G2 Hermite Interpolation with Curves Represented by Multi-valued Trigonometric Support Functions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F12%3A43898297" target="_blank" >RIV/49777513:23520/12:43898297 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/978-3-642-27413-8_9" target="_blank" >http://dx.doi.org/10.1007/978-3-642-27413-8_9</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-642-27413-8_9" target="_blank" >10.1007/978-3-642-27413-8_9</a>

Jazyk výsledku

angličtina

Název v původním jazyce

G2 Hermite Interpolation with Curves Represented by Multi-valued Trigonometric Support Functions

Popis výsledku v původním jazyce

It was recently proved in that all rational hypocycloids and epicycloids are Pythagorean hodograph curves, i.e., rational curves with rational offsets. In this paper, we extend the discussion to a more general class of curves represented by trigonometricpolynomial support functions. We show that these curves are offsets to translated convolutions of scaled and rotated hypocycloids and epicycloids. Using this result, we formulate a new and very simple G2 Hermite interpolation algorithm based on solvinga small system of linear equations. The efficiency of the designed method is then presented on several examples. In particular, we show how to approximate general trochoids, which, as we prove, are not Pythagorean hodograph curves in general.

Název v anglickém jazyce

G2 Hermite Interpolation with Curves Represented by Multi-valued Trigonometric Support Functions

Popis výsledku anglicky

It was recently proved in that all rational hypocycloids and epicycloids are Pythagorean hodograph curves, i.e., rational curves with rational offsets. In this paper, we extend the discussion to a more general class of curves represented by trigonometricpolynomial support functions. We show that these curves are offsets to translated convolutions of scaled and rotated hypocycloids and epicycloids. Using this result, we formulate a new and very simple G2 Hermite interpolation algorithm based on solvinga small system of linear equations. The efficiency of the designed method is then presented on several examples. In particular, we show how to approximate general trochoids, which, as we prove, are not Pythagorean hodograph curves in general.

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)

Rok uplatnění

2012

Kód důvěrnosti údajů

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

Název periodika

Lecture Notes in Computer Science

ISSN

0302-9743

e-ISSN

—

Svazek periodika

2012

Číslo periodika v rámci svazku

6920

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

15

Strana od-do

142-156

Kód UT WoS článku

—

EID výsledku v databázi Scopus

—