Title: Polyhelices through n points

Authors: Alain Goriely, Sebastien Neukirch, Andrew Hausrath

Addresses: Program in Applied Mathematics and Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA. ' Laboratoire de Modelisation en Mecanique, UMR 7607: CNRS and Universite Pierre et Marie Curie, Paris, France. ' Department of Biochemistry and Molecular Biophysics, University of Arizona, Tucson, AZ 85721, USA

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: Frenet triad; helices geometry; helical segments; polyhelix; bioinformatics; polyhelices; continuous space curves; arc length.

DOI: 10.1504/IJBRA.2009.024032

International Journal of Bioinformatics Research and Applications, 2009 Vol.5 No.2, pp.118 - 132

Published online: 24 Mar 2009 *

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