geometry2

合集下载

Geometry对象2

//使环封闭��
下面的代码使用
Segment 对象来组成一个环
pRing.Close();
在Geometry中，封闭的几何形体包括Envelope、 Ring和Polygon，封闭的几何形体可以确定其面积，因此它们都实现了IArea接口。IArea:Centroid可以返回这些几何形体的重心；IArea:LabelPoint可以返回这些几何形体的标注点。
IGeometryCollection Polyline
Polygon对象
Polygon对象是一个有序环对象的集合，这些环可以是一个或者多个。多边形对象通常可以用于描述具有面积的多边形离散矢量对象。
IPolygon接口是 Polygon类主要接口。 ExteriorRingCount 属性可以返回一个多边形全部外部环的数目。 InteriorRingCount 返回一个多边形的内部环数目。
(1)ConstructEnvelope可以通过一个给定的包络线来产生一个内置的椭圆对象。 (2)ConstructQuarterEllipse构造器要求输入起始点和终止点和方向属性以产生一个椭圆弧。 (3)ConstructTwoPointsEnvelope 方法需要输入四个参数，起始点、终止点、包络线、以及方向属性。 (4)ConstructUpToFivePoints可以输入5个点来构造一个椭圆弧，这五个点分别是起始点、终止点、一个弧上任意点以及两个椭圆对象上的附加点。
口�� IPoint pPoint1; IPoint pPoint2; pPoint1 = new PointClass(); pPoint1.PutCoords(100, 20); pPoint2 = new PointClass(); pPoint2.PutCoords(20, 310); IGeometryCollection pPolyline; pPolyline = new PolylineClass(); ISegmentCollection pPath; pPath = new PathClass(); //产生线段对象将其添加到路径对象�� ILine pLine; object Missing1 = Type.Missing; object Missing2 = Type.Missing; pLine = new LineClass(); pLine.PutCoords(pPoint1, pPoint2); pPath.AddSegment(pLine as ISegment,ref Missing, ref Missing2); //将路径对象添加到多义线对象��

ArcGIS_REST_API常用参数简要说明

范例: sr
searchFields=AREANAME,SUB_REGION
说明: 在输入和输出中的几何要素以及地图视图范围(mapExtent)所采用的空间参考所对应的公开的 WKID 值。如果没有指定 SR，几何要素和地图视图范围将被默认为使用几何要素所在地图的空间参考坐标系，并以此空间参考为输出值的空间参考。必要值说明:需要执行查找操作的所有层。列表被指定使用一个逗号来分隔这些图层 ID。语法: layers=<layerId1>,<layerId2> 从 map service resource 获取到的图层 ID
语法:

JSON 结构:
geometryType=<geometryType>&geometry={geometry} geometryType=esriGeometryPoint&geometry=<x>,<y>
点的简单语法: 视图边框：
geometryType=esriGeometryEnvelope&geometry=<xmin>,<ymin>,<xmax>,<ymax> 范例:
layers
3 / 14

top: 只识别指定位置的最上层图层。 visible: 识别所有显示的图层。 all: 所有图层。 layers=all
范例:
默认: 默认识别最上层图层(i.e. layers=top) 你即可以选择如上所述本身，也可根据选择的图层 ID 列表，来指定操作图层。如果使用了图层 ID 列表，服务器将会把它当成布尔值来操作。例如，如果参数为： layers=visible:2,5 则在所有显示的图层中只有 ID 为 2 和 5 的图层被识别操作。语法: [top | visible | all]:layerId1,layerId2 从 map service resource 获取到的图层 ID

计算机辅助工程 5-2

摆刀平面对A轴：Z-Y平面对C轴：X-Y平面
对于某些狭窄通道或Z轴方向不单调的曲面铣削加工，其刀位坐标的计算方法与三轴加工的不同。需要用五轴联动铣削加工，通过摆动刀轴矢量保证刀轴不与加工表面及约束面发生干涉或碰撞。
• 刀轴控制方法
Away from point Toward point Away from Line Toward Line Normal to Part Normal to Drive Relative to Part
Click the ICON Type : mill_planar
to Create New Operation
Subtype: PLANAR_MILL
Use Geometry:
Use Tool Use Method:
Name:
Click OK
1). Part → Select to set Boundary Geometry 2). Curve/Edges 用Edges 定义加工边界
10、后置处理Postprocess
后置处理是按数控机床控制系统的要求了设置机床数据文件*.PUI，后置处理器根据*.pui文件把刀位数据、刀具命令及各种功能要求通过变换、计算、翻译等，生成具体某一数控系统能够接受的NC指令。后置处理与具体机床的控制系统及机床参数有关，机床不同，采用的 pui文件也不同。
操作导航器
刀轨管理边界管理
加工方式 Point to Point 点位加工 Planar Mill 平面铣 Fixed Contour 固定轴曲面铣 Varible Contour 变轴曲面铣 Cavity Mill 型腔铣 ...
Operation type

数学专业英语第二版的课文翻译

2－A Why study geometry Many leading institutions of higher learning have recognized that positive benefits can be gained by all who study this branch of mathematics. This is evident from the fact that they require study of geometry as a prerequisite to matriculation in those schools. 许多居于领导地位的学术机构承认，所有学习这个数学分支的人都将得到确实的受益，许多学校把几何的学习作为入学考试的先决条件，从这一点上可以证明。

Geometry had its origin long ago in the measurement by the Babylonians and Egyptians of their lands inundated by the floods of the Nile River. The greek word geometry is derived from geo, meaning “earth” and metron, meaning “measure” . As early as 2000 . we find the land surveyors of these people re-establishing vanishing landmarks and boundaries by utilizing the truths of geometry . 几何学起源于很久以前巴比伦人和埃及人测量他们被尼罗河洪水淹没的土地，希腊语几何来源于geo ，意思是”土地“，和metron 意思是”测量“。

