Study of Parametrization of a Kind of Cubic Implicit Algebraic Surface

There are two principal ways to describe a surface in CAGD: parametric surface and algebraic surface. The process of converting the algebraic surface into the parametric surface is called parametrization, which has received much attention in recent years. Studied in this paper is how to parametrize a kind of cubic algebraic surface from literature, which plays an important role in the field of implicit algebraic surface modeling in CAGD. And a kind of parametrization method based on the curves of intersection between a pencil of the planes with the same axis with the cubic surface is put forward. This method is simple on structure and can make the algebraic surface patch lie within the finite parameter interval, and the boundaries of algebraic surface patch lie on isoparametric lines. These peculiarities can be utilized for producing the computer graphics of parametric surface and achieving much geometrical operation in CAGD. Simulation results show it is effective.