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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