The algebraic curve approximation for planar parametric curves

摘要

In this paper, a type of algebraic curve approximation algorithm for planar parametric curves is presented. It is proved that the coefficients vector of the implicit polynomial is the minimizing solving vector of a real symmetric positive define quadratic form. Due to the complexity of practical computation, an algorithm using lower degree algebraic curves to approximate parametric curves by solving an optimal function is introduced also and their coefficients are obtained through the continuity conditions and an optimal function's minimization. Finally, come numerical examples are given.