2 view geometry

MASKS © 2004
Invitation to 3D vision
Example- Two views
Point Feature Matching
MASKS © 2004
Invitation to 3D vision
Example – Epipolar Geometry
Camera Pose and Sparse Structure Recovery
E is 5 diml. sub. mnfld. in
• 8-point linear algorithm • Recover the unknown pose:
MASKS © 2004
Invitation to 3D vision
Pose Recovery
• There are exactly two pairs essential matrix . • There are also two pairs essential matrix . corresponding to each corresponding to each
measurements
unknowns
Find such Rotation and Translation and Depth that the reprojection error is minimized
Two views ~ 200 points 6 unknowns – Motion 3 Rotation, 3 Translation - Structure 200x3 coordinates - (-) universal scale Difficult optimization problem
•
•
•

gis二次开发几何形体对象Geometry

Path几何对象 Path是连续的Segment的集合，除了路径的第一个Segment和最后一个 Segment外其余的Segment的起始点都是前一个Segment的终止点，即 Path对象的中的Segment不能出现分离，Path可以是任意数的Segment 子类的组合。
Path几何对象该Path对象有很多我们经常用到的方法，如平滑曲线，对曲线抽稀等操作，如下图：。
IEnvelope接口
• 属性
– 空间坐标XMax XMin YMax YMin Height Width – 四个角点的坐标：UpperLeft UpperRight LowerLeft LowerRight – – – – – – – PutCoords：构造包络线的方法 QueryCoords：查询包络线的 Expand：按比例缩放包络线的范围 offset：偏移包络线本身 CenterAt：改变包络线的中心点 Intersect：两个包络线相交的方法 Union：两个包络线对象的并集
Polyline几何对象 Polyline是有序path组成的集合，可以拥有M、Z和ID属性值，Polyline对象的 IPointCollection接口包含了所有的节点信息，IGeometryCollection接口可以获取 polyline的paths，ISegmentCollection接口可以获取 polyline的segments。一个Polyline对象必须满足以下准则： 1.组成Polyline对象的所有Path对象必须是有效的。 2.组成Polyline对象的所有Path对象不能重合，相交或自相交。 3.组成Polyline对象的多个Path对象可以连接与某一点，也可以分离。 4.Path对象的长度不能为0. IPolyline是Polyline类的主要接口，IPolyline的Reshape方法可以使用一个Path对象为一个Polyline对象整形，IPolyline的SimplifyNetwork方法用于简化网络。 Polyline对象可以使用IGeometryCollection接口添加Path对象的方法来创建，使用该接口需注意以下情况： 1.每一个Path对象必须是有效的，或使用IPath::Simplify方法后有效。 2.由于Polyline是Path对象的有序集合，所以添加Path对象时必须注意顺序和方向。 3.为了保证Polyline是有效的，可以创建完Polyline对象后使用 ITopologicalOperator接口的Simplify方法。

LMS Test.Lab中文操作指南_Geometry几何建模

LMS b中文操作指南— Geometry几何建模比利时LMS国际公司北京代表处2009年2月LMS b中文操作指南— Geometry 几何建模目录第一步，软件启动 (3)第二步，界面及工作表流程 (4)1. Geometry界面 (4)2. Geometry工作表 (4)第三步，创建几何 (5)1. 创建组件 (6)2. 创建节点 (7)3. 创建线 (9)4. 创建面 (10)5. 创建从节点 (10)第四步，几何操作 (11)1. 平移、缩放及旋转 (11)2. 右键菜单操作 (11)3. 其他操作 (13)第五步，如何在柱坐标或球坐标下建立模态分析几何模型 (14)1. 坐标系的选择： (14)2. 关于整体坐标系和局部坐标系的说明 (16)3. 关于欧拉角的使用说明 (17)第六步，外部几何模型文件的导入 (18)第一步，软件启动¾通过Windows开始菜单¾通过桌面图标当安装LMS Test. Lab后，系统会在桌面上创建一个LMS Test. Lab文件夹，通过此文件夹也可启动软件。

通过打开Test lab 9A文件夹，双击Geometry按钮，作为一项独立的任务开始¾在任意Test lab的模块中，通过add ins…进行添加第二步，界面及工作表流程1. Geometry 界面2. Geometry 工作表节点工作表 ¾ 从节点 – 创建主/从自由度Geometry 工作表组成: ¾ 组件工作表 – 创建组件 ¾ – 创建节点¾ 线工作表 – 创建线 ¾ 面工作表 – 创建面第三步，创建几何几何坐标的输入有三种方式¾直角坐标¾柱坐标¾球坐标在部件工作表中可以选取不同的坐标输入方式下面以直角坐标输入方式为例创建几何¾ １－－定义组件名称； ¾ ２－－定义对应组件颜色； ¾ ３－－定义组件间的相对位置 ¾ ４－－接受输入状态；¾ ５－－在单击Accept Table 后文件列表中会显示相应的组件名如下图中1也可选取显示组件的位置position 应x,y,z); 选取显示组向(orientatio 另外，单击Table Options 后，弹出组件表设置对话框，在其中可进行组件表显示的设置，所示。

ICEM 原版培训教程(ANSYS 公司提供)2

• • • •
Align Edge to Curve Close Faceted Holes Trim by Screen Loop Trim by Surface Loop
Facetted (triangulated) surfaces
ANSYS, Inc. Proprietary © 2009 ANSYS, Inc. All rights reserved.
Training Manual
– Surfaces are internally represented as triangulated data
• Resolution or approximation of true spline surface data set by Triangulation Tolerance • Smaller value = better resolution • 0.001 works best for most models • U a hi h t i t l Use high tri tolerance t work with a l to k ith large model, but lower the tolerance when it comes time to compute the mesh y • Not used if surfaces are already facetized (e.g. STL, VRML)
• • • • • • • •
Convert from B Bspline Coarsen Surface Create Surface Merge Edges Split Edges Swap Edges Move Nodes Merge Nodes

geometry函数

geometry函数一、介绍geometry函数是一个用于处理几何图形的函数，它可以实现一系列几何图形的计算和操作。

几何图形是指二维或三维空间中的点、线、面等物体，是数学和物理学中重要的研究对象。

geometry函数可以帮助我们在程序中轻松地处理各种几何图形，包括计算它们的面积、周长、体积等。

二、基本概念在使用geometry函数之前，我们需要了解一些基本概念：1. 点：在二维平面上表示为(x,y)，在三维空间中表示为(x,y,z)。

2. 直线：由两个点确定，在二维平面上通常用斜率截距式表示为y=kx+b，在三维空间中通常用参数方程表示为x=x0+t*a,y=y0+t*b,z=z0+t*c。

3. 圆：由一个圆心和半径确定，在二维平面上通常用标准式表示为(x-a)^2+(y-b)^2=r^2，在三维空间中通常用参数方程表示为x=a+r*cos(t), y=b+r*sin(t), z=c。

