Singular Point of Curves - Structure, Visualization and Application in Geometric Modeling

Abstract

During the computations of non-linear problems such as optimization, classification of varieties in algebraic geometry, analysis of complex functions, an occurence of singular points in the area of interest plays a significant role. Singularities often appear during a qualitative change of the computed object. We consider them in case of real and complex curves as well as complex functions. We provide visualization of certain invariants arising during their description as well as elementary methods and tools used during their analysis. The covered areas form a necessary theoretical background of many application areas such as robotics, geometric modeling, computational geometry, numerical mathematics, approximation theory.