Apollonian de Casteljau-type algorithms for complex rational Bézier curves
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10474940" target="_blank" >RIV/00216208:11320/23:10474940 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=cIj2gMfgTK" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=cIj2gMfgTK</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.cagd.2023.102254" target="_blank" >10.1016/j.cagd.2023.102254</a>
Alternative languages
Result language
angličtina
Original language name
Apollonian de Casteljau-type algorithms for complex rational Bézier curves
Original language description
We describe a new de Casteljau-type algorithm for complex rational Bezier curves. After proving that these curves exhibit the maximal possible circularity, we construct their points via a de Casteljau-type algorithm over complex numbers. Consequently, the line segments that correspond to convex linear combinations in affine spaces are replaced by circular arcs. In difference to the algorithm of Sanchez-Reyes (2009), the construction of all the points is governed by (generically complex) roots of the denominator, using one of them for each level. Moreover, one of the bi-polar coordinates is fixed at each level, independently of the parameter value. A rational curve of the complex degree n admits generically n! distinct de Casteljau-type algorithms, corresponding to the different orderings of the denominator's roots.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
—
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Computer Aided Geometric Design
ISSN
0167-8396
e-ISSN
1879-2332
Volume of the periodical
107
Issue of the periodical within the volume
December 2023
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
9
Pages from-to
102254
UT code for WoS article
001092701800001
EID of the result in the Scopus database
2-s2.0-85174437009