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• W2000651678 abstract "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 rational parameterizations as well. Recently, it has been proved that quadratic triangular Bezier patches in R^3^,^1 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 R^3^,^1. The paper focuses mainly on the geometric aspects of the algorithm. 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. One of the main advantages of this approach to offsetting is the fact that the trimming procedure becomes considerably simpler." @default.
• W2000651678 created "2016-06-24" @default.
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• W2000651678 date "2010-06-01" @default.
• W2000651678 modified "2023-09-23" @default.
• W2000651678 title "Volumes with piecewise quadratic medial surface transforms: Computation of boundaries and trimmed offsets" @default.
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• W2000651678 doi "https://doi.org/10.1016/j.cad.2010.02.007" @default.
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