Polyhelices through n points

Alain Goriely; Sébastien Neukirch; Andrew Hausrath

doi:10.1504/IJBRA.2009.024032

Polyhelices through n points

Alain Goriely, Sébastien Neukirch, Andrew Hausrath

Chemistry and Biochemistry

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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 language	English (US)
Pages (from-to)	118-132
Number of pages	15
Journal	International Journal of Bioinformatics Research and Applications
Volume	5
Issue number	2
DOIs	https://doi.org/10.1504/IJBRA.2009.024032
State	Published - Mar 2009

Keywords

Bioinformatics
Frenet triad
Geometry of helices
Helical segments
Polyhelices
Polyhelix

ASJC Scopus subject areas

General Medicine

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10.1504/IJBRA.2009.024032

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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.",

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AU - Neukirch, Sébastien

AU - Hausrath, Andrew

PY - 2009/3

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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

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AN - SCOPUS:63149109154

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JO - International Journal of Bioinformatics Research and Applications

JF - International Journal of Bioinformatics Research and Applications

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ER -

Polyhelices through n points

Abstract

Keywords

ASJC Scopus subject areas

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