Construction of \(C^ 2\) Pythagorean-hodograph interpolating splines by the homotopy method
type: Item
instance of: scholarly article
title: Construction of \(C^ 2\) Pythagorean-hodograph interpolating splines by the homotopy method
zbMATH Open document ID: 0866.65008
DOI: 10.1007/BF02124754
author: Gudrun Albrecht
author: Rida T. Farouki
published in: Advances in Computational Mathematics
publication date: 1996-12-18T00:00:00Z
review text: \(C^2\) Pythagorean-hodograph interpolating splines are investigated. The authors demonstrate how to set up a system of quadratic equations that insure the prescribed continuity of the spline interpolant. The analysis of the solution set of this system is presented in detail. Numerical examples are included.
Mathematics Subject Classification ID: 65D07
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 947618
zbMATH Keywords: homotopy method
zbMATH Keywords: numerical examples
zbMATH Keywords: Pythagorean-hodograph interpolating splines
Wikidata QID: Q114233882
reviewed by: Edward Neuman
describes a project that uses: HOMPACK
MaRDI profile type: Publication
cites work: Q3998344
cites work: Q3139554
cites work: Constructing roadmaps of semi-algebraic sets. I: Completeness
cites work: Q4026160
cites work: The conformal map \(z\to z^ 2\) of the hodograph plane
cites work: The elastic bending energy of Pythagorean-hodograph curves
cites work: Hermite Interpolation by Pythagorean Hodograph Quintics
cites work: Q4000024
cites work: A homotopy for solving general polynomial systems that respects m- homogeneous structures
cites work: Computing all solutions to polynomial systems using homotopy continuation
cites work: Algorithm 652
cites work: A Simple Homotopy Method for Determining all Isolated Solutions to Polynomial Systems
full work available at URL: https://doi.org/10.1007/bf02124754
OpenAlex ID: W2022994234
Recommended article: On interpolation by Planar cubic $G^2$ pythagorean-hodograph spline curves
Recommended article: $C^2$ Hermite interpolation by Pythagorean Hodograph space curves
Recommended article: An approach to geometric interpolation by Pythagorean-hodograph curves
Recommended article: Construction of hyperbolic interpolation splines
Recommended article: An explicit method of \(C^ 2\) interpolation using splines
Recommended article: \(C^d\) Hermite interpolations with spatial Pythagorean hodograph B-splines
Recommended article: C3 spline interpolation by pythagorean hodograph closed curves of degree seven
Recommended article: Q4841302
Recommended article: Construction of \(C^2\) cubic splines on arbitrary triangulations
Recommended article: Construction of Minkowski Pythagorean hodograph B-spline curves
description: scientific article; zbMATH DE number 947618