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

Result code in 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>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Evolution-based Least-Squares fitting using Pythagorean Hodograph Spline curves
Original language 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 initialpositions for the evolution are suggested.
Czech name
Aproxiamce PH křivkami za pomoci evoluce a metody nejmenších čtverců
Czech description
Konstruujeme PH křivky aproximující dané body.

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2007
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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