydání: 2011
Místo konání: Amsterdam
Název zdroje: Elsevier
Autoři: Ing. Bohumír Bastl Ph.D. , Prof. Bert Jüttler , RNDr. Miroslav Lávička Ph.D. , Prof. Josef Schicho , RNDr. Zbyněk Šír Ph.D.
Abstrakt EN: We consider special rational triangular Bézier 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.
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