Based on researching and developing intrinsic character of fixed direction hulls , this paper develops and proves the property which make it can be apply to collision detection in complex environment and resolves the problems about intersection tests between bounding volumes , updating bounding volumes after rotation and updating bounding volume hierarchy after deformation 本文在充分研究了固定方向凸包的固有特性的基础上，开发并证明了它适用于复杂环境中软体碰撞检测的性质，并着重解决了包围盒间的相交测试、对象运动后包围盒的更新、对象变形后包围盒树的更新等问题。
In unigraphics , there are some methods of dealing with large assembly in advanced assembly application , such as representations , product outline , linked exterior and wrap assembly . in the thesis , the disadvantages of those methods were found out and improved . while author summarizes methods of rapid display large assembly using wireframe model , namely simple curves or simple features 在ug高级装配功能中小平面表示、产品轮廓、链接外部和凸包外形的基础上改进原来方法操作使用不便的问题；同时研究了大装配模型的线框模型简化表示方法，即用简单曲线和简单特征简化大装配。
Two - dimensional texture mappings are summarized in this paper including catmull algorithm and blinn algorithm , two - step texture mapping , environment mapping and bump mapping . moreover , a new method of regional texture mapping based on intermediate surface is presented and a new algorithm is promoted to reduce texture distortion in the process of mapping onto the sphere surface 在二维纹理方面，本文讨论了适用于参数曲面的catmull算法与blinn算法，适用于一般曲面的两步纹理映射技术，现已广为应用的环境纹理映射技术及凸包纹理映射技术，还分析了纹理映射的几种快速反走样技术。
Cross section is a set of polygons and for this reason some relative algorithms for polygon are studied firstly . new algorithms for orientation and inclusion test for simple polygon are proposed . and ghosh ' s convex hull algorithms for simple polygon and convex polygons , subramanian ' s triangulation algorithm for arbitrary planar domain and o ' rourke ' s intersection algorithm for convex polygons are modified to make them more robust 断层轮廓为简单多边形，首先对多边形的一些相关算法进行了研究，提出了一种判断简单多边形方向及点在多边形内外的新方法，改进了subramanian的平面多连通域的三角划分方法、 ghosh的多边形的凸包及多个多边形的凸包算法和o ' rourke的凸多边形的求交算法。
This paper brings forward and proves a rapid interval test for resolving intersection tests between bounding volumes . it determine two bounding volume do not overlap by checking if one of their bound intervals on direction axis defined by the fix direction set does not overlap 文中提出并证明了一种快速区间测试法以解决两个固定方向凸包包围盒间的相交测试问题，通过查找两个包围盒在由固定方向集合所定义的方向轴上的范围区间是否存在不重叠的情况，来判断它们是否不相交。
In the same time , to the point set obeying even distributing and zt distributing , which lie in the most problem , using an acceleration factor optimize the method , it can work even better . at last , make use of the ordered - partly point set after the first step to improve the classical algorithm and to optimize the process 另外，根据研究，绝大多数的点集都服从均匀分布和正态分布，所以在求取边界的过程中，本文对这两种分布的边界求法进行了优化，得到了一个加速凸包算法的两种分布情况下的合理权值。
It has been illustrated by experiment results and concrete application that the method based on bounding volume hierarchy of fixed direction hull can not only resolve collision detection between solid objects , but also provide an reliable and efficient way to resolve and deal with collision detection in flexible environment 实验结果和具体应用表明，基于固定方向凸包包围盒层次的碰撞检测方法不仅能很好地解决刚体间的碰撞检测，而且为解决和处理软体对象环境中的碰撞检测问题提供了一种可靠而有效的途径。
An updating algorithm based on linear programming is proposed in this paper based on the definition and property of fixed direction hulls . this method need not add any additional computation and memory during building bounding volume hierarchies . it can update a bounding volume through 3k multiplication 根据固定方向凸包的定义和性质，文中提出了一种基于线性规划的更新算法，不需要在构造包围盒层次时增加任何额外的计算量和存储量，在对象运动后可以仅通过3k次乘法得到更新后的包围盒。
Secondly , we introduce the recurrence definition of the non - uniform algebraic - hyperbolic b - spline basis using divided differences and the de boor - fix recurrence definition on polynomial functions , and based on the new forms , algebraic - hyperbolic b - spline curves are obtained . they share most of the properties as those of the b - spline curves in the polynomial space . we focus on deducing the calculating and knot inserting formulae for this new kind of curves and then prove that they have the variation diminishing properties 二、利用广义差商,基于多项式b样条的deboor - fix递推定义,给出了任意阶非均匀代数双曲b样条的递推定义,由此构造曲线,证明它的几何不变性、仿射不变性、凸包性、 v . d .性等,重点给出了非均匀代数双曲b样条曲线的递归求值和节点插入算法,算法简单且稳定,便于在计算机上实现
So , in these instances , we should find out a new method to improve the efficiency for this problem . this article put forward a new method for a problem in general ( not in the worst ) instance . adopting an acceleration method in the basis of classical . it worked very well in general instance and in the worst instance the runtime complexity is still o ( nlogn ) 本文在研究了计算几何的基本规律的基础上，分析了传统的凸包算法的优缺点，同时提出了一个新的方法对于一般情况下的凸包的算法进行了加速和优化，它在一般的情况下工作得很好，对于最坏的情况，也没有增加运算的复杂度。
