曲线曲面的若干几何处理基础算法研究

FUNDAMENTAL ALGORITHMS FOR PROCESSING OF CURVES AND SURFACES

给出了实用的曲线曲面的离散、投影、直线－圆环求交、空间直线距离计算等算法．曲线用密切圆逼近，采用差商计算离散点参数，算法速度快．根据几何性质构造了点的投影及曲线投影跟踪算法，用拟牛顿法加大收敛范围，利用相关性减少迭代次数．采用矢量方法和局部坐标系技巧，如空间直线间距离计算。

Presents a general and robust algorithm for geometric processing such as discretion of curve and surface, projection of points,curves and surfaces,distance between two 3D lines etc.Main attentions are paid to robustness and efficiency.The algorithms applies Quasi Newton iteration into intersection calculating of the ray and surface.With the coherence between two adjacent points,projections of curves and surfaces are solved with significant computational savings.Geometric properties are fully employed to design many ingenious algorithms such as intersection between line and torus.