4. 矩形：由四个顶点确定，在二维平面上通常用左下角坐标和右上角坐标表示为(x1,y1,x2,y2)，在三维空间中通常用六个面的坐标表示为(x1,y1,z1,x2,y2,z2)。

5. 三角形：由三个点确定，在二维平面上通常用三个顶点坐标表示为(x1,y1,x2,y2,x3,y3)，在三维空间中通常用三个顶点坐标表示为(x1,y1,z1,x2,y2,z2,x3,y3,z3)。

6. 多边形：由多个点确定，在二维平面上通常用顶点坐标数组表示，每个顶点的坐标为(x[i],y[i])，在三维空间中通常用顶点坐标数组表示，每个顶点的坐标为(x[i],y[i],z[i])。

7. 立体图形：包括球体、立方体、圆柱、圆锥等，在三维空间中通常用各自的参数方程表示。

三、函数列表geometry函数包含以下几种类型的函数：1. 点相关函数：包括计算两点之间距离、计算两点之间的中点、判断一个点是否在某条直线上等。

2. 直线相关函数：包括计算两条直线之间的夹角、计算两条直线是否相交、计算一条直线与一个矩形是否相交等。

学习笔记

描述：判断geometry1是否覆盖geometry2（或者说geometry2完全在geometry1的内部）。作用和SDO_RELATE方法中参数mask=COVEREDBY时是一样的。
例子：
SELECT c.mkt_id,
FROM cola_markets c
WHERE SDO_COVERS(c.shape,
geometry2 可以是表中的geometry字段，也可以是实例化的geometry对象。
描述：判断geometry1是否包含geometry2。作用和SDO_RELATE方法中参数mask=CONSTAINS时是一样的。
例子：SELECT c.mkt_id,
FROM cola_markets c
5.SDO_EQUAL（相等）
格式：SDO_EQUAL(geometry1,geometry2)
参数：geometry1 必须是表中的geometry字段，而且该字段必须存在空间索引。
geometry2 可以是表中的geometry字段，也可以是实例化的geometry对象。
SDO_ORDINATE_ARRAY(4,6, 8,8))
) = 'TRUE';
2.SDO_CONTAINS（包含）
格式：SDO_CONTAINS(geometry1,geometry2)
参数：geometry1 必须是表中的geometry字段，而且该字段必须存在空间索引。
SDO_ORDINATE_ARRAY(5,6, 12,12))
) = 'TRUE';
8.SDO_JOIN（合并几何对象）？？？？？？？？
9.SDO_NN(查找最近)

JTS (Geometry)

JTS Geometry关系判断和分析关系判断Geometry之间的关系有如下几种：相等(Equals)：几何形状拓扑上相等。

脱节(Disjoint)：几何形状没有共有的点。

相交(Intersects)：几何形状至少有一个共有点（区别于脱节）接触(Touches)：几何形状有至少一个公共的边界点，但是没有内部点。

交叉(Crosses)：几何形状共享一些但不是所有的内部点。

内含(Within)：几何形状A的线都在几何形状B内部。

包含(Contains)：几何形状B的线都在几何形状A内部（区别于内含）重叠(Overlaps)：几何形状共享一部分但不是所有的公共点，而且相交处有他们自己相同的区域。

