Previous protocols for determining whether a point is inside a circle are not secure enough . we present a two - round protocol for computing the distance between two private points and develop a more efficient protocol for the point - circle inclusion problem based on the distance protocol . in comparison with previous solutions , our protocol not only is more secure but also reduces the number of communication rounds and the number of modular multiplications significantly 保护私有信息的计算几何问题是一类特殊的安全多方计算问题， attalah等首先提出了安全多方计算几何的概念，介绍了点的包含多边形相交判定最近点对及凸包问题，并分别基于茫然传送协议及置换协议设计了两个不同的点积协议，在此基础上提出了解决点在多边形中的包含判定及两个多边形相交判定的初步方法，但正如作者所指出，其方法还不够完善，协议效率有待进一步改进。
Instead of 640 fibers , it realized the large area multi - object observation by use of 4 000 fibers . according the request of project , mechanical character , controlling and positioning method were firstly analysized . then through studying geometry modeling , convex hull , polygon collision test and other arithmetic , the positioning , controlling and collision test method are proposed which are suitable for radial coordinates unit 本文根据工程的要求，首先对光纤定位装置的机械特征、控制方式、定位方法做了分析，然后通过研究现有的几何造型、凸包构建、多边形碰撞判断等算法理论，研究出适合极坐标运动单元的表示、控制、判断方法，并最终在虚拟系统中实现了4000个光纤定位单元的存储表示、定位控制、碰撞判断(即实时监控) 。
Grpcs provides a unified framework for parametric curve and surface . it does not only inherit a lot of good properties from nurbs such as locality , convex hull , affine and perspective invariance etc . , but also has the ability to directly represent trimmed surfaces and closed surfaces 广义有理参数曲线曲面在表示形式和计算方法上具有高度的统一性，它不仅继承了nurbs的很多优良性质，比如局部控制性、凸包性、仿射和投影不变性等，而且可以直接表示裁剪曲面和闭合的曲线曲面。
Finally , a split algorithm is put forward to calculate the minimum distance between two general nurbs surfaces , in which the technique of splitting the nurbs surfaces and the convergence of control points are used , and spatial classification using the upper & lower bound and the convex hull property of the nurbs surfaces are applied to avoid unnecessary subdivisions 最后，探讨了nurbs曲面的分裂技术与控制网的收敛性问题，充分利用nurbs曲面的凸包性和距离值上下边界分类的思想，避免大量不必要的细分，提出了一般nurbs曲面间最短距离求解的分裂算法。
