3^(1/2)互细分曲面的误差分析  

ERROR ANALYSIS FOR 3^(1/2) SUBDIVISION SURFACES

作　　者：吴剑煌[1] 刘伟军[1] 王天然[1] 

机构地区：[1]中国科学院沈阳自动化所先进制造技术实验室

出　　处：《机械工程学报》2007年第2期104-109,共6页Journal of Mechanical Engineering

基　　金：国家863计划资助项目(2001AA421160)。

摘　　要：针对细分控制网格与细分极限曲面的逼近度这一问题,基于细分控制网格的拓扑结构和细分模式的几何规则,提出一种3^(1/2)细分曲面的误差估计方法并给出一个误差估计公式。利用该公式,根据给定的精度,可事先知道细分之后控制网格满足该精度的最少细分次数而不需要实际对一个模型细分。结合该误差估计方法,给出一种3^(1/2)细分曲面数控加工刀具轨迹生成方法和一种用于直接在STL文件基础上提高精度的方法。试验结果表明这种误差估计方法的有效性。Subdivision surfaces have become popular geometric modeling primitive for representing free form shapes. An Efficient and effective error estimating method for subdivision surfaces is presented. A computing formula for the error estimating is derived based on the topological structure of the control mesh and subdivision rules. With this formula, one can predict how many steps of subdivision are necessary to meet a user-specified error tolerance without subdividing the control meshes actually. Two examples in practical engineering application are given to show the usefulness and importance of the computing formula for √3 subdivision surfaces. One is three-axis NC tool path generation for √3 subdivision surface; The other is an approach which can improve the surface smoothness of the produced objects in rapid prototyping directly without referring to original CAD models. Our proposed method can be extended to other subdivision schemes and other free form surfaces.

关 键 词：细分曲面 √3细分模式 误差估计 几何造型 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]