如下例子展示了如何使用Equals,Disjoint,Intersects,Within操作：复制代码package com.alibaba.autonavi;import com.vividsolutions.jts.geom.*;import com.vividsolutions.jts.io.ParseException;import com.vividsolutions.jts.io.WKTReader;/*** gemotry之间的关系* @author xingxing.dxx**/public class GeometryRelated {private GeometryFactory geometryFactory = new GeometryFactory();/*** 两个几何对象是否是重叠的* @return* @throws ParseException*/public boolean equalsGeo() throws ParseException{WKTReader reader = new WKTReader( geometryFactory );LineString geometry1 = (LineString) reader.read("LINESTRING(0 0, 2 0, 5 0)");LineString geometry2 = (LineString) reader.read("LINESTRING(5 0, 0 0)");return geometry1.equals(geometry2);//true}/*** 几何对象没有交点(相邻)* @return* @throws ParseException*/public boolean disjointGeo() throws ParseException{WKTReader reader = new WKTReader( geometryFactory );LineString geometry1 = (LineString) reader.read("LINESTRING(0 0, 2 0, 5 0)");LineString geometry2 = (LineString) reader.read("LINESTRING(0 1, 0 2)");return geometry1.disjoint(geometry2);}/*** 至少一个公共点(相交)* @return* @throws ParseException*/public boolean intersectsGeo() throws ParseException{WKTReader reader = new WKTReader( geometryFactory );LineString geometry1 = (LineString) reader.read("LINESTRING(0 0, 2 0, 5 0)");LineString geometry2 = (LineString) reader.read("LINESTRING(0 0, 0 2)");Geometry interPoint = geometry1.intersection(geometry2);//相交点System.out.println(interPoint.toText());//输出POINT (0 0)return geometry1.intersects(geometry2);}/*** 判断以x,y为坐标的点point(x,y)是否在geometry表示的Polygon中* @param x* @param y* @param geometry wkt格式* @return*/public boolean withinGeo(double x,double y,String geometry) throws ParseException {Coordinate coord = new Coordinate(x,y);Point point = geometryFactory.createPoint( coord );WKTReader reader = new WKTReader( geometryFactory );Polygon polygon = (Polygon) reader.read(geometry);return point.within(polygon);}/*** @param args* @throws ParseException*/public static void main(String[] args) throws ParseException {GeometryRelated gr = new GeometryRelated();System.out.println(gr.equalsGeo());System.out.println(gr.disjointGeo());System.out.println(gr.intersectsGeo());System.out.println(gr.withinGeo(5,5,"POLYGON((0 0, 10 0, 10 10, 0 10,0 0))"));}}复制代码关系分析关系分析有如下几种缓冲区分析（Buffer）包含所有的点在一个指定距离内的多边形和多多边形凸壳分析（ConvexHull）包含几何形体的所有点的最小凸壳多边形（外包多边形）交叉分析（Intersection）A∩B 交叉操作就是多边形AB中所有共同点的集合联合分析（Union）AUB AB的联合操作就是AB所有点的集合差异分析（Difference）(A-A∩B) AB形状的差异分析就是A里有B里没有的所有点的集合对称差异分析（SymDifference）(AUB-A∩B) AB形状的对称差异分析就是位于A中或者B中但不同时在AB中的所有点的集合2. 我们来看看具体的例子复制代码package com.alibaba.autonavi;import java.util.ArrayList;import java.util.List;import com.vividsolutions.jts.geom.Coordinate;import com.vividsolutions.jts.geom.Geometry;import com.vividsolutions.jts.geom.GeometryFactory;import com.vividsolutions.jts.geom.LineString;/*** gemotry之间的关系分析** @author xingxing.dxx*/public class Operation {private GeometryFactory geometryFactory = new GeometryFactory();/*** create a Point** @param x* @param y* @return*/public Coordinate point(double x, double y) {return new Coordinate(x, y);}/*** create a line** @return*/public LineString createLine(List<Coordinate> points) {Coordinate[] coords = (Coordinate[]) points.toArray(new Coordinate[points.size()]);LineString line = geometryFactory.createLineString(coords);return line;}/*** 返回a指定距离内的多边形和多多边形** @param a* @param distance* @return*/public Geometry bufferGeo(Geometry a, double distance) {return a.buffer(distance);}/*** 返回(A)与(B)中距离最近的两个点的距离** @param a* @param b* @return*/public double distanceGeo(Geometry a, Geometry b) {return a.distance(b);}/*** 两个几何对象的交集** @param a* @param b* @return*/public Geometry intersectionGeo(Geometry a, Geometry b) { return a.intersection(b);}/*** 几何对象合并** @param a* @param b* @return*/public Geometry unionGeo(Geometry a, Geometry b) { return a.union(b);}/*** 在A几何对象中有的，但是B几何对象中没有** @param a* @param b* @return*/public Geometry differenceGeo(Geometry a, Geometry b) { return a.difference(b);}public static void main(String[] args) {Operation op = new Operation();//创建一条线List<Coordinate> points1 = new ArrayList<Coordinate>();points1.add(op.point(0, 0));points1.add(op.point(1, 3));points1.add(op.point(2, 3));LineString line1 = op.createLine(points1);//创建第二条线List<Coordinate> points2 = new ArrayList<Coordinate>();points2.add(op.point(3, 0));points2.add(op.point(3, 3));points2.add(op.point(5, 6));LineString line2 = op.createLine(points2);System.out.println(op.distanceGeo(line1, line2));//out 1.0System.out.println(op.intersectionGeo(line1, line2));//out GEOMETRYCOLLECTION EMPTYSystem.out.println(op.unionGeo(line1, line2)); //out MULTILINESTRING ((0 0, 1 3, 2 3), (3 0, 3 3, 5 6))System.out.println(op.differenceGeo(line1, line2));//out LINESTRING (0 0, 1 3, 2 3) }}。

JTS（Geometry）（转）

JTS（Geometry）（转）原⽂链接：空间数据模型(1)、JTS Geometry model(2)、ISO Geometry model (Geometry Plugin and JTS Wrapper Plugin)GeoTools has two implementations of these interfaces:Geometry Plugin a port of JTS 1.7 to the ISO Geometry interfacesJTS Wrapper Plugin an implementation that delegates all the work to JTSJTS包结构系（linearref包）、计算交点（noding包）、⼏何图形操作（operation包）、平⾯图（planargraph包）、多边形化（polygnize包）、精度（precision）、⼯具（util包）重点理解JTS Geometry model(1) JTS提供了如下的空间数据类型PointMultiPointLineStringLinearRing 封闭的线条MultiLineString 多条线PolygonMultiPolygonGeometryCollection 包括点，线，⾯(2) ⽀持接⼝CoordinateCoordinate（坐标）是⽤来存储坐标的轻便的类。

