PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Geometric Lagrange interpolation by planar cubic Pythagorean-hodograph curves
Gašper Jaklic, Jernej Kozak, Marjetka Krajnc, Vito Vitrih and Emil Žagar
Comput. aided geom. des. Volume 25, Number 9, pp. 720-728, 2008. ISSN 0167-8396

Abstract

n this paper, the geometric Lagrange interpolation of four points by planar cubic Pythagorean-hodograph (PH) curves is studied. It is shown that such an interpolatory curve exists provided that the data polygon, formed by the interpolation points, is convex, and satisfies an additional restriction on its angles. The approximation order is 4. This gives rise to a conjecture that a PH curve of degree n can, under some natural restrictions on data points, interpolate up to n+1 points.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:8202
Deposited By:Boris Horvat
Deposited On:21 February 2012