Identifying and approximating monotonous segments of algebraic curves using support function representation

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10285488" target="_blank" >RIV/00216208:11320/14:10285488 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.cagd.2014.05.006" target="_blank" >http://dx.doi.org/10.1016/j.cagd.2014.05.006</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.cagd.2014.05.006" target="_blank" >10.1016/j.cagd.2014.05.006</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Identifying and approximating monotonous segments of algebraic curves using support function representation

Popis výsledku v původním jazyce

Algorithms describing the topology of real algebraic curves search primarily the singular points and they are usually based on algebraic techniques applied directly to the curve equation. We adopt a different approach, which is primarily based on the identification and approximation of smooth monotonous curve segments, which can in certain cases cross the singularities of the curve. We use not only the primary algebraic equation of the planar curve but also (and more importantly) its implicit support function representation. This representation is also used for an approximation of the segments. This way we obtain an approximate graph of the entire curve which has several nice properties. It approximates the curve within a given Hausdorff distance. Theactual error can be measured efficiently and behaves as O(N-3) where N is the number of segments. The approximate graph is rational and has rational offsets. In the simplest case it consists of arc segments which are efficiently represent

Název v anglickém jazyce

Identifying and approximating monotonous segments of algebraic curves using support function representation

Popis výsledku anglicky

Algorithms describing the topology of real algebraic curves search primarily the singular points and they are usually based on algebraic techniques applied directly to the curve equation. We adopt a different approach, which is primarily based on the identification and approximation of smooth monotonous curve segments, which can in certain cases cross the singularities of the curve. We use not only the primary algebraic equation of the planar curve but also (and more importantly) its implicit support function representation. This representation is also used for an approximation of the segments. This way we obtain an approximate graph of the entire curve which has several nice properties. It approximates the curve within a given Hausdorff distance. Theactual error can be measured efficiently and behaves as O(N-3) where N is the number of segments. The approximate graph is rational and has rational offsets. In the simplest case it consists of arc segments which are efficiently represent

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

S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2014

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

31

Číslo periodika v rámci svazku

7-8

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

15

Strana od-do

358-372

Kód UT WoS článku

000345056400004

EID výsledku v databázi Scopus

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