它不同于点，点是Geometry的⼦类。

不像模范Point的对象（包含额外的信息，例如⼀个信包，⼀个精确度模型和空间参考系统信息），Coordinate只包含纵座标值和存取⽅法。

Envelope(矩形)⼀个具体的类，包含⼀个最⼤和最⼩的x 值和y 值。

GeometryFactoryGeometryFactory提供⼀系列的有效⽅法⽤来构造来⾃Coordinate类的Geometry对象。

⽀持接⼝import org.geotools.geometry.jts.JTSFactoryFinder;import com.vividsolutions.jts.geom.Coordinate;import com.vividsolutions.jts.geom.Envelope;import com.vividsolutions.jts.geom.Geometry;import com.vividsolutions.jts.geom.GeometryCollection;import com.vividsolutions.jts.geom.GeometryFactory;import com.vividsolutions.jts.geom.LineString;import com.vividsolutions.jts.geom.LinearRing;import com.vividsolutions.jts.geom.Point;import com.vividsolutions.jts.geom.Polygon;import com.vividsolutions.jts.geom.MultiPolygon;import com.vividsolutions.jts.geom.MultiLineString;import com.vividsolutions.jts.geom.MultiPoint;import com.vividsolutions.jts.io.ParseException;import com.vividsolutions.jts.io.WKTReader;/*** Class GeometryDemo.java* Description Geometry ⼏何实体的创建，读取操作* Company mapbar* author Chenll E-mail: Chenll@* Version 1.0* Date 2012-2-17 上午11:08:50*/public class GeometryDemo {private GeometryFactory geometryFactory = JTSFactoryFinder.getGeometryFactory( null );/*** create a point* @return*/public Point createPoint(){Coordinate coord = new Coordinate(109.013388, 32.715519);Point point = geometryFactory.createPoint( coord );return point;}/*** create a rectangle(矩形)* @return*/public Envelope createEnvelope(){Envelope envelope = new Envelope(0,1,0,2);return envelope;}/*** create a point by WKT* @return* @throws ParseException*/public Point createPointByWKT() throws ParseException{WKTReader reader = new WKTReader( geometryFactory );Point point = (Point) reader.read("POINT (109.013388 32.715519)");return point;}/*** create multiPoint by wkt* @return*/public MultiPoint createMulPointByWKT()throws ParseException{WKTReader reader = new WKTReader( geometryFactory );MultiPoint mpoint = (MultiPoint) reader.read("MULTIPOINT(109.013388 32.715519,119.32488 31.435678)");return mpoint;}/**** create a line* @return*/public LineString createLine(){Coordinate[] coords = new Coordinate[] {new Coordinate(2, 2), new Coordinate(2, 2)};LineString line = geometryFactory.createLineString(coords);return line;}/*** create a line by WKT* @return* @throws ParseException*/public LineString createLineByWKT() throws ParseException{WKTReader reader = new WKTReader( geometryFactory );LineString line = (LineString) reader.read("LINESTRING(0 0, 2 0)");return line;}/*** create multiLine* @return*/public MultiLineString createMLine(){Coordinate[] coords1 = new Coordinate[] {new Coordinate(2, 2), new Coordinate(2, 2)};LineString line1 = geometryFactory.createLineString(coords1);Coordinate[] coords2 = new Coordinate[] {new Coordinate(2, 2), new Coordinate(2, 2)};LineString line2 = geometryFactory.createLineString(coords2);LineString[] lineStrings = new LineString[2];lineStrings[0]= line1;lineStrings[1] = line2;MultiLineString ms = geometryFactory.createMultiLineString(lineStrings);return ms;}/*** create multiLine by WKT* @return* @throws ParseException*/public MultiLineString createMLineByWKT()throws ParseException{WKTReader reader = new WKTReader( geometryFactory );MultiLineString line = (MultiLineString) reader.read("MULTILINESTRING((0 0, 2 0),(1 1,2 2))");return line;}/*** create a polygon(多边形) by WKT* @return* @throws ParseException*/public Polygon createPolygonByWKT() throws ParseException{WKTReader reader = new WKTReader( geometryFactory );Polygon polygon = (Polygon) reader.read("POLYGON((20 10, 30 0, 40 10, 30 20, 20 10))");return polygon;}/*** create multi polygon by wkt* @return* @throws ParseException*/public MultiPolygon createMulPolygonByWKT() throws ParseException{WKTReader reader = new WKTReader( geometryFactory );MultiPolygon mpolygon = (MultiPolygon) reader.read("MULTIPOLYGON(((40 10, 30 0, 40 10, 30 20, 40 10),(30 10, 30 0, 40 10, 30 20, 30 10)))");return mpolygon;}/*** create GeometryCollection contain point or multiPoint or line or multiLine or polygon or multiPolygon* @return* @throws ParseException*/public GeometryCollection createGeoCollect() throws ParseException{LineString line = createLine();Polygon poly = createPolygonByWKT();Geometry g1 = geometryFactory.createGeometry(line);Geometry g2 = geometryFactory.createGeometry(poly);Geometry[] garray = new Geometry[]{g1,g2};GeometryCollection gc = geometryFactory.createGeometryCollection(garray);return gc;}/*** create a Circle 创建⼀个圆，圆⼼(x,y) 半径RADIUS* @param x* @param y* @param RADIUS* @return*/public Polygon createCircle(double x, double y, final double RADIUS){final int SIDES = 32;//圆上⾯的点个数Coordinate coords[] = new Coordinate[SIDES+1];for( int i = 0; i < SIDES; i++){double angle = ((double) i / (double) SIDES) * Math.PI * 2.0;double dx = Math.cos( angle ) * RADIUS;double dy = Math.sin( angle ) * RADIUS;coords[i] = new Coordinate( (double) x + dx, (double) y + dy );}coords[SIDES] = coords[0];LinearRing ring = geometryFactory.createLinearRing( coords );Polygon polygon = geometryFactory.createPolygon( ring, null );return polygon;}/*** @param args* @throws ParseException*/public static void main(String[] args) throws ParseException {GeometryDemo gt = new GeometryDemo();Polygon p = gt.createCircle(0, 1, 2);//圆上所有的坐标(32个)Coordinate coords[] = p.getCoordinates();for(Coordinate coord:coords){System.out.println(coord.x+","+coord.y);}Envelope envelope = gt.createEnvelope();System.out.println(envelope.centre());}}：WKT - 概念WKT(Well-known text)是⼀种⽂本标记语⾔，⽤于表⽰⽮量⼏何对象、空间参照系统及空间参照系统之间的转换。

数学专业英语(2)

