Study on Parametrization of A Kind of Quartic Implicit Algebraic Surface

Parametrization of implicit algebraic surface is one of the most active research topics in CAGD. This paper proposes a piecewise geometric approach to parametrize a kind of quartic implicit algebraic surface. Its main ideas are as follows: (1) dividing the quartic implicit algebraic surface into several patches; (2) computing the intersection curves of each surface patch with a pencil of planes rotated successively along a certain fixed axis; (3) parametrizing the curves. This algorithm is accurate and its computation is simple. It may make the algebraic surface patch lie within the finite parameter interval and the boundaries of algebraic surface patches lie on isoparametric lines. These characteristics are beneficial to automatically plotting the parametric surface and realizing some geometrical operations. Simulation results show it is effective.