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Statements

Subject Item
n2:RIV%2F49777513%3A23520%2F09%3A00501788%21RIV10-MSM-23520___
rdf:type
skos:Concept n21:Vysledek
dcterms:description
In this paper, we describe an algorithm for generating an exact rational envelope of a two-parameter family of spheres given by a quadratic patch in R^{3,1}, which is considered as a medial surface transform (MST) of a spatial domain. Recently, it has been proved that quadratic triangular Bézier patches in R^{3,1} belong to the class of MOS surfaces (i.e., surfaces providing rational envelopes of the associated two-parameter family of spheres). We give a detailed description of the symbolic and numerical steps of the envelope algorithm and study the error involved in the numerical part. The presented method is then demonstrated on several examples. Moreover, since quadratic MOS patches are capable of producing C1 approximations of MSTs, this algorithm offers a good basis for consequent methods, e.g. computing rational approximations of envelopes associated to general (free-form) MSTs and inner offsets trimming. In this paper, we describe an algorithm for generating an exact rational envelope of a two-parameter family of spheres given by a quadratic patch in R^{3,1}, which is considered as a medial surface transform (MST) of a spatial domain. Recently, it has been proved that quadratic triangular Bézier patches in R^{3,1} belong to the class of MOS surfaces (i.e., surfaces providing rational envelopes of the associated two-parameter family of spheres). We give a detailed description of the symbolic and numerical steps of the envelope algorithm and study the error involved in the numerical part. The presented method is then demonstrated on several examples. Moreover, since quadratic MOS patches are capable of producing C1 approximations of MSTs, this algorithm offers a good basis for consequent methods, e.g. computing rational approximations of envelopes associated to general (free-form) MSTs and inner offsets trimming.
dcterms:title
A Symbolic-Numerical Envelope Algorithm Using Quadratic MOS Patches A Symbolic-Numerical Envelope Algorithm Using Quadratic MOS Patches
skos:prefLabel
A Symbolic-Numerical Envelope Algorithm Using Quadratic MOS Patches A Symbolic-Numerical Envelope Algorithm Using Quadratic MOS Patches
skos:notation
RIV/49777513:23520/09:00501788!RIV10-MSM-23520___
n3:aktivita
n6:Z
n3:aktivity
Z(MSM4977751301)
n3:dodaniDat
n10:2010
n3:domaciTvurceVysledku
n12:1043161 n12:3013626
n3:druhVysledku
n20:D
n3:duvernostUdaju
n8:S
n3:entitaPredkladatele
n14:predkladatel
n3:idSjednocenehoVysledku
301619
n3:idVysledku
RIV/49777513:23520/09:00501788
n3:jazykVysledku
n19:eng
n3:klicovaSlova
MOS surfaces; quadratic patches; envelope formula; Bézier clipping; inner offsets; trimming
n3:klicoveSlovo
n4:B%C3%A9zier%20clipping n4:envelope%20formula n4:quadratic%20patches n4:trimming n4:inner%20offsets n4:MOS%20surfaces
n3:kontrolniKodProRIV
[036513DFEFE9]
n3:mistoKonaniAkce
San Francisco, California
n3:mistoVydani
New York, NY, USA
n3:nazevZdroje
ACM Symposium on Solid and Physical Modeling: 2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
n3:obor
n11:BA
n3:pocetDomacichTvurcuVysledku
2
n3:pocetTvurcuVysledku
3
n3:rokUplatneniVysledku
n10:2009
n3:tvurceVysledku
Lávička, Miroslav Kosinka, Jiří Bastl, Bohumír
n3:typAkce
n16:WRD
n3:zahajeniAkce
2009-10-08+02:00
n3:zamer
n9:MSM4977751301
s:numberOfPages
12
n7:hasPublisher
ACM
n15:isbn
978-1-60558-711-0
n18:organizacniJednotka
23520