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Construction of spline curves on smooth manifolds by action of Lie groups

Part of: Numerical approximation and computational geometry

Published online by Cambridge University Press:  01 February 2015

A. P. Pobegailo
A. P. Pobegailo*
Affiliation:
Belarusian State University, Faculty of Applied Mathematics and Computer Science, Pr. Nezavisimosti 4, 220030, Minsk, Belarus email [email protected]

Abstract

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Polynomials for blending parametric curves in Lie groups are defined. Properties of these polynomials are proved. Blending parametric curves in Lie groups with these polynomials is considered. Then application of the proposed technique to construction of spline curves on smooth manifolds is presented. As an example, construction of spherical spline curves using the proposed approach is depicted.

MSC classification

Primary: 65D05: Interpolation
Secondary: 65D07: Splines 65D17: Computer aided design (modeling of curves and surfaces)
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 18 , Issue 1 , 2015 , pp. 217 - 230
Copyright
© The Author 2015 

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