Spatial C2 closed loops of prescribed arc length defined by Pythagorean-hodograph curves

Rida T. Farouki, Marjeta Knez, Vito Vitrih and Emil Žagar

Applied Mathematics and Computation, 2021, vol. 391, issue C

Abstract: We investigate the problem of constructing spatial C2 closed loops from a single polynomial curve segment r(t), t∈[0,1] with a prescribed arc length S and continuity of the Frenet frame and curvature at the juncture point r(1)=r(0). Adopting canonical coordinates to fix the initial/final point and tangent, a closed-form solution for a two-parameter family of interpolants to the given data can be constructed in terms of degree 7 Pythagorean-hodograph (PH) space curves, and continuity of the torsion is also obtained when one of the parameters is set to zero. The geometrical properties of these closed-loop PH curves are elucidated, and certain symmetry properties and degenerate cases are identified. The two-parameter family of closed-loop​ C2 PH curves is also used to construct certain swept surfaces and tubular surfaces, and a selection of computed examples is included to illustrate the methodology.

Keywords: Spatial closed-loop curves; Continuity conditions; Arc length; Pythagorean-hodograph curves; Euler–Rodrigues frame; Tubular surfaces (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S009630032030607X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:391:y:2021:i:c:s009630032030607x

DOI: 10.1016/j.amc.2020.125653

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().