凸多面体

In order to solvepiecewise algebraic varieties, we propose a new method to compute an algebraic varietyon a convex polyhedron by adding hyperplanes with the method of Groebner bases. Thus,the algebraic variety on the convex polyhedron is transformed to the positive solutionsof a system of polynomials. Besides, the minimal decomposition is also obtained.

通过添加超平面技巧将Groebner基方法应用到凸多面体内任意维代数簇的计算上，从而把凸多面体内的代数簇转化为另外一组多项式方程组的正解，并且得到了该代数簇在凸多面体内的极小分解。

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。

To increase the running speed of the collision detection algorithm, a new approach is proposed, which uses convex Bounding Volume Hierarchies to express convex polyhedron. Thus the distance problem of two convex polyhedrons is come down to a nonlinear programming problem with constraints. The nonlinear programming problem can be solved by simulated annealing genetic algorithm.

为了提高碰撞检测算法的速度，提出用顶点的凸包表示凸多面体，将两个凸多面体间距离的问题归结为一个带约束条件的非线性规划问题，利用模拟退火遗传算法对该问题进行求解。

In elliptic case,the compactness of"convex polyhedrons"is destinedto be true because of the"local Lipschitz continuity of convex functions",whilein parabolic case,we cannot expect convex-monotone functions have such goodproperties as convex functions.

在广义解存在性的证明中，参考椭圆情形由"凸多面体"逼近的思想，我们采用了由一种特殊构造的"凸单调多面体"逼近的途径，但在证明这种凸单调多面体族的紧性时，我们遇到了困难。

The authors present a new algorithm in this paper. Firstly, a vector pointing from one polyhedron to the other is picked. Then the authors start to find an intersection plane of one polyhedron based on the scalar product of the norm vector of the plane and the picked vector.

就这一问题，给出了一种新的算法，其思想是取一个从一个凸多面体指向另一个多面体的向量，根据两个多面体中的面与这一向量的相对位置关系来寻找相交的平面。

Polyhedral links are a class of topological links with polyhedral shape which are linked with a collection of finitely separate closed curves..

多面体链环是将古老的凸多面体结构和重要的纽结理论相结合，在解决近年来实验室中发现的病毒结构和合成的超分子结构的理论研究中，得到的理论成果。

Finally,carried out the stopped search procedure in the polyhedrons on the slices.

该算法通过目标函数超平面截线性规划松弛问题的有效约束锥而形成一个单纯形；然后，引入一串平行片来切割该单纯形产生更低维的凸多面体；最后，在片上的这些凸多面体上执行阻止搜寻程序。

Since the vertices of the simplex and the polyhedrons on the slices could directly be determined by the formulas, and the intervals of the variables in the polyhedrons on the slices were narrower, the algorithm was convenient and efficient.

由于单纯形和片上凸多面体的极顶点可以直接通过公式计算，且变量在片上凸多面体上的取值区间更窄，改进的定界阻止算法既方便又高效，这得到了一些经典算例和随机产生的算例的验证。

Based on the theory mentioned above we present a algorithm to decide if the intersection of two convex polyhedra is empty.

当限制在一个凸多面体的一个面上处理问题时就需要确定另一个凸多面体在这个面上的限制是否为空的问题，这样就要用到向量定位算法。

It respectively constructs quasi projection-separation facet sets of two convex polytopes while their orthogonal projection on the centerline overlap mutually. Afterward it judges the separation of two convex polytopes by confirming non-overlap in orthographic projection on the centerline or by finding out a projection-separation facet from two quasi projection-separation facet sets, otherwise a collision is judged.

该算法通过判断2个凸多面体在中心线上的正投影不相交，或者分别构造它们的准投影分离面集合，并从这2个集合中找到一个投影分离面，来判断2个凸多面体分离；否则，判断为相交。

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 。