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  • 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. (en)
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 (en)
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 (en)
skos:notation
  • RIV/49777513:23520/12:43898297!RIV13-MSM-23520___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • Z(MSM4977751301)
http://linked.open...iv/cisloPeriodika
  • 6920
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 138564
http://linked.open...ai/riv/idVysledku
  • RIV/49777513:23520/12:43898297
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • Hypocycloids, epicycloids, Pythagorean hodograph curves, support function, Hermite Interpolation (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV
  • [2320F4BCC576]
http://linked.open...i/riv/nazevZdroje
  • Lecture Notes in Computer Science
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 2012
http://linked.open...iv/tvurceVysledku
  • Bastl, Bohumír
  • Lávička, Miroslav
  • Šír, Zbyněk
http://linked.open...n/vavai/riv/zamer
issn
  • 0302-9743
number of pages
http://bibframe.org/vocab/doi
  • 10.1007/978-3-642-27413-8_9
http://localhost/t...ganizacniJednotka
  • 23520
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