Optimal G2 Hermite interpolation for 3D curves

Herzog, Raoul (School of Management and Engineering Vaud, HES-SO // University of Applied Sciences Western Switzerland) ; Blanc, Philippe (School of Management and Engineering Vaud, HES-SO // University of Applied Sciences Western Switzerland)

We consider a Hermite interpolation problem for a 3D curve where the functional to be minimized is defined as the integral of squared norm of the third parametric derivative, subject to continuity constraints at the end points. The first order necessary optimality condition of the variational problem leads to a parametric transition curve with quintic polynomials. The determination of coefficients is given by a polynomial system with 2 unknowns. Stationary points correspond to positive roots of the resultant which is a degree 9 polynomial. Although the formulated variational problem is non-convex, the proposed approach leads to the global solution, which can be computed in a reliable and fast manner.


Keywords:
Article Type:
scientifique
Faculty:
Ingénierie et Architecture
School:
HEIG-VD
Institute:
iAi-Institut d'Automatisation Industrielle
Date:
2019-12
Pagination:
6 p.
Published in:
Computer-Aided Design
Numeration (vol. no.):
2019, vol. 117, art. no. 102752
DOI:
ISSN:
0010-4485
Appears in Collection:

Note: The status of this file is: restricted


 Record created 2019-11-26, last modified 2019-12-05

Fulltext:
Download fulltext
PDF

Rate this document:

Rate this document:
1
2
3
 
(Not yet reviewed)