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曲面交线的B样条优化逼近
引用本文:董辰世,陈志杨,汪国昭,叶修梓.曲面交线的B样条优化逼近[J].计算机辅助设计与图形学学报,2004,16(4):449-453,T004.
作者姓名:董辰世  陈志杨  汪国昭  叶修梓
作者单位:1. 浙江大学数学系,杭州,310027
2. 浙江大学计算机科学与技术学院,杭州,310027;浙江大学CAD&CG国家重点实验室,杭州,310027;浙江工业大学信息学院,杭州,310014
3. 浙江大学计算机科学与技术学院,杭州,310027;浙江大学CAD&CG国家重点实验室,杭州,310027
基金项目:国家自然科学基金 ( 60 2 73 0 60 ),科技部重大软件专项基金( 2 0 0 3AA4Z10 2 0 )资助
摘    要:目前,在比较成熟的商业几何核心系统中,曲面的交线是一种基于位置算子的“精确”表示或称为“过程”表示.这样的交线如果用在几何建模操作中,必须输出为系统支持的曲线表示(如B样条表示).现有的几何核心系统中曲面交线的B样条逼近算法存在控制点数目过多和连续性偏低(C^1)的缺点,导致下游操作结果太复杂且连续性低.基于此,提出了一种曲面交线的B样条逼近算法,使控制点数目减少为原来的三分之一,而连续阶上升为C^2.该算法已经在SolidWorks系统中得到应用,效果良好.

关 键 词:CAD  几何造型  曲面交线  输出过程曲线  B样条曲线  曲线拟合

Optimal B-Spline Approximation of Intersection Curves of Two Surfaces
Dong Chenshi Chen Zhiyang , Wang Guozhao Ye Xiuzi ,.Optimal B-Spline Approximation of Intersection Curves of Two Surfaces[J].Journal of Computer-Aided Design & Computer Graphics,2004,16(4):449-453,T004.
Authors:Dong Chenshi Chen Zhiyang    Wang Guozhao Ye Xiuzi  
Affiliation:Dong Chenshi 1) Chen Zhiyang 2,3,4) Wang Guozhao 1) Ye Xiuzi 2,3) 1)
Abstract:In commercial geometric engines, intersection curves of surfaces are expressed procedurally by position operators that can evaluate the curve position information precisely. To be able to use such kinds of procedural curves in geometric modelling operations, intersection curves should be output as system available forms, such as B-spline. The existing approximation algorithms in the geometry engines have the disadvantages that:(1) The number of B-spline control points is unnecessarily large; and (2) the B-spline curves have low continuity (C 1). A novel algorithm to optimally approximate intersection curves of surfaces with C 2 B-spline curves is presented that have approximately only 1/3 of the number of control points of the B-spline output from geometry engines. Our algorithm has been integrated into SolidWorks system successfully with very good application performances.
Keywords:CAD  geometric modeling  surface-surface intersection  output procedural curves  B-spline curve  curve fitting
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