About: Evolution-based Least-Squares fitting using Pythagorean Hodograph Spline curves     Goto   Sponge   NotDistinct   Permalink

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Description
  • The problem of approximating a given set of data points by splines composed of Pythagorean Hodograph (PH) curves is addressed. We discuss this problem in a framework that is not only restricted to PH spline curves, but can be applied to more general representations of shapes. In order to solve the highly nonlinear curve fitting problem, we formulate an evolution process within the family of PH spline curves. This process generates a family of curves which depends on a timelike variable t. The best approximant is shown to be a stationary point of this evolution process, which is described by a differential equation. Solving it numerically by Euler's method is shown to be related to GaussNewton iterations. Different ways of constructing suitable initial positions for the evolution are suggested.
  • The problem of approximating a given set of data points by splines composed of Pythagorean Hodograph (PH) curves is addressed. We discuss this problem in a framework that is not only restricted to PH spline curves, but can be applied to more general representations of shapes. In order to solve the highly nonlinear curve fitting problem, we formulate an evolution process within the family of PH spline curves. This process generates a family of curves which depends on a timelike variable t. The best approximant is shown to be a stationary point of this evolution process, which is described by a differential equation. Solving it numerically by Euler's method is shown to be related to GaussNewton iterations. Different ways of constructing suitable initial positions for the evolution are suggested. (en)
  • Konstruujeme PH křivky aproximující dané body. (cs)
Title
  • Evolution-based Least-Squares fitting using Pythagorean Hodograph Spline curves
  • Aproxiamce PH křivkami za pomoci evoluce a metody nejmenších čtverců (cs)
  • Evolution-based Least-Squares fitting using Pythagorean Hodograph Spline curves (en)
skos:prefLabel
  • Evolution-based Least-Squares fitting using Pythagorean Hodograph Spline curves
  • Aproxiamce PH křivkami za pomoci evoluce a metody nejmenších čtverců (cs)
  • Evolution-based Least-Squares fitting using Pythagorean Hodograph Spline curves (en)
skos:notation
  • RIV/00216208:11320/07:00005638!RIV08-MSM-11320___
http://linked.open.../vavai/riv/strany
  • 125;141
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • Z(MSM0021620839)
http://linked.open...iv/cisloPeriodika
  • 24
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
  • 420894
http://linked.open...ai/riv/idVysledku
  • RIV/00216208:11320/07:00005638
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • Evolution-based; Least-Squares; fitting; using; Pythagorean; Hodograph; Spline; curves (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • NL - Nizozemsko
http://linked.open...ontrolniKodProRIV
  • [861B9C514E23]
http://linked.open...i/riv/nazevZdroje
  • Computer Aided Geometric Design
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 24
http://linked.open...iv/tvurceVysledku
  • Šír, Zbyněk
http://linked.open...n/vavai/riv/zamer
issn
  • 0167-8396
number of pages
http://localhost/t...ganizacniJednotka
  • 11320
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