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

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An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://dx.doi.org/10.1016/j.cagd.2014.05.006
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. The actual 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 represented via the support function. The question of topological equivalence of the approximate and precise graphs of the curve is also addressed and solved using bounding triangles and axis projections. The theoretical description of the whole procedure is accompanied by several examples which show the efficiency of our method. 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. The actual 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 represented via the support function. The question of topological equivalence of the approximate and precise graphs of the curve is also addressed and solved using bounding triangles and axis projections. The theoretical description of the whole procedure is accompanied by several examples which show the efficiency of our method. (en)
Title	Identifying and approximating monotonous segments of algebraic curves using support function representation Identifying and approximating monotonous segments of algebraic curves using support function representation (en)
skos:prefLabel	Identifying and approximating monotonous segments of algebraic curves using support function representation Identifying and approximating monotonous segments of algebraic curves using support function representation (en)
skos:notation	RIV/00216208:11320/14:10285488!RIV15-MSM-11320___
http://linked.open...avai/riv/aktivita	I S
http://linked.open...avai/riv/aktivity	I, S
http://linked.open...iv/cisloPeriodika	7-8
http://linked.open...vai/riv/dodaniDat	2015
http://linked.open...aciTvurceVysledku	Blažková, Eva Šír, Zbyněk
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	20376
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/14:10285488
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Arc-splines; Inflections approximation; Critical points; Support function; Algebraic curve (en)
http://linked.open.../riv/klicoveSlovo	Critical points Algebraic curve Support function Arc-splines Inflections approximation
http://linked.open...odStatuVydavatele	NL - Nizozemsko
http://linked.open...ontrolniKodProRIV	[09DF9CB2F896]
http://linked.open...i/riv/nazevZdroje	Computer Aided Geometric Design
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...UplatneniVysledku	2014
http://linked.open...v/svazekPeriodika	31
http://linked.open...iv/tvurceVysledku	Blažková, Eva Šír, Zbyněk
http://linked.open...ain/vavai/riv/wos	000345056400004
issn	0167-8396
number of pages	15 (xsd:int)
http://bibframe.org/vocab/doi	10.1016/j.cagd.2014.05.006
http://localhost/t...ganizacniJednotka	11320

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