在JavaScript中查找多边形的中心点

Question

我有一个来自谷歌地图的"地方"对象,它有一组坐标,代表一个给定位置的边界框,比如伦敦.每组坐标都有纬度和经度.

我写了下面的代码来找到中心点,但我不确定它是否确实产生了中心点.如果多边形有5个点而不是4个怎么办？此外,这可以通过更少的操作以更有效的方式完成吗？

function average(array) {
  // Add together and then divide by the length
  return _.reduce(array, function (sum, num) {
    return sum + num;
  }, 0) / array.length;
}

// I have a two-dimensional array that I want to get the average of

var coords = [
  [ -1.2, 5.1 ],
  [ -1.3, 5.2 ],
  [ -1.8, 5.9 ],
  [ -1.9, 5.8 ]
]

// So I get the first column

var lats = coords.map(function (coord) {
  return coord[0];
})

// Then the second

var longs = coords.map(function (coord) {
  return coord[1];
})

// And average each column out

console.log([average(lats), average(longs)])

例子.

Answer 1

这应该得到质心的的区域任意多边形

/*jslint sub: true, maxerr: 50, indent: 4, browser: true */
/*global console */

(function () {
    "use strict";

    function Point(x, y) {
        this.x = x;
        this.y = y;
    }

    function Region(points) {
        this.points = points || [];
        this.length = points.length;
    }

    Region.prototype.area = function () {
        var area = 0,
            i,
            j,
            point1,
            point2;

        for (i = 0, j = this.length - 1; i < this.length; j=i,i++) {
            point1 = this.points[i];
            point2 = this.points[j];
            area += point1.x * point2.y;
            area -= point1.y * point2.x;
        }
        area /= 2;

        return area;
    };

    Region.prototype.centroid = function () {
        var x = 0,
            y = 0,
            i,
            j,
            f,
            point1,
            point2;

        for (i = 0, j = this.length - 1; i < this.length; j=i,i++) {
            point1 = this.points[i];
            point2 = this.points[j];
            f = point1.x * point2.y - point2.x * point1.y;
            x += (point1.x + point2.x) * f;
            y += (point1.y + point2.y) * f;
        }

        f = this.area() * 6;

        return new Point(x / f, y / f);
    };

    var polygon = [
            {"x": -1.2, "y": 5.1},
            {"x": -1.3, "y": 5.2},
            {"x": -1.8, "y": 5.9},
            {"x": -1.9, "y": 5.8}
        ],
        region = new Region(polygon);

    console.log(region.centroid());
}());

在jsfiddle

Answer 2

这将获得任何形状的中心点和数组[centerX,centerY]:

var center = function (arr)
{
    var minX, maxX, minY, maxY;
    for (var i = 0; i < arr.length; i++)
    {
        minX = (arr[i][0] < minX || minX == null) ? arr[i][0] : minX;
        maxX = (arr[i][0] > maxX || maxX == null) ? arr[i][0] : maxX;
        minY = (arr[i][1] < minY || minY == null) ? arr[i][1] : minY;
        maxY = (arr[i][1] > maxY || maxY == null) ? arr[i][1] : maxY;
    }
    return [(minX + maxX) / 2, (minY + maxY) / 2];
}

其他方式:

var center = function (arr)
{
    var x = arr.map (function (a){ return a[0] });
    var y = arr.map (function (a){ return a[1] });
    var minX = Math.min.apply (null, x);
    var maxX = Math.max.apply (null, x);
    var minY = Math.min.apply (null, y);
    var maxY = Math.max.apply (null, y);
    return [(minX + maxX) / 2, (minY + maxY) / 2];
}
getCenter (coords);

或者,如果您的浏览器支持ECMAScript 6,那么您可以使用箭头函数和Spread语法,如下所示:

var center = function (arr)
{
    var x = arr.map (x => x[0]);
    var y = arr.map (x => x[1]);
    var cx = (Math.min (...x) + Math.max (...x)) / 2;
    var cy = (Math.min (...y) + Math.max (...y)) / 2;
    return [cx, cy];
}

的jsfiddle

Answer 3

要在 Google Maps API v3（未测试）中获取多边形的边界（使用您的数据）：

var coords = [
  [ -1.2, 5.1 ],
  [ -1.3, 5.2 ],
  [ -1.8, 5.9 ],
  [ -1.9, 5.8 ]
];

var bounds = new google.maps.LatLngBounds();
for (var i = 0; i<coords.length; i++) {
   bounds.extend(new google.maps.LatLng(coords[i][0], coords[i][1]));
}
var center = bounds.getCenter();

var latitude = center.lat();           // latitude=-1.5499999999999998
var longitude = center.lng();          // longitude=5.5
var coordinates = center.toUrlValue(); // coordinates=-1.55,5.5

var coords = [
  [ -1.2, 5.1 ],
  [ -1.3, 5.2 ],
  [ -1.8, 5.9 ],
  [ -1.9, 5.8 ]
];

var bounds = new google.maps.LatLngBounds();
for (var i = 0; i<coords.length; i++) {
   bounds.extend(new google.maps.LatLng(coords[i][0], coords[i][1]));
}
var center = bounds.getCenter();

var latitude = center.lat();           // latitude=-1.5499999999999998
var longitude = center.lng();          // longitude=5.5
var coordinates = center.toUrlValue(); // coordinates=-1.55,5.5

var coords = [
  [-1.2, 5.1],
  [-1.3, 5.2],
  [-1.8, 5.9],
  [-1.9, 5.8]
];

var bounds = new google.maps.LatLngBounds();
for (var i = 0; i < coords.length; i++) {
  bounds.extend(new google.maps.LatLng(coords[i][0], coords[i][1]));
}
var center = bounds.getCenter();

var latitude = center.lat();
console.log("latitude=" + latitude);
var longitude = center.lng();
console.log("longitude=" + longitude);
var coordinates = center.toUrlValue();
console.log("coordinates=" + coordinates);

Answer 4

这是我的 es6 解决方案，用于平均纬度和经度数组。平均值并不是确切的中心点，但在我的例子中它可以完成工作。

getLatLonCenterFromGeom = (coords) => {
    const arrAvg = arr => arr.reduce((a,b) => a + b, 0) / arr.length;

    const centerLat = arrAvg(coords.map(c=>c.latitude));
    const centerLon = arrAvg(coords.map(c=>c.longitude));

    if (isNaN(centerLat)|| isNaN(centerLon))
        return null;
    else return {latitude: centerLat, longitude:centerLon};
}