Mathematical English Dr. Xiaomin Zhang Email: zhangxiaomin@§2.2 Geometry and TrigonometryTEXT A Why study geometry?Why do we study geometry? The student beginning the study of this text may well ask, “What is geometry? What can I expect to gain fro m this study?”Many leading institutions of higher learning have recognized that positive benefits can be gained by all who study this branch of mathematics. This is evident from the fact that they require study of geometry as a prerequisite to matriculation in those schools. Geometry had its origin long ago in the measurements by the Babylonians and Egyptians of their lands inundated by the floods of the Nile River. The Greek word geometry is derived from geo, meaning “earth”, and metron, meaning “measure”. As early as2000 B.C. we find the land surveyors of these people re-establishing vanishing landmarks and boundaries by utilizing the truths of geometry.Geometry is a science that deals with forms made by lines. A study of geometry is an essential part of the training of the successful engineer, scientist, architect, and draftsman. The carpenter, machinist, stonecutter, artist, and designer all apply the facts of geometry in their trades. In this course the student will learn a great deal about geometric figures such as lines, angles, triangles, circles, and designs and patterns of many kinds. One of the most important objectives derived from a study of geometry is making the student be more critical in his listening, reading, and thinking. In studying geometry he is led away from the practice of blind acceptance of statements and ideas and is taught to think clearly and critically before forming conclusions.There are many other less direct benefits the student of geometry may gain. Among these one must include training in the exact use of the English language and in the ability to analyze a new situation or problem into its basic parts, and utilizing perseverance, originality, and logical reasoning in solving the problem. An appreciation for the orderliness and beauty of geometric forms that abound in man’s works and of the creations of nature will be a byproduct of the study of geometry. The student should also develop an awareness of the contributions of mathematics and mathematicians to our culture and civilization.TEXT B Some geometrical terms1. Solids and planes.A solid is a three-dimensional figure. Common examples of solid are cube, sphere, cylinder, cone and pyramid.A cube has six faces which are smooth and flat. These faces are called plane surfaces or simply planes. A plane surface has two dimensions, length and width .The surface of a blackboard or a tabletop is an example of a plane surface.2. Lines and line segments.We are all familiar with lines, but it is difficult to define the term. A line may be represented by the mark made by moving a pencil or pen across a piece of paper. A line may be considered as having only one dimension, length. Although when we draw a line we give it breadth and thickness, we think only of the length of the trace when considering the line. A point has no length, no width, and no thickness, but marks a position. We arefamiliar with such expressions as pencil point and needle point. We represent a point by a small dot and name it by a capital letter printed beside it, as “point A” in Fig. 2-2-1.The line is named by labeling two points on it with capital letters or one small letter near it. The straight line in Fig. 2-2-2 is read “line AB” or “line l”. A straight line extends infinitely far in two directions and has no ends. The part of the line between two points on the line is termed a line segment. A line segment is named by the two end points. Thus, in Fig. 2-2-2, we refer to AB as line segment of line l. When no confusion may result, the expression “line segment AB” is often replace d by segment AB or, simply, line A B.There are three kinds of lines: the straight line, the broken line, and the curved line. A curved line or, simply, curve is line no part of which is straight. A broken line is composed of joined, straightline segments, as ABCDE of Fig. 2-2-3.3. Parts of a circle.A circle is a closed curve lying in one plane, all points of which are equidistant from a fixed point called the center (Fig. 2-2-4). The symbol for a circle is ⊙. In Fig. 2-2-4, O is the center of ⊙ABC, or simply of ⊙O. A line segment drawn from the center of the circle to a point on the circle is a radius (plural, radii) of the circle. OA, OB, and OC are radii of ⊙O, A diameter of a circle is a line segment through the center of the circle with endpoints on the circle. A diameter is equal to two radii.A chord is any line segment joining two points on the circle. ED is a chord of the circle in Fig. 2-2-4.From this definition is should be apparent that a diameter is a chord. Any part of a circle is an arc, such as arc AE. Points A and E divide the circle into minor arc AE and major arc ABE. A diameter divides a circle into two arcs termed semicircles, such as AB. Thecircumference is the length of a circle.SUPPLEMENT A Ruler-and-compass constructionsA number of ancient problems in geometry involve the construction of lengths or angles using only an idealised ruler and compass. The ruler is indeed a straightedge, and may not be marked; the compass may only be set to already constructed distances, and used to describe circular arcs.Some famous ruler-and-compass problems have been proved impossible, in several cases by the results of Galois theory. In spite of these impossibility proofs, some mathematical amateurs persist in trying to solve these problems. Many of them fail to understand that many of these problems are trivially soluble provided that other geometric transformations are allowed: for example, squaring the circle is possible using geometric constructions, but not possible using ruler and compasses alone. Mathematician Underwood Dudley has made a sideline of collecting false ruler-and-compass proofs, as well as other work by mathematical cranks, and has collected them into several books.Squaring the circle The most famous of these problems, “squaring the circle”, involves constructing a square with the same area as a given circle using only ruler and compasses. Squaring the circle has been proved impossible, as it involves generating a transcendental ratio, namely 1:√π.Only algebraic ratios can be constructed with ruler and compasses alone. The phrase “squaring the circle” is often used to mean “doing the impossible”for this reason.Without the constraint of requiring solution by ruler and compasses alone, the problem is easily soluble by a wide variety of geometric and algebraic means, and has been solved many times in antiquity.Doubling the cube Using only ruler and compasses, construct the side of a cube that has twice the volume of a cube with a given side. This is impossible because the cube root of 2, though algebraic, cannot be computed from integers by addition, subtraction, multiplication, division, and taking square roots.Angle trisection Using only ruler and compasses, construct an angle that is one-third of a given arbitrary angle. This requires taking the cube root of an arbitrary complex number with absolute value 1 and is likewise impossible.Constructing with only ruler or only compassIt is possible, as shown by Georg Mohr, to construct anything with just a compass that can be constructed with ruler and compass. It is impossible to take a square root with just a ruler, so some things cannot be constructed with a ruler that can be constructed with a compass; but given a circle and its center, they can be constructed.Problem How can you determine the midpoint of any given line segment with only compass?SUPPLEMENT B Archimedes and On the Sphere and the CylinderArchimedes(287 BC-212 BC) was an Ancient mathematician, astronomer, philosopher, physicist and engineer born in the Greek seaport colony of Syracuse. He is considered by some math historians to be one of history's greatest mathematicians, along with possibly Newton, Gauss and Euler.He was an aristocrat, the son of an astronomer, but little is known of his early life except that he studied under followers of Euclid in Alexandria, Egypt before returning to his native Syracuse, then an independent Greek city-state. Several of his books were preserved by the Greeks and Arabs into the Middle Ages, and, fortunately, the Roman historian Plutarch described a few episodes from his life. In many areas of mathematics as well as in hydrostatics and statics, his work and results were not surpassed for over 1500 years!He approximated the area of circles (and the value of ¼) by summing the areas of inscribed and circumscribed rectang les, and generalized this "method of exhaustion," by taking smaller and smaller rectangular areas and summing them, to find the areas and even volumes of several other shapes. This anticipated the results of the calculus of Newton and Leibniz by almost 2000 years!He found the area and tangents to the curve traced by a point moving with uniform speed along a straight line which is revolving with uniform angular speed about a fixed point. This curve, described by r = a in polar coordinates, is now called the "spiral of Archimedes." With calculus it is an easy problem; without calculus it is very difficult.The king of Syracuse once asked Archimedes to find a way of determining if one of his crowns was pure gold without destroying the crown in the process. The crown weighed the correct amount but that was not a guarantee that it was pure gold. Thestory is told that as Archimedes lowered himself into a bath he noticed that some of the water was displaced by his body and flowed over the edge of the tub. This was just the insight he needed to realize that the crown should not only weigh the right amount but should displace the same volume as an equal weight of pure gold. He was so excited by this idea that he reportedly ran naked through the streets shouting "Eureka" ("I have found it")."Give me a place to stand and I will move the earth" was his boast when he discovered the laws of levers and pulleys. Since it was impossible to challenge that statement directly, he was asked to move a ship which had required a large group of laborers to put into position. Archimedes did so easily by using a compound pulley system.During the war between Rome and Carthage, the Roman fleet decided to attack Syracuse, but Archimedes had been at work devising a few surprises. There were catapults with adjustable ranges which could throw objects which weighted over 500 pounds. The ships which survived the catapults were met with poles which reached over the city walls and dropped heavy stones onto the ships. Large grappling hooks attached to levers lifted the ships out of the water and then dropped them. During another failed assault, it is said that Archimedes had the soldiers of Syracuse use specially shaped and shined shields to focus the sunlight onto the sails to set them afire. This was more than the terrified sailors could stand, and the fleet withdrew. Unfortunately, the city began celebrating a bit early, and Marcellus captured Syracuse by attackingfrom the landward side during the celebration. "Archimedes, who was then, as fate would have it, intent upon working out some problem by a diagram, and having fixed his mind alike and his eyes upon the subject of his speculation, he never noticed the incursion of the Romans, nor that the city was taken. In this transport of study and contemplation, a soldier, unexpectedly coming upon him, commanded him to follow to Marcellus, which he declined to do before he had worked out his problem to a demonstration; the soldier, enraged, drew his sword and ran him through." (Plutarch)Archimedes requested that his tombstone be decorated with a sphere contained in the smallest possible cylinder and inscribed with the ratio of the cylinder's volume to that of the sphere. Archimedes considered the discovery of this ratio the greatest of all his accomplishments.Archimedes Discovers the Volume of a SphereArchimedes balanced a cylinder, a sphere, and a cone. All of the following dimensions shown in blue are equal.Archimedes imagined taking a circular slice out of all three solids.He then imagined hanging the cylinder and the sphere from point A and suspending the solids at point F (the fulcrum).By the law of the lever Archimedes showed that2r ⨯ (cone volume + sphere volume) = 4r ⨯ (cylinder volumes)Since cylinder volume = base ⨯ height = πr2⨯2r = 2πr3and cone volume = 1/3base ⨯ height = 1/3[π⨯ (2r)2] ⨯ (2r) = 8/3πr3so sphere volume = 2 cylinder volumes - cone volume = 4/3πr3Problem 1 Can you obtain the volume of a cone by the same argument above?Problem 2 (about π) Among the earliest Chinese circle-squarers mention must be made of Chang Hung in the first place. Chang’s calculation of the circle, however, has been lost, although his value of π is given in commentary on Arithmetic in Nine Sections in the form that the ratio of the square of the circular circumference to that of the perimeter of the circumscribed squareis 5 to 8. This is equivalent to taking π at ____.。

