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COMPUTER GRAPHICS & GEOMETRY

Issue Year: 2007
Date: Autumn
Volume: 9
Number: 2
Pages: 43-63

Article Name: GEOMETRY OF SPACE CURVES AND APPLICATIONS TO POLYMERS' CONFORMATIONS INVESTIGATION
Author: A. Ivanov (Russia), A. Mishchenko (Russia), A. Tuzhilin (Russia)
Address: A. Ivanov

Moscow State University, Russia
 
A. Mishchenko

Moscow State University, Russia
 
A. Tuzhilin

Moscow State University, Russia
Abstract:

The main aim of the present work is to demonstrate how to use geometrical characteristics of space polygonal lines to investigate polymers' conformations. The geometrical characteristics suggested below, are discrete analogue of the curvature and the torsion of the space curves which are well-known in Classical Differential Geometry. Main Theorem of Curves Theory says that a space curve can be uniquely reconstructed (up to a motion) starting from its curvature and torsion functions. It turns out that complicated curves may have sufficiently simple curvature and torsion functions. The latter makes us expect to obtain a more simple representation of complicated forms of polymers, which may lead to some progress in the conformations investigations.

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