一类三次隐式代数曲面参数化研究

Study of Parametrization of a Kind of Cubic Implicit Algebraic Surface

在CAGD中隐式曲面和参数曲面作为曲面的两种表示形式各有其内在的优点 ,多年来如何有效地实现二者的相互转换一直是CAGD的一个热点问题 对一类GC1拼接两个二次曲面的三次混合代数曲面进行了研究 ,提出一种基于同轴平面束与代数曲面相交的几何化参数化方法 与传统参数化方法相比 ,该方法结构直观且具有可使三次代数曲面位于 [0 ,1]× [0 ,1]参数区间内 ,以及曲面的边界位于等参数线上等特点 ,利用这种参数曲面可以方便地实现机器作图和各种操作

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.