geometry宏包使用说明

geometry宏包使用说明Hideo UmekiReleased by ChinaT E X Documentation Workshop.April30,2011Maker:Ruifeng DuTranslator:Ruifeng Dugeometry宏包使用说明2011年3月21日摘要这个宏包提供了一个能够方便灵活地管理页面规格的接口。

用户能够利用直观的参数来改变页面的布局。

比如说：如果你想让文章边缘和纸张边缘的距离为2厘米，你只需要输入如下命令：\usepackage[margin=2cm]{geometry}。

页面的布局可以利用\newgeometry命令在文章的任意位置来修改。

1第五版前言•能够在文章中改变页面样式这里要利用两个新的命令：\newgeometry{···}和\restoregeometry。

这两个新的命令使得用户能够在文章中改变页面的布局。

\newgeometry这个命令使得在之前声明的所有关于页面布局的选项无效化，并将忽略一切与纸张大小相关的参数，这些参数包括：landscape，portrait和纸张大小的参数（比如说papersize，paper=a4paper等）。

在其他的方面\newgeometry和\geometry命令相同。

•加入了一些新的表示布局区域的参数一些新的参数在计算页面区域和布局的时候可以用到，这些参数有：layout，layoutsize，layoutwidth，layoutheight等等。

这些参数可以帮助我们在不同的纸张大小下打印特定的页面布局。

举例来说，在a4paper和layout=a5paper这两个命令的作用下，geometry宏包会在’A4’的纸张上使用’A5’的布局来计算边界。

•一个新的驱动选项——xetex在第五版中新加入了一个驱动选项xetex。

程序自动检测驱动系统已经做了完善，以避免’undeﬁned control sequences’这种错误。

patran_教程_第2章__几何建模(Geometry)

▲坐标系(Coord)
■坐标系类型
三坐标分量均用1，2，3表示
■坐标系建立
方式 3Point 说明
过三个点，即：原点（origin），3轴方向上某点和1-3平面内一点，建坐标系
输入参数
说明
根据给定矢量平移或拷贝点给定转轴及转角，转动或拷贝点在指定坐标系，放大或收缩点位置根据指定镜面，产生点镜面映射坐标值不变，参考坐标系由1变为2。在将模型装配对准时有用根据三个点所定义的转轴和转角，转动一个点
ห้องสมุดไป่ตู้
注：变换操作对所有几何一样
■硬点、硬线（Associate/Disassociate) 硬点: 指网格划分中必须为有限元结点的几何点
IGES标准可读入，也可输出几何 bdf 文件, Nastran标准输入文件，也可在Menu Bar中Analysis输入可合并Patran数据库,自动处理重复名称、编号可进行参数设置
在Patran读模型时,隐去(Suppress)分析中不必要的CAD细节
3. 创建、编辑几何
Create(创建) Delete(删除) Edit(编辑) Show(显示) Transform(变换) Verify(检验) Associate(相关) Disassociate(删相关) Renumber(重编号)
简单曲线
简单曲线简单曲线简单曲线简单曲线简单曲线
二曲线公切线从点向曲线作切线输入起点，对应矢量，产生线产生渐开线，形成齿廓曲线有用由点，回转轴和转角创建园弧
■线产生方法
平面曲线产生：都须输入“Construction Plane List”，即曲线所在平面
2d Normal 在平面内作一条垂线

