代数拼接曲面的参数调整  

Parameter Adjustment to Algebraic Surfaces Blending

作　　者：李耀辉[1] 宣兆成[1] 武志峰[1] 

机构地区：[1]天津工程师范学院计算机科学与技术系,天津300222

出　　处：《计算机辅助设计与图形学学报》2013年第3期350-355,共6页Journal of Computer-Aided Design & Computer Graphics

基　　金：天津市教委高校自然科学基金项目(20071311);天津工程师范学院自然科学基金项目(KJ20080039);天津工程师范学院引进人才基金(KYQD06005)

摘　　要：针对代数曲面拼接中存在直接通过符号计算方法得到的拼接曲面有时不能满足实际拼接需求的问题,提出2种对二次曲面的拼接曲面进行调整的方法:1)计算拼接曲面之前,在构造的方程中加入参数,然后利用结式能够对含有参数的代数方程进行消元的性质得到带有参数的过渡曲面,调整参数的值改变从一个曲面过渡到另一个曲面的速度使得曲面形状改变;2)在计算出结式后,通过增加补偿参数或函数使得曲面的形状改变.文中还从理论上分析并证明了这2种方法可以保持原来拼接曲面光滑连续性的阶数.实验结果表明,文中方法具有很强的通用性且易于实现.Generally, the blending surface directly constructed by symbolic computation can not satisfy the practical requirement. To overcome it, two adjusting methods of blending surface are presented in the paper. The first is to add parameters to the equations of algebraic surfaces and their auxiliary surfaces. Then, the different resultant methods are used to eliminate the auxiliary variable and obtain the blending polynomial equation of parameters and coordinates variables. The shape of blending surface can be adjusted by evaluating different values to the parameters in blending polynomial equation. The second is to add compensation parameters in the resultant so as to adjust the shape of blending surface. Besides, the paper analyzes and proves that these methods blend the algebraic surfaces with Gk Continuity. Meanwhile, the experiments show the two methods are efficient and can be implemented easily.

关 键 词：代数曲面 结式 曲面拼接 拼接曲面调整 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]