Apollonian de Casteljau-type algorithms for complex rational Bézier curves

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Apollonian de Casteljau-type algorithms for complex rational Bézier curves

Popis výsledku v původním jazyce

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&apos;s roots.

Název v anglickém jazyce

Apollonian de Casteljau-type algorithms for complex rational Bézier curves

Popis výsledku anglicky

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&apos;s roots.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Computer Aided Geometric Design

ISSN

0167-8396

e-ISSN

1879-2332

Svazek periodika

107

Číslo periodika v rámci svazku

December 2023

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

9

Strana od-do

102254

Kód UT WoS článku

001092701800001

EID výsledku v databázi Scopus

2-s2.0-85174437009