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  • MOS surfaces are rational surfaces in R^{3,1} which provide rational envelopes of the associated two-parameter family of spheres. Recently, it has been proved that quadratic triangular Bezier patches in R^{3,1} are MOS surfaces. In this paper, we describe an algorithm for computing an exact rational envelope of a 2-parameter family of spheres given by a quadratic patch in R3,1. Since these patches are capable of producing C1 smooth approximations of medial surface transforms of spatial domains, we use this algorithm to generate rational approximations of envelopes of general medial surface transforms. One of the main advantages of this approach to envelope computations is the fact that the trimming procedure for the inner offsets becomes very simple.
  • MOS surfaces are rational surfaces in R^{3,1} which provide rational envelopes of the associated two-parameter family of spheres. Recently, it has been proved that quadratic triangular Bezier patches in R^{3,1} are MOS surfaces. In this paper, we describe an algorithm for computing an exact rational envelope of a 2-parameter family of spheres given by a quadratic patch in R3,1. Since these patches are capable of producing C1 smooth approximations of medial surface transforms of spatial domains, we use this algorithm to generate rational approximations of envelopes of general medial surface transforms. One of the main advantages of this approach to envelope computations is the fact that the trimming procedure for the inner offsets becomes very simple. (en)
  • Jako MOS plochy se označují ty racionální plochy v R^{3,1}, jež mají racionální obálky odpovídajících 2-parametrických systémů kulových ploch. V nedávné době se podařilo dokázat, že kvadratické Bézierovy pláty v R^{3,1} patří mezi MOS plochy. Obsahem tohoto článku je popis algoritmu na výpočet exaktního racionálního popisu obálky 2-parametrického systému kulových ploch, jenž je dán jakožto kvadratický plát v R^{3,1}. Vzhledem k tomu, že tyto pláty umožňují sestrojit C^1 hladkou aproximaci MST (medial surface transform) dané prostorové oblasti, lze uvedený algoritmus použít k sestrojení racionální aproximace obálky obecné MST. Jednou z hlavních výhod předloženého postupu je jednoduchost ořezávání vnitřních offsetových (ekvidistantních) ploch. (cs)
Title
  • Trimmed Offsets of General Surfaces Using Quadratic MOS Patches
  • Konference o geometrii a grafice 2008 (cs)
  • Trimmed Offsets of General Surfaces Using Quadratic MOS Patches (en)
skos:prefLabel
  • Trimmed Offsets of General Surfaces Using Quadratic MOS Patches
  • Konference o geometrii a grafice 2008 (cs)
  • Trimmed Offsets of General Surfaces Using Quadratic MOS Patches (en)
skos:notation
  • RIV/49777513:23520/08:00500797!RIV09-MSM-23520___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • Z(MSM4977751301)
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 400720
http://linked.open...ai/riv/idVysledku
  • RIV/49777513:23520/08:00500797
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • Quadratic Bézier triangles; MOS surfaces; trimmed offsets (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...ontrolniKodProRIV
  • [D3161A75A0FE]
http://linked.open...v/mistoKonaniAkce
  • Lednice
http://linked.open...i/riv/mistoVydani
  • Brno
http://linked.open...i/riv/nazevZdroje
  • Sborník příspěvků 28. konference o geometrii a grafice
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...UplatneniVysledku
http://linked.open...iv/tvurceVysledku
  • Bastl, Bohumír
  • Kosinka, Jiří
  • Lávička, Miroslav
http://linked.open...vavai/riv/typAkce
http://linked.open.../riv/zahajeniAkce
http://linked.open...n/vavai/riv/zamer
number of pages
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  • Mendelova zemědělská a lesnická univerzita v Brně
https://schema.org/isbn
  • 978-80-7375-249-1
http://localhost/t...ganizacniJednotka
  • 23520
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