Algebraic characterization of generic strongly semi-regular rational PH plane curves

In this paper, we introduce a new algebraic method to characterize rational PH plane curves. And using this method, we study the algebraic characterization of generic strongly regular rational plane PH curves expressed in the complex formalism which is introduced by R.T. Farouki. We prove that generic strongly semi-regular rational PH plane curves are completely characterized by solving a simple functional equation script H sign(f, g) = h2 where h is a complex polynomial and script H sign is a bi-linear operator defined by script H sign(f, g) = f′g - fg′ for complex polynomials f, g. © 2005 Korean Society for Computational &: Applied Mathematics and Korean SIGCAM.