Planar C^1 Hermite interpolation with uniform and non-uniform TC-biarcs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F13%3A43916872" target="_blank" >RIV/49777513:23520/13:43916872 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.cagd.2012.07.003" target="_blank" >http://dx.doi.org/10.1016/j.cagd.2012.07.003</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.cagd.2012.07.003" target="_blank" >10.1016/j.cagd.2012.07.003</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Planar C^1 Hermite interpolation with uniform and non-uniform TC-biarcs

Popis výsledku v původním jazyce

Pythagorean hodograph curves (shortly PH curves), introduced in Farouki and Sakkalis (1990), form an important subclass of polynomial parametric curves and currently represent standard objects in geometric modelling. In this paper, we focus on Tschirnhausen cubic as the only one Pythagorean hodograph cubic and we study planar C^1 Hermite interpolation with two arcs of Tschirnhausen cubic joined with C^1 continuity (the so-called TC-biarc). We extend results presented in Farouki and Peters (1996) in several ways. We study an asymptotical behaviour of the conversion of an arbitrary planar curve with well defined tangent vectors everywhere to a C^1 PH cubic spline curve and we prove that the approximation order is 3. Further, we analyze the shape of TC-biarcs and provide a sufficient condition for input data guaranteeing TC-biarc without local and pairwise self-intersections. Finally, we generalize the basic uniform method to the non-uniform case, which introduces a free shape parameter,

Název v anglickém jazyce

Planar C^1 Hermite interpolation with uniform and non-uniform TC-biarcs

Popis výsledku anglicky

Pythagorean hodograph curves (shortly PH curves), introduced in Farouki and Sakkalis (1990), form an important subclass of polynomial parametric curves and currently represent standard objects in geometric modelling. In this paper, we focus on Tschirnhausen cubic as the only one Pythagorean hodograph cubic and we study planar C^1 Hermite interpolation with two arcs of Tschirnhausen cubic joined with C^1 continuity (the so-called TC-biarc). We extend results presented in Farouki and Peters (1996) in several ways. We study an asymptotical behaviour of the conversion of an arbitrary planar curve with well defined tangent vectors everywhere to a C^1 PH cubic spline curve and we prove that the approximation order is 3. Further, we analyze the shape of TC-biarcs and provide a sufficient condition for input data guaranteeing TC-biarc without local and pairwise self-intersections. Finally, we generalize the basic uniform method to the non-uniform case, which introduces a free shape parameter,

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

—

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)<br>S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2013

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

30

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

20

Strana od-do

58-77

Kód UT WoS článku

—

EID výsledku v databázi Scopus

—