Volumes with piecewise quadratic medial surface transforms: Computation of boundaries and trimmed offsets

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F10%3A00503240" target="_blank" >RIV/49777513:23520/10:00503240 - 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
Volumes with piecewise quadratic medial surface transforms: Computation of boundaries and trimmed offsets
Original language description
MOS surfaces (i.e., medial surface transforms obeying a sum of squares condition) are rational surfaces in R^{3,1} which possess rational envelopes of the associated two-parameter families of spheres. Moreover, all offsets of the envelopes admit rationalparameterizations as well. Recently, it has been proved that quadratic triangular Bézier patches in View the MathML source are MOS surfaces. Following this result, we describe an algorithm for computing an exact rational envelope of a two-parameter family of spheres given by a quadratic patch in View the MathML source. The paper focuses mainly on the geometric aspects of the algorithm. 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 offsetting is the fact that the trimming procedure becomes considerably simpler.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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