Cited By
View all- Bastl BJüttler BKosinka JLávička M(2010)Volumes with piecewise quadratic medial surface transformsComputer-Aided Design10.1016/j.cad.2010.02.00742:6(571-579)Online publication date: 1-Jun-2010
A symbolic-numerical envelope algorithm using quadratic MOS patches
Pages 175 - 186
Abstract
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 R3, 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 R3, 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 algorithm offers a good basis for consequent methods, e.g. computing rational approximations of envelopes associated to general (free-form) MSTs and inner offsets trimming.
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October 2009
380 pages
ISBN:9781605587110
DOI:10.1145/1629255
- Conference Chair:
- Wim Bronsvoort,
- General Chairs:
- Daniel Gonsor,
- William Regli,
- Thomas Grandine,
- Jan Vandenbrande,
- Program Chairs:
- Jens Gravesen,
- John Keyser
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Published: 05 October 2009
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SIAM '09: 2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
October 5 - 8, 2009
California, San Francisco
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View all- Bastl BJüttler BKosinka JLávička M(2010)Volumes with piecewise quadratic medial surface transformsComputer-Aided Design10.1016/j.cad.2010.02.00742:6(571-579)Online publication date: 1-Jun-2010
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