凸点

Convex hull of point set and that of a polygon are two classes of it.

凸包问题是计算几何的基本问题，分为平面点集凸包和多边形凸包2类。

Based on quickqull algorithm,an improved algorithm to determine the convex hull of 2-D point set was proposed in this paper.

凸包问题是计算几何的基本问题，分为平面点集凸包和多边形凸包2类。

On fuzzy mapping F :〓→〓, the concepts of directional derivative and integralover a line segment are defined, and the increase, convexity and continuity are investigated.

作为应用，给出了一个这类凸模糊映射在〓的某一凸子集中某一点达到最小值的等价条件，并得到了某点是一个凸模糊优化问题的最优解的一个充分条件。

First, the two convex hulls from the training set of approximate linear classification are similarly squeezed into the linearly separable ones, and based on the two similarly squeezed linearly separable convex hulls, an optimal separating hyperplane is figured out by using the method of halving the nearest points and the maximal margin method.

首先对近似线性分类中的训练集所形成的两类凸壳进行了相似压缩，使压缩后的凸壳线性可分；基于压缩后线性可分的凸壳，再用平分最近点和最大间隔法求出最优的分划超平面。

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。

We established abstract functional spaces, proved that the plastic deformation power rate functional is strict convex and the friction power rate functional and the tensional stress power rate functional are convex. So, strict convexity of the total power rate functional 〓 can be obtained. Further, By nonlinear analysis theory, we proved the existence and uniqueness of minimal point of functional 〓.

本文首先建立了抽象的泛函空间，证明了塑性变形功率泛函是严格凸泛函，摩擦功率泛函和外力功率泛函是凸泛函，从而得到总能耗率泛函的严格凸性，进一步地，利用非线性分析的理论，得到总能耗率泛函有唯一的极小值点。

By using the theorem of alternative,we obtain the necessary and sufficient conditions for strong efficient solutions to be the generalized saddle point in vector optimization problems with set-valued maps under the assumption of nearly cone-subconvexlikeness.

Yang[1]引进了近似锥-次类凸集值映射的概念，其他广义凸集值映射都是它的特殊形式。最近，Sach[2]在集值优化问题中引进了一种广义鞍点，通常的Lagrange泛函的鞍点是它的一种特殊形式。

In the paper, we give the notion of the pointwise convex modulus, the relation between the pointwise convex modulus and some geometric propertries are discussed.

本文主要是给出点态凸性模的定义，并讨论了点态凸性模与一些几何性质之间的关系。

3D topographies also show that there are a small amount of summits on the surface. The high summits is about 2~3 times higher than the low summits.

三维形貌图显示，金刚石表面存在较少数量的由点到凸峰，且较大凸峰的高度在50~60 nm之间，是较小凸峰高度的2~3倍。

Based on analyzing the algorithms of Delaunay triangulation creation in domestic and abroad, in view of the situation of building DTM and the need of realizing railway 3D visual design, a divide-and-conquer algorithm to build DTM is presented, the algorithm use square grids to manage disordered points, to form triangular meshes in grids, DTM can be obtained by merging the triangular meshes, so that the work of sorting of the disordered points before building DTM is reduced greatly; moreover, the algorithm utilize subarea to control the vertices of convex hull so that the range which support points locate in can be predefined when searching support points, the workload of searching support points can be reduced and the speed of merging two triangulations is raised.

在分析了国内外构建DTM算法的基础上，针对DTM算法的现状及铁路线路三维可视化设计的需要，创立了一种构建DTM的分治算法。算法引入方格网管理离散点数据，在格中构建三角网，然后再将这些三角网合并形成DTM，极大地减少了构网前对所有参加构网的离散点进行排序的工作量。此外，通过对凸包顶点数据进行分区管理，在搜寻凸包支撑线时，能预先确定出支撑点的范围，减少了搜索工作量，提高了三角网的合并速度。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。