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计算几何：算法设计与分析（第4版）

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Jingdong book

计算几何：算法设计与分析（第4版）

Name: 计算几何：算法设计与分析（第4版）
Brand: Jingdong book
SKU: 3118050141
Price: 52.60 USD
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面对棘手的构造性几何问题，怎么办？
从本书中可以找到有效方法，帮助你排忧解难！
《计算几何--算法设计与分析（第4版）》（作者周培德）系统地介绍了计算几何中的基本概念、求解诸多问题的算法及复杂性分析，概括了求解几何问题所特有的许多思想方法、几何结构与数据结构。

Content Description

《计算几何：算法设计与分析（第4版）》系统地介绍了计算几何中的基本概念、求解诸多问题的算法及复杂性分析，概括了求解几何问题所特有的许多思想方法、几何结构与数据结构。全书共分10章，包括：预备知识，几何查找（检索），多边形，凸壳及其应用，Voronoi图、三角剖分及其应用，交与并及其应用，多边形的获取及相关问题，几何体的划分与等分，路径与回路，几何拓扑网络设计等。
《计算几何：算法设计与分析（第4版）》可作为高等院校计算机、自动化等专业研究生或本科高年级学生的教材或教学参考书，也可供软件开发人员、相关专业科技工作者参考。

Author Description

周培德，1941年生，湖北省武穴市人。1956年毕业于武汉大学数学系。任北京理工大学计算机系教授。
2001年9月退休。长期担任本科生“算法设计与分析”及研究生“计算理论”等课程的教学工作。主要精力集中于计算机算法分析与设计、计算几何等方面的研究。以个人名义在多种学术刊物和全国学术交流会上发表论文60篇，出版学术专著一部、全国统编高等学校教材一部、校"九五"规划研究生教材一部、内部教材八部。主要论著有《计算几何--算法分析与设计》、《算法设计与分析》、《计算中的基本理论与方法》。代表性论文有《求解K-中心问题的快速算法》、《平面散乱点线集三角剖分的算法》、《平面线段集三角剖分的算法》、《连接不相交线段成简单多边形的算法》等。《算法设计与分析》获第三届全国普通高校部级优秀教材一等奖。退休以来，专心从事计算几何及其应用领域的研究工作，为6个课题组，公司设计了20来个算法，在多种期刊上发表学术论文20来篇，提出一批新的问题及解决相应问题的算法。

Catalogue

第0章预备知识
0.1 算法与数据结构
0.1.1 算法
0.1.2 数据结构
0.2 相关的几何知识
0.2.1 基本定义
0.2.2 线性变换群下的不变量
0.2.3 几何对偶性
0.3 计算模型

第1章几何查找(检索)
1.1 点定位问题
1.1.1 点□是否在多边形P内
1.1.2 确定点□在平面剖分中的位置
1.1.3 Z□算法(判定点q在哪个三角形的算法)
1.2 判定点集是否在多边形内
1.3 平面网络的处理与点q的定位
1.4 平面上链的处理与点q的定位
1.5 平面上线段的处理与点q的定位
1.6 判定点是否在多边形内部的新算法

第2章多边形
2.1 凸多边形
2.2 简单多边形
2.3 多边形的三角剖分
2.4 多边形的凸划分
2.5 对多边形链的监视
2.6 线段划分多边形
2.7 凸多边形的内接最大三角形及外切最小三角形

第3章凸壳及其应用
3.1 凸壳的基本概念
3.2 计算平面点集凸壳的算法
3.3 计算平面多边形顶点凸壳的算法
3.4 计算平面多边形链顶点凸壳的算法
3.4.1 概念、算法思想与描述
3.4.2 解释与时间复杂性
3.5 计算平面线段集凸壳的算法
3.6 计算三维空间点集凸壳的算法
3.6.1 基本概念
3.6.2 Z粥算法(三维凸壳)
3.7 时间复杂性低于下界O(nlogn)的凸壳算法
3.8 凸壳的应用
3.8.1 确定任意多边形的凸、凹顶点
3.8.2 利用凸壳求解货郎担问题
3.8.3 凸多边形直径
3.8.4 连接两个多边形成一条回路

