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 so-called 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).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.