Approximate Implicitization Using Linear Algebra
Joint Authors
Barrowclough, Oliver J. D.
Dokken, Tor
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-25, 25 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-02-07
Country of Publication
Egypt
No. of Pages
25
Main Subjects
Abstract EN
We consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces.
The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore well suited to floating-point implementation in computer-aided geometric design (CAGD) systems.
We unify the approaches under the names of commonly known polynomial basis functions and consider various theoretical and practical aspects of the algorithms.
We offer new methods for a least squares approach to approximate implicitization using orthogonal polynomials, which tend to be faster and more numerically stable than some existing algorithms.
We propose several simple propositions relating the properties of the polynomial bases to their implicit approximation properties.
American Psychological Association (APA)
Barrowclough, Oliver J. D.& Dokken, Tor. 2012. Approximate Implicitization Using Linear Algebra. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-25.
https://search.emarefa.net/detail/BIM-993122
Modern Language Association (MLA)
Barrowclough, Oliver J. D.& Dokken, Tor. Approximate Implicitization Using Linear Algebra. Journal of Applied Mathematics No. 2012 (2012), pp.1-25.
https://search.emarefa.net/detail/BIM-993122
American Medical Association (AMA)
Barrowclough, Oliver J. D.& Dokken, Tor. Approximate Implicitization Using Linear Algebra. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-25.
https://search.emarefa.net/detail/BIM-993122
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-993122