第4章 Voronoi图、三角剖分及其应用
4.1 Voronoi图的基本概念
4.2 构造Voronoi图的算法
4.2.1 z□算法(计算平面点集的Voronoi图)
4.2.2 构造最远点意义下Voronoi图的算法
4.3 平面点集的三角剖分
4.3.1 Delaunay三角剖分与多边形内部点集的三角剖分
4.3.2 平面点集三角剖分的算法
4.4 平面线段集的三角剖分
4.5 平面点线集的三角剖分
4.6 平面点集的伪三角剖分
4.7 伪三角形的产生
4.8 三角剖分的表示
4.9 推广及应用
4.9.1 最近邻近
4.9.2 最大化最小角的三角剖分
4.9.3 最大空圆
4.9.4 最小生成树
4.9.5 货郎担问题
4.9.6 中轴
4.9.7 Voronoi图与凸壳的关系
4.9.8 Voronoi图的推广
4.9.9 有约束的Voronoi图
4.9.10 线段集的Voronoi图
4.9.11 关联于多边形的Voronoi图
4.9.12 点线集的Voronoi图
4.9.13 点、水平、垂直正交线段集的Voronoi图
4.9.14 几何数据压缩
4.9.15 车辆定位导航系统的新定位算法
4.9.16 调色
4.9.17 点集增(删)点之后的三角剖分

第5章交与并及其应用
5.1 线段交的算法
5.2 多边形的交
5.2.1 凸多边形交的算法
5.2.2 星形多边形交的算法
5.2.3 任意简单多边形交的算法
5.3 半平面的交及其应用
5.3.1 半平面的交
5.3.2 两个变量的线性规划
5.4 多边形的并
5.5 凸多面体的交
5.6 应用
5.6.1 地图匹配
5.6.2 地图数据的处理
5.6.3 线段与凸多面体面的交
5.6.4 与线段集中线段均相交的直线及其存在区域
5.6.5 特定射线询问

第6章多边形的获取及相关问题
6.1 连接不相交线段成简单多边形(链)
6.2 红外图像边缘提取
6.3 提取可见光图像的边缘
6.4 图像边界点行排列转换为顺序排列
6.5 数字图像中目标边界的多边形表示
6.6 包含密集点、线集多边形的获取
6.7 满足特定条件的多边形划分
6.8 多边形与多边形链
6.9 圆弧、直线段组成的多边形顶点凸、凹性的确定
6.10 多边形放大、缩小及移动
6.11 带状多边形的处理
6.12 下料问题(1)
6.13 下料问题(2)
6.14 下料问题(3)
6.15 线锯问题
6.16 多边形(链)的匹配(1)
6.17 多边形(链)的匹配(2)
6.18 构造凸多边形
6.19 具有属性点集的控制区域
6.20 多边形内区域的划分及多边形(点集)中心点的确定
6.21 满足一定条件的多边形划分
6.22 特定条件下凸多边形的缩小与放大

第7章几何体的划分与等分
7.1 平面上不同类型点集的划分
7.2 多边形内不同类型点集的等分
7.3 平面上不同类型线段集的划分
7.4 平面上不同类型线段集的等分
7.5 平面上不同类型点线集的划分与等分
7.6 链、多边形的划分与等分

第8章路径与回路
8.1 最短路径
8.1.1 可视图及其构造
8.1.2 Z□算法(寻求网络中任意两点间最短路径的算法
8.1.3 多面体面上任意两点之间的最短路径
8.1.4 货运汽车调度及行驶路径问题
8.2 最短路径问题的变型
8.3 满足一定条件的运动规划
8.4 多边形内点之间的可视图
8.5 多边形内任意两点之间的最短路径
8.6 自主车自动定位及确定行车方向
8.7 迷宫问题
8.8 棋盘上的路径与回路
8.9 选择道路及判定道路的通过能力
8.10 多边形内中心区域的确定

第9章几何拓扑网络设计
9.1 G(S)问题
9.1.1 最大间隙问题(MAX G)
9.1.2 点集中最大空凸多边形问题及最大空矩形问题
9.1.3 线段集中最大空凸多边形问题
9.1.4 点线集中最大空凸多边形问题
9.1.5 最小覆盖问题(MIN C)
9.1.6 包含平面点集的最小正方形
9.1.7 子点集包含问题
9.1.8 2-中心问题
9.1.9 k-中心问题
9.1.10 最近对问题(CPP)
9.1.11 所有最近邻近问题(ANNP)
9.1.12 邮局问题(POFP)
9.1.13 寻找具有属性点集的最近点对或点团
9.2 G(E)问题
9.2.1 EMST问题
9.2.2 线段集、点线集的最小生成树
9.2.3 直线最小生成树及其相关问题
9.2.4 欧几里得TSP
9.2.5 欧几里得最大生成树问题(EMXT)
9.2.6 最小生成网络
9.3 G(S，E)问题
9.3.1 欧几里得Steiner最小树问题(ESMT)
9.3.2 直线Steiner最小树问题(RSMT)
9.3.3 求解ESMT问题的算法
9.4 G(□)问题
9.4.1 有障碍物的最大空隙问题(MAX G(□)
9.4.2 多边形集中最大空隙问题
9.4.3 具有障碍物的欧几里得最短路径问题(ESPO)
9.4.4 求解E3中ESPO问题的算法
9.4.5 具有障碍物的Steiner最小树问题(ESMTO)
待解决的问题
算法一览
参考文献
名词索引

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