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Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F14%3A10285488%21RIV15-MSM-11320___
rdf:type
skos:Concept n16:Vysledek
rdfs:seeAlso
http://dx.doi.org/10.1016/j.cagd.2014.05.006
dcterms: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.
dcterms: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
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
skos:notation
RIV/00216208:11320/14:10285488!RIV15-MSM-11320___
n3:aktivita
n13:S n13:I
n3:aktivity
I, S
n3:cisloPeriodika
7-8
n3:dodaniDat
n9:2015
n3:domaciTvurceVysledku
n11:4296133 n11:8545634
n3:druhVysledku
n15:J
n3:duvernostUdaju
n8:S
n3:entitaPredkladatele
n18:predkladatel
n3:idSjednocenehoVysledku
20376
n3:idVysledku
RIV/00216208:11320/14:10285488
n3:jazykVysledku
n17:eng
n3:klicovaSlova
Arc-splines; Inflections approximation; Critical points; Support function; Algebraic curve
n3:klicoveSlovo
n4:Inflections%20approximation n4:Arc-splines n4:Algebraic%20curve n4:Critical%20points n4:Support%20function
n3:kodStatuVydavatele
NL - Nizozemsko
n3:kontrolniKodProRIV
[09DF9CB2F896]
n3:nazevZdroje
Computer Aided Geometric Design
n3:obor
n19:BA
n3:pocetDomacichTvurcuVysledku
2
n3:pocetTvurcuVysledku
2
n3:rokUplatneniVysledku
n9:2014
n3:svazekPeriodika
31
n3:tvurceVysledku
Šír, Zbyněk Blažková, Eva
n3:wos
000345056400004
s:issn
0167-8396
s:numberOfPages
15
n10:doi
10.1016/j.cagd.2014.05.006
n5:organizacniJednotka
11320