Paper Info
Title
Volumes with piecewise quadratic medial surface transforms: Computation of boundaries and trimmed offsets
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.
Year
DOI
Venue
2010
10.1016/j.cad.2010.02.007
Computer-Aided Design
Keywords
Field
DocType
rational envelope,mos surfaces,trimmed offsets,exact rational envelope,rational approximation,piecewise quadratic medial surface,quadratic patch,mos surface,quadratic bézier triangles,medial surface,general medial surface,associated two-parameter family,rational surface,rational parameterizations,sum of squares
Mathematical optimization,Quadratic equation,Approximations of π,Bézier curve,SPHERES,Explained sum of squares,Trimming,Mathematics,Piecewise,Computation
Journal
Volume
Issue
ISSN
42
6
Computer-Aided Design
Citations 
PageRank 
References 
7
0.47
57
Authors
4
Name
Order
Citations
PageRank
Bohumír Bastl113610.49
Bert Jüttler2114896.12
Jiří Kosinka3916.53
Miroslav LáVičKa415811.36