About: C2 Hermite interpolation by Pythagorean hodograph space curves     Goto   Sponge   NotDistinct   Permalink

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Description
  • We solve the problem of C2 Hermite interpolation by Pythagorean Hodograph (PH) space curves. More precisely, for any set of C2 space boundary data (two points with associated Żrst and second derivatives) we construct a four{dimensional family of PH interpolants of degree 9 and introduce a symetrically invariant parameterization of this family. This parameterization is used to identify a particular solution, which has the following properties. Firstly, it preserves planarity, i.e., the interpolant to planar data is a planar PH curve. Secondly, it has the best possible approximation order 6. Thirdly, it is symmetric in the sense that the interpolant of the \reversed' set of boundary data is simply the \reversed' original interpolant. This particular PH interpolant is exploited for designing algorithms for converting (possibly piecewise) analytical curves into a piecewise PH curve of degree 9 which is globally C2.
  • We solve the problem of C2 Hermite interpolation by Pythagorean Hodograph (PH) space curves. More precisely, for any set of C2 space boundary data (two points with associated Żrst and second derivatives) we construct a four{dimensional family of PH interpolants of degree 9 and introduce a symetrically invariant parameterization of this family. This parameterization is used to identify a particular solution, which has the following properties. Firstly, it preserves planarity, i.e., the interpolant to planar data is a planar PH curve. Secondly, it has the best possible approximation order 6. Thirdly, it is symmetric in the sense that the interpolant of the \reversed' set of boundary data is simply the \reversed' original interpolant. This particular PH interpolant is exploited for designing algorithms for converting (possibly piecewise) analytical curves into a piecewise PH curve of degree 9 which is globally C2. (en)
  • V tomto článku plně řešíme problem C2 interpolace PH křivkami. (cs)
Title
  • C2 Hermite interpolation by Pythagorean hodograph space curves
  • C2 Hermite interpolation by Pythagorean hodograph space curves (en)
  • C2 Hermitovská interpolace Pythagorejskými křivkami (cs)
skos:prefLabel
  • C2 Hermite interpolation by Pythagorean hodograph space curves
  • C2 Hermite interpolation by Pythagorean hodograph space curves (en)
  • C2 Hermitovská interpolace Pythagorejskými křivkami (cs)
skos:notation
  • RIV/00216208:11320/07:00005642!RIV08-MSM-11320___
http://linked.open.../vavai/riv/strany
  • 1373;1391
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • Z(MSM0021620839)
http://linked.open...iv/cisloPeriodika
  • 76
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
  • 415649
http://linked.open...ai/riv/idVysledku
  • RIV/00216208:11320/07:00005642
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • Hermite; interpolation; Pythagorean; hodograph; space; curves (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • US - Spojené státy americké
http://linked.open...ontrolniKodProRIV
  • [981D5F6C8BB9]
http://linked.open...i/riv/nazevZdroje
  • Mathematics of Computation
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 2007
http://linked.open...iv/tvurceVysledku
  • Šír, Zbyněk
http://linked.open...n/vavai/riv/zamer
issn
  • 0025-5718
number of pages
http://localhost/t...ganizacniJednotka
  • 11320
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