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Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F07%3A00005638%21RIV08-MSM-11320___
rdf:type
n5:Vysledek skos:Concept
dcterms: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. Konstruujeme PH křivky aproximující dané body.
dcterms:title
Aproxiamce PH křivkami za pomoci evoluce a metody nejmenších čtverců Evolution-based Least-Squares fitting using Pythagorean Hodograph Spline curves Evolution-based Least-Squares fitting using Pythagorean Hodograph Spline curves
skos:prefLabel
Evolution-based Least-Squares fitting using Pythagorean Hodograph Spline curves Evolution-based Least-Squares fitting using Pythagorean Hodograph Spline curves Aproxiamce PH křivkami za pomoci evoluce a metody nejmenších čtverců
skos:notation
RIV/00216208:11320/07:00005638!RIV08-MSM-11320___
n4:strany
125;141
n4:aktivita
n17:Z
n4:aktivity
Z(MSM0021620839)
n4:cisloPeriodika
24
n4:dodaniDat
n12:2008
n4:domaciTvurceVysledku
n18:4296133
n4:druhVysledku
n15:J
n4:duvernostUdaju
n16:S
n4:entitaPredkladatele
n10:predkladatel
n4:idSjednocenehoVysledku
420894
n4:idVysledku
RIV/00216208:11320/07:00005638
n4:jazykVysledku
n7:eng
n4:klicovaSlova
Evolution-based; Least-Squares; fitting; using; Pythagorean; Hodograph; Spline; curves
n4:klicoveSlovo
n6:curves n6:using n6:fitting n6:Evolution-based n6:Hodograph n6:Least-Squares n6:Spline n6:Pythagorean
n4:kodStatuVydavatele
NL - Nizozemsko
n4:kontrolniKodProRIV
[861B9C514E23]
n4:nazevZdroje
Computer Aided Geometric Design
n4:obor
n14:BA
n4:pocetDomacichTvurcuVysledku
1
n4:pocetTvurcuVysledku
3
n4:rokUplatneniVysledku
n12:2007
n4:svazekPeriodika
24
n4:tvurceVysledku
Šír, Zbyněk
n4:zamer
n13:MSM0021620839
s:issn
0167-8396
s:numberOfPages
17
n11:organizacniJednotka
11320