HERMITE GEOMETRIC INTERPOLATION BY RATIONAL BÉZIER SPATIAL CURVES

Polynomial geometric interpolation by parametric curves has become one of the standard techniques for interpolation of geometric data. An obvious generalization leads to rational geometric interpolation schemes, which are a much less investigated research topic. The aim of this paper is to present a...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 2012-01, Vol.50 (5), p.2695-2715
Main Authors: JAKLIČ, GAŠPER, KOZAK, JERNEJ, KRAJNC, MARJETA, VITRIH, VITO, ŽAGAR, EMIL
Format: Article
Language:English
Subjects:
Approximation
Coefficients
Curvature
Curves
Degrees of polynomials
Interpolation
Mathematical theorems
Parametric curves
Polynomials
Tangents
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Summary:Polynomial geometric interpolation by parametric curves has become one of the standard techniques for interpolation of geometric data. An obvious generalization leads to rational geometric interpolation schemes, which are a much less investigated research topic. The aim of this paper is to present a general framework for Hermite geometric interpolation by rational Bézier spatial curves. In particular, cubic G² and quartic G³ interpolations are analyzed in detail. Systems of nonlinear equations are derived in a simplified form, and the existence of admissible solutions is studied. For the cubic case, geometric conditions implying solvability of the nonlinear system are also stated. The asymptotic analysis is done in both cases, and optimal approximation orders are proved. Numerical examples are given, which confirm the theoretical results.
ISSN:0036-1429
1095-7170
DOI:10.1137/11083472X