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Computing rational boundaries of quadratic medial surface transforms

Citace: [] BASTL, B. Computing rational boundaries of quadratic medial surface transforms . Tonsberg, 2008.
Druh: PŘEDNÁŠKA, POSTER
Jazyk publikace: eng
Anglický název: Computing rational boundaries of quadratic medial surface transforms
Rok vydání: 2008
Místo konání: Tonsberg
Autoři: Bohumír Bastl
Abstrakt EN: The talk presents an algorithm for computation of rational envelope approximations of two-parameter families of sphere of quadratic MOS surfaces. Generally, 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 B\'ezier patches in R^{3,1} possess this property, i.e., they belong into the class of MOS surfaces. In this talk we give a direct proof of this fact and formulate an algorithm for computing the parametrization of a quadratic triangular B\'ezier patches in R^{3,1} fulfilling the MOS condition. Since these patches are capable of producing C^1 smooth approximations of medial surface transforms of spatial domains, we use this algorithm to generate rational approximations of envelopes of general medial surface transforms.
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