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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Identifying and approximating monotonous segments of algebraic curves using support function representation
Original language description
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
Czech name
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Czech description
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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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Project
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Continuities
S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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