摘要
本文从分片线性逼近的基本思想出发,运用离散细分的手法,讨论了一般参数曲面的求交问题。利用插值逼近的误差估计,给出了一种可根据精度要求,事先确定细分次数的离散求交方法。该方法采用任意三角分划的分片线性逼近,避免了以每个子曲面的四个角点的拟合平面代替原子曲面,保证了分片线性逼近曲面的整体连续性,从而所得交线在逼近和光顺等方面的效果都比采用矩形分划的离散求交方法好。而且该方法可适用于三角域、矩形域或多边形区域上的任何K阶(K≥1)连续可微或者Lipschitz连续的参数曲面,具有较强的通用性,其算法所需的存贮量和计算量都较小,易于在微型计算机上实现。本文给出了一个由DXY-880A绘图机绘制的算法实例的图形。
In this paper, the problem of finding the intersection of two parametric surfaces is discussed, by using the subdivision technique based on the idea of piecewise linear approximation and its error estimation, and a subdivision method that can determine the number of times of subdivision in advance according to the demanded precision is proposed, which uses the arbitrary triangular piecewise linear approximation to avoid replacing each original sub-surface by the fitting plane of its four vertices and guarantees global continuity of the piecewise linear approximating surface. So the intersection line obtained by this method is better than that got by the rectangular subdivision method in the effect of approximation and fairing. Furthermore, this method is suitable for all continuously differentiable parametric surfaces for K-times (K≥1) or merely lipschitz continuous one over triangles, rectangles or polygons. The capacity of its storage and the calculation are small. It is easily implemented on a microcomputer. An example is given by the DXY-880A plotter.
基金
航空科学基金
关键词
曲面
插值
三角域
CAD
参数
求交
computer aided design, interpolation, triangles, surface
