一类四次隐式代数曲面参数化研究

隐式代数曲面的参数化是 CAGD的热点问题之一 .针对一类四次隐式代数曲面 ,提出一种基于分片的几何参数化方法 .首先对四次代数曲面进行分片 ,然后对每一个分片曲面利用一组同轴平面束与其求交线 ,通过对求得交线的参数化来完成对整个分片曲面的参数化 .该方法是一种精确的参数化方法 ,其结构直观、计算简单 ,并且具有可使分片的四次代数曲面位于 [0 ,1]× [0 ,1]参数区间内 ,以及分片曲面的边界位于等参数线上等特点 ,利用该参数曲面可以方便地实现机器作图和几何操作 .实验结果验证了文中方法的有效性 .

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.