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  • 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. (en)
Title
  • A Symbolic-Numerical Envelope Algorithm Using Quadratic MOS Patches
  • A Symbolic-Numerical Envelope Algorithm Using Quadratic MOS Patches (en)
skos:prefLabel
  • A Symbolic-Numerical Envelope Algorithm Using Quadratic MOS Patches
  • A Symbolic-Numerical Envelope Algorithm Using Quadratic MOS Patches (en)
skos:notation
  • RIV/49777513:23520/09:00501788!RIV10-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
  • 301619
http://linked.open...ai/riv/idVysledku
  • RIV/49777513:23520/09:00501788
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • MOS surfaces; quadratic patches; envelope formula; Bézier clipping; inner offsets; trimming (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...ontrolniKodProRIV
  • [036513DFEFE9]
http://linked.open...v/mistoKonaniAkce
  • San Francisco, California
http://linked.open...i/riv/mistoVydani
  • New York, NY, USA
http://linked.open...i/riv/nazevZdroje
  • ACM Symposium on Solid and Physical Modeling: 2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
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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  • ACM
https://schema.org/isbn
  • 978-1-60558-711-0
http://localhost/t...ganizacniJednotka
  • 23520
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