Paper Info
Title
A symbolic-numerical method for computing approximate parameterizations of canal surfaces
Abstract
A canal surface is the envelope of a one-parameter family of spheres centered at the spine curve m(t) and with the radii described by the function r(t). It was proved in Peternell and Pottmann (1997) [9] that any canal surface to a rational spine curve and a rational radius function possesses a rational parameterization. Then a symbolic method for generating rational parameterizations of canal surfaces was developed in Landsmann et al. (2001) [21]. Indeed, this method leads to the problem of decomposing a polynomial into a sum of two squares over reals, which is solved numerically in general. Hence, approximate techniques generating a parameterization within a certain region of interest are also worth studying. In this paper, we present a method for the computation of approximate rational parameterizations of canal surfaces. A main feature of our approach is a combination of symbolic and numerical techniques yielding approximate topology-based parameterizations of contour curves which are then applied to compute an approximate parameterization of the given canal surface. The algorithm is mainly suitable for implicit blend surfaces of the canal-surface-type.
Year
DOI
Venue
2012
10.1016/j.cad.2012.04.001
Computer-Aided Design
Keywords
Field
DocType
symbolic-numerical method,approximate parameterizations,rational radius function,implicit blend surface,approximate parameterization,canal surface,approximate topology-based parameterizations,rational spine curve,approximate rational parameterizations,approximate technique,rational parameterizations,rational parameterization,critical points
Mathematical optimization,Polynomial,Parametrization,SPHERES,Critical point (mathematics),Fermat's theorem on sums of two squares,Numerical analysis,Mathematics,Symbolic method,Computation
Journal
Volume
Issue
ISSN
44
9
0010-4485
Citations 
PageRank 
References 
6
0.43
33
Authors
2
Name
Order
Citations
PageRank
Michal Bizzarri1518.12
Miroslav LáVičKa215811.36