geometry 点距离多边形距离

《探究几何：点到多边形的距离》一、引言在我们的日常生活中，几何学是一个不可或缺的学科，它涉及着空间、形状和距离等方面的知识。

而点到多边形的距离作为几何学中的重要概念，更是牵扯着我们对空间关系的理解和抽象能力。

本文将深入探讨点到多边形的距离，旨在帮助读者全面、深刻地理解这一主题。

二、点到多边形的距离概述1. 点到多边形的距离是指空间中一个点到一个多边形的最短距离。

2. 在二维空间中，点到多边形的距离可以通过数学方法进行计算，而在三维空间中，由于多边形的形状复杂，计算点到多边形的距离较为复杂。

3. 点到多边形的距离是几何学中的重要概念，其在实际应用中具有广泛的意义和价值。

三、点到多边形的距离计算方法1. 对于二维平面上的点P和多边形ABCD，点P到多边形ABCD的距离可以通过以下步骤进行计算：（1）将点P与多边形的各边进行垂直延长，得到多个垂直线段。

（2）计算点P到多边形各边的垂直距离，取其中的最小值即为点P 到多边形的最短距离。

2. 如果考虑三维空间中的点到多边形的距离计算，可以通过向量的方法进行求解，涉及到投影和向量运算等内容。

3. 点到多边形的距离计算方法需要根据具体情况做出调整，以确保计算结果准确可靠。

四、点到多边形的距离在实际应用中的意义1. 汽车导航系统中，点到多边形的距离可以帮助确定车辆与道路的关系，从而提供更准确的导航信息。

2. 在地图制作和测量领域，点到多边形的距离可以帮助确定地图上各地点之间的距离关系，为地理信息系统的应用提供基础数据。

3. 在建筑设计和规划领域，点到多边形的距离可以帮助确定建筑物与周围环境的空间关系，为设计和规划提供参考依据。

五、个人观点和理解在我看来，点到多边形的距离是一个十分有趣和实用的概念。

通过深入研究和了解，我们可以更好地理解空间关系，并在实际应用中发挥作用。

点到多边形的距禿计算方法也可以启发我们对几何学和数学的思考，对于培养抽象思维和解决实际问题具有积极的意义。

第2章 patran几何建模(Geometry)

输入参数
说明
根据给定矢量平移或拷贝点给定转轴及转角，转动或拷贝点在指定坐标系，放大或收缩点位置根据指定镜面，产生点镜面映射坐标值不变，参考坐标系由 1变为 2。在将模型装配对准时有用根据三个点所定义的转轴和转角，转动一个点
注：变换操作对所有几何一样
■硬点、硬线（Associate/Disassociate) 硬点: 指网格划分中必须为有限元结点的几何点
打断曲线或边，可通过参数或点来定断开位置
把二条或多条曲线(或边)合并成一条曲线；新曲线一阶导数连续,不会与原曲线一致
把(Chained曲线分解成一组简单曲线延长曲线把多条曲线(边)合成一条;新曲线在指定公差内与原曲线一致将曲线转换成相互连续的分段三次曲线改变曲线参数方向修剪曲线到指定位置
示例
任何几何在Patran中都由Point、Curve、Surface、Solid构成
▲▲点
0 维几何，用X,Y,Z三坐标描述，缺省蓝绿色（cyan）
▲ ▲曲线
Patran中分为：简单曲线（ASM Curve）和复杂曲线（Chained Curve）简单曲线：由两端点P1，P2及参数坐标ξ(0~1)描述。缺省黄色((Yellow) ξ=0 起点参数，ξ=1 终点参数
新曲线在指定公差内与原曲线一致refit将曲线转换成相互连续的分段三次曲线reverse改变曲线参数方向trim修剪曲线到指定位置editcurve示例attribute显示曲线几何类型长度和起始点等arc显示有关圆弧信息angles显示二线间夹角lengthrange显示长度在指定范围的部分特性并求长度和node显示曲线或边上所有硬点showcurve示例面surface面的selectmenu任何面曲面体表面curve过23或4个点产生一次二次或三次曲面composite将多个曲面合并成一大复杂曲面decompose将复杂曲面重构成由三角形四边形曲面组成的简单曲面edge由3条或4条封闭曲线生成三角形或四边形曲面extract提取实体表面或按一定参数提取实体内某一面fillet二个面间产生倒角面match当二面交接处有裂纹时用match消除间隙以保证连接协调ruled二曲线间产生有理面trimmed指定母面上一外边界或一外边界和多条内边界创建trimmedvertex过3或4个顶点创建面或在母面上创建面xyz指定原点及一矢量创建矩形面extrude曲线或边沿指定方向拉伸出一面拉伸时可进行缩放和转动glide基线basecurve沿路径directioncurve滑动形成曲面normal曲线或边沿法向偏置产生曲面revolve曲线绕轴旋转产生曲面面产生法示例editbreak曲面按某方式如曲线参数位置等分割成多个小曲面blend合并多个曲面为一个且边界一阶导数连续disassemble把trimmedsurface打散分解成简单曲面edgematch消除相邻曲面间缝隙使协调一致refit将复杂曲面用简单三次曲面parametriccubes替换新曲面在指定公差内与原始面一致reverse将曲面及其相应单元反向sew自动缝补曲面即自动执行editpointequivalence和editsurfaceedgematch示例surface根据2个3个或4个简单面建1次2次或3次简单实体brep根据一组协调封闭曲面生成brep实体decompose指定实体内一些顶点位置分解实体face指定56个封闭边界面创建简单实体vertex指定顶点建实体xyz根据一矢量原点及一个矢量建长方体extrude将曲面沿矢量方向拉伸成实体注