Aproxiamce PH křivkami za pomoci evoluce a metody nejmenších čtverců

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F07%3A00005638" target="_blank" >RIV/00216208:11320/07:00005638 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Evolution-based Least-Squares fitting using Pythagorean Hodograph Spline curves

Popis výsledku v původním jazyce

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 initialpositions for the evolution are suggested.

Název v anglickém jazyce

Evolution-based Least-Squares fitting using Pythagorean Hodograph Spline curves

Popis výsledku anglicky

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 initialpositions for the evolution are suggested.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2007

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Computer Aided Geometric Design

ISSN

0167-8396

e-ISSN

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Svazek periodika

24

Číslo periodika v rámci svazku

24

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

17

Strana od-do

125-141

Kód UT WoS článku

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EID výsledku v databázi Scopus

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