Polyhelices through n points

Alain Goriely, Sébastien Neukirch, Andrew Hausrath

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

A polyhelix is continuous space curve with continuous Frenet frame that consists of a sequence of connected helical segments. The main result of this paper is that given n points in space, there exist infinitely many polyhelices passing through these points. These curves are by construction continuous with continuous derivatives and are completely specified by 3n numbers, i.e., the initial position, the signed curvature, torsion, and length of each helical segment. Polyhelices can be parametrised by the arc length and easily expressed in terms of product of matrices.

Original languageEnglish (US)
Pages (from-to)118-132
Number of pages15
JournalInternational Journal of Bioinformatics Research and Applications
Volume5
Issue number2
DOIs
StatePublished - Mar 2009

Fingerprint

Torsional stress
Derivatives

Keywords

  • Bioinformatics
  • Frenet triad
  • Geometry of helices
  • Helical segments
  • Polyhelices
  • Polyhelix

ASJC Scopus subject areas

  • Health Informatics
  • Health Information Management
  • Biomedical Engineering
  • Clinical Biochemistry

Cite this

Polyhelices through n points. / Goriely, Alain; Neukirch, Sébastien; Hausrath, Andrew.

In: International Journal of Bioinformatics Research and Applications, Vol. 5, No. 2, 03.2009, p. 118-132.

Research output: Contribution to journalArticle

Goriely, Alain ; Neukirch, Sébastien ; Hausrath, Andrew. / Polyhelices through n points. In: International Journal of Bioinformatics Research and Applications. 2009 ; Vol. 5, No. 2. pp. 118-132.
@article{b9056fe8054c49d8aaad80c005a0e9af,
title = "Polyhelices through n points",
abstract = "A polyhelix is continuous space curve with continuous Frenet frame that consists of a sequence of connected helical segments. The main result of this paper is that given n points in space, there exist infinitely many polyhelices passing through these points. These curves are by construction continuous with continuous derivatives and are completely specified by 3n numbers, i.e., the initial position, the signed curvature, torsion, and length of each helical segment. Polyhelices can be parametrised by the arc length and easily expressed in terms of product of matrices.",
keywords = "Bioinformatics, Frenet triad, Geometry of helices, Helical segments, Polyhelices, Polyhelix",
author = "Alain Goriely and S{\'e}bastien Neukirch and Andrew Hausrath",
year = "2009",
month = "3",
doi = "10.1504/IJBRA.2009.024032",
language = "English (US)",
volume = "5",
pages = "118--132",
journal = "International Journal of Bioinformatics Research and Applications",
issn = "1744-5485",
publisher = "Inderscience Enterprises Ltd",
number = "2",

}

TY - JOUR

T1 - Polyhelices through n points

AU - Goriely, Alain

AU - Neukirch, Sébastien

AU - Hausrath, Andrew

PY - 2009/3

Y1 - 2009/3

N2 - A polyhelix is continuous space curve with continuous Frenet frame that consists of a sequence of connected helical segments. The main result of this paper is that given n points in space, there exist infinitely many polyhelices passing through these points. These curves are by construction continuous with continuous derivatives and are completely specified by 3n numbers, i.e., the initial position, the signed curvature, torsion, and length of each helical segment. Polyhelices can be parametrised by the arc length and easily expressed in terms of product of matrices.

AB - A polyhelix is continuous space curve with continuous Frenet frame that consists of a sequence of connected helical segments. The main result of this paper is that given n points in space, there exist infinitely many polyhelices passing through these points. These curves are by construction continuous with continuous derivatives and are completely specified by 3n numbers, i.e., the initial position, the signed curvature, torsion, and length of each helical segment. Polyhelices can be parametrised by the arc length and easily expressed in terms of product of matrices.

KW - Bioinformatics

KW - Frenet triad

KW - Geometry of helices

KW - Helical segments

KW - Polyhelices

KW - Polyhelix

UR - http://www.scopus.com/inward/record.url?scp=63149109154&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=63149109154&partnerID=8YFLogxK

U2 - 10.1504/IJBRA.2009.024032

DO - 10.1504/IJBRA.2009.024032

M3 - Article

C2 - 19324599

AN - SCOPUS:63149109154

VL - 5

SP - 118

EP - 132

JO - International Journal of Bioinformatics Research and Applications

JF - International Journal of Bioinformatics Research and Applications

SN - 1744-5485

IS - 2

ER -