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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F11%3A43898295" target="_blank" >RIV/49777513:23520/11:43898295 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.cagd.2010.11.001" target="_blank" >http://dx.doi.org/10.1016/j.cagd.2010.11.001</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.cagd.2010.11.001" target="_blank" >10.1016/j.cagd.2010.11.001</a>

Result language
angličtina
Original language name
Spherical quadratic Bézier triangles with chord length parameterization and tripolar coordinates in space
Original language description
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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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