Details:
Title  On convolutions of algebraic curves  Author(s)  Miroslav Lávička, Jan Vršek  Type  Article in Journal  Abstract  We focus on the investigation of relations between plane algebraic curves and their convolution. Since the convolution of irreducible algebraic curves is not necessarily irreducible, an upper bound for the number of components is given. Then, a formula expressing the convolution degree using the algebraic degree and the genus of the curve is derived. In addition, a detailed analysis of the socalled special and degenerated components is discussed. We also present some special results for curves with low convolution degree and for rational curves, and use our results to investigate the relation with the theory of the classical offsets and Pythagorean Hodograph (PH) curves presented in Arrondo et al. (1997).  Keywords  Algebraic curves, Convolutions, Convolution degree, Offsets, Genus, Rational curves  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717110000222 
Language  English  Journal  Journal of Symbolic Computation  Volume  45  Number  6  Pages  657  676  Year  2010  Edition  0  Translation 
No  Refereed 
No 
