کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
440329 | 691000 | 2010 | 9 صفحه PDF | دانلود رایگان |

MOS surfaces (i.e., medial surface transforms obeying a sum of squares condition) are rational surfaces in R3,1R3,1 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 Bézier patches in R3,1R3,1 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 R3,1R3,1. The paper focuses mainly on the geometric aspects of the algorithm. Since these patches are capable of producing C1C1 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.
Journal: Computer-Aided Design - Volume 42, Issue 6, June 2010, Pages 571–579