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Statements

Subject Item
n2:RIV%2F49777513%3A23520%2F12%3A43898297%21RIV13-MSM-23520___
rdf:type
skos:Concept n15:Vysledek
dcterms:description
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 trigonometric polynomial 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 solving a 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. 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 trigonometric polynomial 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 solving a 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.
dcterms:title
G2 Hermite Interpolation with Curves Represented by Multi-valued Trigonometric Support Functions G2 Hermite Interpolation with Curves Represented by Multi-valued Trigonometric Support Functions
skos:prefLabel
G2 Hermite Interpolation with Curves Represented by Multi-valued Trigonometric Support Functions G2 Hermite Interpolation with Curves Represented by Multi-valued Trigonometric Support Functions
skos:notation
RIV/49777513:23520/12:43898297!RIV13-MSM-23520___
n15:predkladatel
n16:orjk%3A23520
n3:aktivita
n12:Z
n3:aktivity
Z(MSM4977751301)
n3:cisloPeriodika
6920
n3:dodaniDat
n11:2013
n3:domaciTvurceVysledku
n5:4296133 n5:1043161 n5:3013626
n3:druhVysledku
n18:J
n3:duvernostUdaju
n14:S
n3:entitaPredkladatele
n6:predkladatel
n3:idSjednocenehoVysledku
138564
n3:idVysledku
RIV/49777513:23520/12:43898297
n3:jazykVysledku
n7:eng
n3:klicovaSlova
Hypocycloids, epicycloids, Pythagorean hodograph curves, support function, Hermite Interpolation
n3:klicoveSlovo
n10:Hypocycloids n10:epicycloids n10:support%20function n10:Pythagorean%20hodograph%20curves n10:Hermite%20Interpolation
n3:kodStatuVydavatele
DE - Spolková republika Německo
n3:kontrolniKodProRIV
[2320F4BCC576]
n3:nazevZdroje
Lecture Notes in Computer Science
n3:obor
n17:BA
n3:pocetDomacichTvurcuVysledku
3
n3:pocetTvurcuVysledku
3
n3:rokUplatneniVysledku
n11:2012
n3:svazekPeriodika
2012
n3:tvurceVysledku
Šír, Zbyněk Bastl, Bohumír Lávička, Miroslav
n3:zamer
n4:MSM4977751301
s:issn
0302-9743
s:numberOfPages
15
n20:doi
10.1007/978-3-642-27413-8_9
n13:organizacniJednotka
23520