空间索引（Spatial Indexing）
回忆下数据库最基本的操作：增删改查以及稍复杂些的比如连接操作，基本都需要先锁定数据位置，再执行操作。而定位这个步骤，如果没有index，基本都是O(n)的时间复杂度，这是一个非常“耗时”的操作。“找”这个操作就需要定位。注意这里的定位不再是指在存储器上的位置，而是在空间中的位置，这里的空间，是由数据的维度张成的空间。空间数据，也即是这些拥有多维度的数据。这是空间数据的一个比较延展性的说法。但通常，空间数据都focus on 几何类型数据，比如点，线，面，球等，当然这些点、线都是可以任意维度的。对于空间数据的搜索，我们需要空间索引spatial index来提升搜素效率（速度）。目前主流数据（SQL server,MySQL,PostgreSQL,etc）都已加入了对spatial data的支持，这其中最主要的就是数据类型和索引的支持。
R-tree
MBR
为了统一描述空间类型，比如点，线，面等，Guttman首先提出了MBR的概念，即Minimum Bounding Box。MBR的含义是用一个最小的矩形（通常默认矩形的边平行于坐标轴），来框住这个几何体。
MBR
R-tree
R-tree主要吸纳了B+tree的思想，对数据进行分割。
R-tree
JTS生成R树索引
JTS提供了如下的空间数据类型，还提供了读取各种空间描述文件（WTK等），线简化，空间操作（求交，计算距离，计算外包矩形等），建立空间索引等多种算法。
参考这篇文章：https://blog.csdn.net/wk1134314305/article/details/76408181
引入依赖包：
// Gradle
compile group: 'com.vividsolutions', name: 'jts', version: '1.13'
// Maven
com.vividsolutions
jts
1.13
Geometry类：所有的空间数据类型，点，线，面，多点，环，多边形等等都是继承自Geometry类的。
Envelope类：该类就是描述一个空间几何对象的外包矩形，由max_x,max_y,min_x,min_y组成。
JTS常用的方法，以及R树索引基本使用：
package com.geotools.geotoolsdemo;
import com.vividsolutions.jts.geom.*;
import com.vividsolutions.jts.io.ParseException;
import com.vividsolutions.jts.io.WKTReader;
import org.springframework.beans.factory.annotation.Autowired;
import org.springframework.stereotype.Component;
/**
* @program: geotoolsdemo
* @description: JTS导入使用
* @author: zhudan
* @create: 2020/7/3 11:39
*/
@Component
public class GeometryDemo {
//使用JTS的GeometryFactory来创建Geometry对象
@Autowired
private GeometryFactory geometryFactory = new GeometryFactory();
/**
* @Description: 创建一个点
* @return: com.vividsolutions.jts.geom.Point
*/
public Point createPoint() {
Coordinate coord = new Coordinate(118.798128, 31.968592);
Point point = geometryFactory.createPoint(coord);
return point;
}
/**
* @Description: 从WKT创建一个点，WKT字符串创建 ，WKT字符串是SQL标准定义的一个实现
* @return: com.vividsolutions.jts.geom.Point
*/
public Point createPointByWKT() throws ParseException {
WKTReader reader = new WKTReader(geometryFactory);
Point point = (Point) reader.read("POINT (118.798128 31.968592)");
return point;
}
/**
* @Description: 从WKT创建多个点
* @return: com.vividsolutions.jts.geom.MultiPoint
*/
@Autowired
public MultiPoint createMulPointByWKT(String wellKnownText) throws ParseException {
WKTReader reader = new WKTReader(geometryFactory);
// MultiPoint mpoint = (MultiPoint) reader.read("MULTIPOINT(119.013388 31.715519, 119.32488 31.435678)");
MultiPoint mpoint = (MultiPoint) reader.read(wellKnownText);
return mpoint;
}
/**
* @Description: create a line
* @return: com.vividsolutions.jts.geom.LineString
*/
public LineString createLine() {
Coordinate[] coords = new Coordinate[]{new Coordinate(119.013388, 31.715519), new Coordinate(119.32488, 31.435678)};
LineString line = geometryFactory.createLineString(coords);
return line;
}
/**
* @Description: create a line by WKT
* @return: com.vividsolutions.jts.geom.LineString
*/
public LineString createLineByWKT() throws ParseException {
WKTReader reader = new WKTReader(geometryFactory);
LineString line = (LineString) reader.read("LINESTRING(119.013388 31.715519, 119.32488 31.435678)");
return line;
}
/**
* @Description: create multiLine
* @return: com.vividsolutions.jts.geom.MultiLineString
*/
public MultiLineString createMLine() {
Coordinate[] coords1 = new Coordinate[]{new Coordinate(119.013388, 31.715519), new Coordinate(119.32488, 31.435678)};
LineString line1 = geometryFactory.createLineString(coords1);
Coordinate[] coords2 = new Coordinate[]{new Coordinate(118.797499, 32.087104), new Coordinate(118.798128, 31.968592)};
LineString line2 = geometryFactory.createLineString(coords2);
LineString[] lineStrings = new LineString[2];
lineStrings[0] = line1;
lineStrings[1] = line2;
MultiLineString ms = geometryFactory.createMultiLineString(lineStrings);
return ms;
}
/**
* @Description: create multiLine by WKT
* @return: com.vividsolutions.jts.geom.MultiLineString
*/
public MultiLineString createMLineByWKT() throws ParseException {
WKTReader reader = new WKTReader(geometryFactory);
MultiLineString line = (MultiLineString) reader.read("MULTILINESTRING((119.013388 31.715519, 119.32488 31.435678),(118.797499 32.087104,118.798128 31.968592))");
return line;
}
/**
* @Description: create a polygon(多边形)
* @return:
*/
public Polygon createPolygon() {
Coordinate[] coords = new Coordinate[]{new Coordinate(20, 10), new Coordinate(30, 0), new Coordinate(40, 10),
new Coordinate(30, 20), new Coordinate(20, 10)};
Polygon polygon = geometryFactory.createPolygon(coords);
return polygon;
}
/**
* @Description: create a polygon(多边形) by WKT
* @return:
*/
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;
}
/**
* @Description: create multi polygon(多边形) by WKT
* @return:
*/
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;
}
/**
* @Description: create GeometryCollection contain point or multiPoint or line or multiLine or polygon or multiPolygon
* @return: com.vividsolutions.jts.geom.GeometryCollection
*/
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 p1 = gt.createCircle(0, 1, 2);
//圆上所有的坐标(32个)
// Coordinate coords[] = p1.getCoordinates();
// for (Coordinate coord : coords) {
// System.out.println(coord.x + "," + coord.y);
// }
Polygon p2 = gt.createCircle(1, 0, 2);
STRtree stRtree = new STRtree();
stRtree.insert(p1.getEnvelopeInternal(), p1);
stRtree.insert(p2.getEnvelopeInternal(), p2);
List results = stRtree.query(new Envelope(0, 0, 0, 0));
for (int i = 0; i < results.size(); i++) {
System.out.println(results.get(i));
}
}
}
参考：
https://zhuanlan.zhihu.com/p/38597148
https://blog.csdn.net/wk1134314305/article/details/76408181