Geometric Lagrange interpolation by planar cubic Pythagorean-hodograph curves

Authors:
Gašper Jaklič;Jernej Kozak;Marjeta Krajnc;Vito Vitrih;Emil Žagar
Affiliations:
FMF, University of Ljubljana, Jadranska 19, Ljubljana, Slovenia and PINT, University of Primorska, Muzejski trg 2, Koper, Slovenia;FMF, University of Ljubljana, Jadranska 19, Ljubljana, Slovenia and IMFM, Jadranska 19, Ljubljana, Slovenia;IMFM, Jadranska 19, Ljubljana, Slovenia;PINT, University of Primorska, Muzejski trg 2, Koper, Slovenia;FMF, University of Ljubljana, Jadranska 19, Ljubljana, Slovenia and IMFM, Jadranska 19, Ljubljana, Slovenia
Venue:
Computer Aided Geometric Design
Year:
2008

Citing 11
Cited 2

Numerical continuation methods: an introduction

Numerical continuation methods: an introduction
Pythagorean hodographs

IBM Journal of Research and Development
The conformal map z→z2 of the hodograph plane

Computer Aided Geometric Design
Hermite interpolation by Pythagorean hodograph quintics

Mathematics of Computation
The elastic bending energy of Pythagorean-hodograph curves

Computer Aided Geometric Design
Geometric Hermite interpolation with maximal order and smoothness

Computer Aided Geometric Design
A general framework for high-accuracy parametric interpolation

Mathematics of Computation
Geometric Hermite interpolation with Tschirnhausen cubics

Journal of Computational and Applied Mathematics
Hermite interpolation by pythagorean hodograph curves of degree seven

Mathematics of Computation
Euclidean and Minkowski Pythagorean hodograph curves over planar cubics

Computer Aided Geometric Design
High accuracy geometric Hermite interpolation

Computer Aided Geometric Design

A unified Pythagorean hodograph approach to the medial axis transform and offset approximation

Journal of Computational and Applied Mathematics
An approach to geometric interpolation by Pythagorean-hodograph curves

Advances in Computational Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

In 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.