On geometric interpolation of parametric surfaces

By exploiting the freedom in the choice of parametrization of a parametric surface, we show that there exist quadratic parametric surfaces that approximate a given parametric surface with the same approximation order as cubics, namely four, in the neighbourhood of a point where the Gaussian curvatur...

Full description

Saved in:
Bibliographic Details
Published inComputer aided geometric design Vol. 22; no. 9; pp. 838 - 848
Main Author Morken, Knut
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 01.12.2005
Elsevier
Subjects
Applied sciences
Computer aided design
Computer science; control theory; systems
Exact sciences and technology
Interpolation
Mechanical engineering. Machine design
Parametric surfaces
Polynomials
Reparametrization
Software
Taylor expansion
Interpolation
Reparametrization
Parametric surfaces
Taylor expansion
Polynomials
Taylor series
Parameterization
Gaussian process
Parametric surface
Series expansion
Cubics
Curve fitting
Curvature
Computer aided design
Online AccessGet full text

Cover

More Information
Summary:By exploiting the freedom in the choice of parametrization of a parametric surface, we show that there exist quadratic parametric surfaces that approximate a given parametric surface with the same approximation order as cubics, namely four, in the neighbourhood of a point where the Gaussian curvature of the surface is nonzero. This provides a first generalization to surfaces of earlier work for curves.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0167-8396
1879-2332
DOI:10.1016/j.cagd.2005.04.007