Support function at inflection points of planar curves

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10389284" target="_blank" >RIV/00216208:11320/18:10389284 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.cagd.2018.05.004" target="_blank" >https://doi.org/10.1016/j.cagd.2018.05.004</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.cagd.2018.05.004" target="_blank" >10.1016/j.cagd.2018.05.004</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Support function at inflection points of planar curves

Popis výsledku v původním jazyce

We study the support function in the neighborhood of inflections of oriented planar curves. Even for a regular curve, the support function is not regular at the inflection and is multivalued on its neighborhood. We describe this function using an implicit algebraic equation and the rational Puiseux series of its branches. Based on these results we are able to approximate the curve at its inflection to any desired degree by curves with a simple support function, which consequently possess rational offsets. We also study the G(1) Hermite interpolation at two points of a planar curve. It is reduced to the functional C-1 interpolation of the support function. For the sake of comparison and better understanding, we show (using standard methods) that its approximation order is 4 for inflection-free curves. In the presence of inflection points this approximation is known to be less efficient. We analyze this phenomenon in detail and prove that by applying a nonuniform subdivision scheme it is possible to receive the best possible approximation order 4, even in the inflection case.

Název v anglickém jazyce

Support function at inflection points of planar curves

Popis výsledku anglicky

We study the support function in the neighborhood of inflections of oriented planar curves. Even for a regular curve, the support function is not regular at the inflection and is multivalued on its neighborhood. We describe this function using an implicit algebraic equation and the rational Puiseux series of its branches. Based on these results we are able to approximate the curve at its inflection to any desired degree by curves with a simple support function, which consequently possess rational offsets. We also study the G(1) Hermite interpolation at two points of a planar curve. It is reduced to the functional C-1 interpolation of the support function. For the sake of comparison and better understanding, we show (using standard methods) that its approximation order is 4 for inflection-free curves. In the presence of inflection points this approximation is known to be less efficient. We analyze this phenomenon in detail and prove that by applying a nonuniform subdivision scheme it is possible to receive the best possible approximation order 4, even in the inflection case.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA17-01171S" target="_blank" >GA17-01171S: Invariantní diferenciální operátory a jejich aplikace v geometrickém modelování a v teorii optimálního řízení</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

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

—

Svazek periodika

63

Číslo periodika v rámci svazku

July

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

13

Strana od-do

109-121

Kód UT WoS článku

000438831800007

EID výsledku v databázi Scopus

2-s2.0-85047000408