HERMITE GEOMETRIC INTERPOLATION BY RATIONAL BEZIER SPATIAL CURVES

作者：Jaklic Gasper^*; Kozak Jernej; Krajnc Marjeta; Vitrih Vito; Zagar Emil

来源：SIAM Journal on Numerical Analysis, 2012, 50(5): 2695-2715.

DOI：10.1137/11083472X

• interpolation
• rational
• geometric
• Hermite

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 Bezier spatial curves. In particular, cubic G(2) and quartic G(3) 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.

• 出版日期2012