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Surfaces with Rational Chord Length Parameterization

BASTL, B., JÜTTLER, B., LÁVIČKA, M., ŠÍR, Z. Surfaces with Rational Chord Length Parameterization. Lecture Notes in Computer Science, 2010, roč. 2010, č. 6130, s. 19-28. ISSN: 0302-9743
Jazyk publikace: eng
Anglický název: Surfaces with Rational Chord Length Parameterization
Rok vydání: 2010
Místo konání: Heidelberg
Název zdroje: Springer
Autoři: Ing. Bohumír Bastl Ph.D. , Prof. Bert Jüttler , RNDr. Miroslav Lávička Ph.D. , RNDr. Zbyněk Šír Ph.D.
Abstrakt EN: We consider a rational triangular Bézier surface of degree n and study conditions under which it is rationally parameterized by chord lengths (RCL surface) with respect to the reference circle. The distinguishing property of these surfaces is that the ratios of the three distances of a point to the three vertices of an arbitrary triangle inscribed to the reference circle and the ratios of the distances of the parameter point to the three vertices of the corresponding domain triangle are identical. This RCL property, which extends an observation about rational curves parameterized by chord lengths, was firstly observed in the surface case for patches on spheres. In the present paper, we analyze the entire family of RCL surfaces, provide their general parameterization and thoroughly investigate their properties.
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