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Spherical quadratic Bezier triangles with chord lengths parameterization and tripolar coordinates in space

Citace: [] BASTL, B., JÜTTLER, B., LÁVIČKA, M., SCHICHO, J., ŠÍR, Z. Spherical quadratic Bezier triangles with chord lengths parameterization and tripolar coordinates in space. 2009.
Druh: DALŠÍ AKTIVITY
Jazyk publikace: eng
Anglický název: Spherical quadratic Bezier triangles with chord lengths parameterization and tripolar coordinates in space
Rok vydání: 2009
Název zdroje: Technische Universität
Autoři: Ing. Bohumír Bastl Ph.D. , Univ.-Prof. Bert Jüttler Dr. , RNDr. Miroslav Lávička Ph.D. , Univ.-Prof. Josef Schicho Dr. , RNDr. Zbyněk Šír Ph.D.
Abstrakt EN: We consider special rational triangular Bezier surfaces of degree 2 on the sphere in standard form and show that these surfaces are parameterized by chord lengths. 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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