简单多面体

In view of that conventional algorithms of collision detection spend a lot of detection time on complex polyhedrons, an algorithm to divide a convex polyhedron was presented and proved.

针对传统的碰撞检测算法对于复杂多面体之间的碰撞检测时间过长的缺陷，提出并证明了一种凸多面体的剖分算法，该算法能将复杂的凸多面体剖分为简单四面体，利用基于MPI(Mes-sagePassingInterface)并行处理的方法来提高碰撞检测的实时性。

With the idea of smoothing Newton method, we propose a new class of smoothing Newton methods for the nonlinear complementarity problem based on a class of special functions. In this paper, complementarity problem is converted into a series of smoothing nonlinear equations and a modified smoothing Newton algorithm is used to solve the equations. We use Newton direction and Gradient direction together in the algorithm which guarantees that our method is globally convergent. Also using another smoothing function, we reformulate the generalized nonlinear complementarity problems defined on a polyhedral cone as a system of smoothing equations and a smooth unconstrained optimization problem. Theoretical results that relate the stationary points of the merit function to the solution of the generalized nonlinear complementarity problems are presented, we use the modified smoothing Newton algorithm in generalized nonlinear complementarity problems, under mild hypothesis, a global convergence is proved.

本文一方面基于现有的各种光滑Newton法的思想和半光滑理论，利用著名的F-B互补函数的光滑形式，首先将互补问题的求解转化为求解一系列光滑的非线性方程组，然后给出了一种修正的光滑Newton法，该方法不仅放宽对函数F的要求，在Newton方程不可解时引入初始效益函数的最速下降方向，而且光滑因子的选择也比较简单可行，同时在适当的条件下，证明了其算法具有全局收敛性；另一方面，借助另一种F-B光滑函数，将多面体锥上的广义互补问题转化为一种光滑形式，讨论了优化问题的稳定点与广义非线性互补问题的解之间的理论关系，并将这种修正的光滑Newton法用于求解广义非线性互补问题中，在适当的条件下，该算法同样具有全局收敛性。

A simple and effective method for investigating cluster polyhedra has been founded.

建立了一种简单而有效的团簇多面体结构研究方法。

Then, the method is extended to the problems of decomposing a polyhedron with or without holes into the minimum number of terrain polyhedra, both of which are also shown to be NP-hard.

然后将证明方法推广到地形多面体剖分的问题：将一个带洞多面体或者简单多面体剖分成最小数量的地形多面体，这两个问题都被证明是NP-hard的。

In this article, we introduce the oriented volume concept of simple tetrahedral, and get the computation formula for polyhedron at last.

引入了简单四面体的有向体积概念，最后得多面体体积计算公式。

Lugalbanda was a god and shepherd king of Uruk where he was worshipped for over a thousand years.

Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

I am coming just now,' and went on perfuming himself with Hunut, then he came and sat.

我来只是现在，'歼灭战perfuming自己与胡努特，那麼，他来到和SAT 。