A Symbolic-Numerical Envelope Algorithm Using Quadratic MOS Patches

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F09%3A00501788" target="_blank" >RIV/49777513:23520/09:00501788 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
A Symbolic-Numerical Envelope Algorithm Using Quadratic MOS Patches
Original language 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 algorithmoffers a good basis for consequent methods, e.g. computing rational approximations of envelopes associated to general (free-form) MSTs and inner offsets trimming.
Czech name
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Czech description
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Publication year
2009
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
ACM Symposium on Solid and Physical Modeling: 2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
ISBN
978-1-60558-711-0
ISSN
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e-ISSN
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Number of pages
12
Pages from-to
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Publisher name
ACM
Place of publication
New York, NY, USA
Event location
San Francisco, California
Event date
Oct 8, 2009
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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