正交环面的正则性分析

Analysis of the Regularity of Normal Ringed Surface

正则性是曲线曲面的代数性质,由曲线曲面的参数形式所决定.在计算机辅助几何设计中,要求所处理的对象是正则的,正交环面在实际应用中会发生两类非正则问题:局部自交和全局自交.从局部正则和全局正则两个角度来分析正交环面的正则性,基于正则性定义,运用代数运算方法分别得到正交环面的局部和全局正则性条件,综合得到正交环面的正则性条件.最后实例验证了该条件的正确性.

Regularity is the algebraic property of curves and surfaces,which is determined by the parameterization of curves and surfaces.In Computer Aided Geometric Design（CAGD）,the processed object should be regular.As an important geometric modeling,it is meaningful to investigate the regularity of normal ringed surface.In practical application of normal ringed surface,two types of irregular problems will occur,that is local self-intersection and global self-intersection,hence the regularity is analyzed from the perspective of both the local regularity and global regularity.Based on the definition of the regularity,both the local and global regularity conditions are obtained by using the method of algebraic operation.The regularity condition of normal ringed surface is obtained by integrating two conditions.Finally,examples are performed to verify the correctness of the condition.