Javascript 在多段线中查找最靠近板条的点

我有一个多边形，我用从谷歌地图方向服务中获得的拉特尼画的。 现在我想在多段线上找到一个离给定点最近的点

（对我来说）最明显的方法是在多段线中的所有点之间进行某种循环，并找到它们与给定点之间的距离，但是这是低效的，因为多段线上的点可能很大

我很高兴听到有其他办法可以这样做。

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提前谢谢。

我认为你无法避免检查所有要点。 如果未检查的点是最近的点怎么办

如果必须多次执行此操作，则可以选择针对此类搜索进行优化的数据结构，例如四叉树。 请注意，不应使用lat lng作为笛卡尔坐标

另见

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这是针对2D平面的，不是针对lat lng，但您可以近似计算：

参见Bill Chadwick的示例：

（答案底部的代码）

在他的页面上，在下面：

点到多段线或多边形的距离

从该职位：

这里有一个类似的、更好的演示

它是在直线上找到离鼠标最近的点。还请注意，这是一个GoogleMapsAPIv2示例（但v3的原理是相同的）

//查找lat/lng点和lat/lng点多段线之间的距离（以米为单位）的代码
//全部在WGS84中。免费使用。
//
//比尔·查德威克2007
//更新至谷歌地图API v3，Lawrence Ross 2014
//根据bdccGeo的纬度和经度（以度为单位）构建bdccGeo
功能bdccGeo（横向、纵向）
{
varθ=（lon*Math.PI/180.0）；
var rlat=BDCCGeocentriclatide（纬度*Math.PI/180.0）；
var c=数学cos（rlat）；
x=c*Math.cos（θ）；
y=c*Math.sin（θ）；
this.z=Math.sin（rlat）；
}
bdccGeo.prototype=新的bdccGeo（）；
//内部辅助函数=========================================
//从地理纬度转换为地心纬度（弧度）。
功能BDCCGeocentriclatude（地理中心）
{
var展平=1.0/298.257223563；//WGS84
var f=（1.0-展平）*（1.0-展平）；
返回Math.atan（（Math.tan（地理位置）*f））；
}
//返回两个大图的两个对交点
//由圆弧geo1到geo2定义的圆，以及
//geo3至geo4。返回一个点作为地理位置，使用.antipode获取另一个点
功能bdccGeoGetIntersection（geo1、geo2、geo3、geo4）
{
var geoCross1=geo1.crossNormalize（geo2）；
var geoCross2=geo3.crossNormalize（geo4）；
返回geoCross1.crossNormalize（geoCross2）；
}
//从弧度到米
函数BDCCG测地仪（rad）
{
返回rad*6378137.0；//WGS84赤道半径（米）
}
//从米到弧度
函数bdccGeoMetersToRadians（m）
{
返回m/6378137.0；//WGS84赤道半径（米）
}
//性质=================================================
bdccGeo.prototype.getLatitudeRadians=函数（）
{
return（bdccgeographicalClatitude）（Math.atan2（this.z，
sqrt（（this.x*this.x）+（this.y*this.yщщ））；
}
bdccGeo.prototype.getLongitudeRadians=函数（）
{
返回（Math.atan2（this.y，this.x））；
}
bdccGeo.prototype.getLatitude=函数（）
{
返回这个.getLatitudeRadians（）*180.0/Math.PI；
}
bdccGeo.prototype.getLongitude=函数（）
{
返回这个.getLongituderAdans（）*180.0/Math.PI；
}
//方法=================================================
//数学
bdccGeo.prototype.dot=函数（b）
{
返回（（this.x*b.x）+（this.y*b.y）+（this.z*b.z））；
}
//更多的数学
bdccGeo.prototype.crossLength=函数（b）
{
var x=（this.y*b.z）-（this.z*b.y）；
变量y=（this.z*b.x）-（this.x*b.z）；
var z=（this.x*b.y）-（this.y*b.x）；
返回Math.sqrt（（x*x）+（y*y）+（z*z））；
}
//更多的数学
bdccGeo.prototype.scale=功能
{
var r=新的bdccGeo（0,0）；
r、 x=这个.x*s；
r、 y=这个。y*s；
r、 z=这个。z*s；
返回r；
}
//更多的数学
bdccGeo.prototype.crossNormalize=函数（b）
{
var x=（this.y*b.z）-（this.z*b.y）；
变量y=（this.z*b.x）-（this.x*b.z）；
var z=（this.x*b.y）-（this.y*b.x）；
var L=Math.sqrt（（x*x）+（y*y）+（z*z））；
var r=新的bdccGeo（0,0）；
r、 x=x/L；
r、 y=y/L；
r、 z=z/L；
返回r；
}
//在世界的另一边指向这一点
bdccGeo.prototype.antipode=函数（）
{
返回此.scale（-1.0）；
}
//从该点到点v2的距离（弧度）
bdccGeo.prototype.distance=函数（v2）
{
返回Math.atan2（v2.crossLength（this），v2.dot（this））；
}
//返回该点与线段geo1-geo2之间的最小垂直距离（以米为单位）
//从该点到线段的距离以geo1和geo2结束
bdccGeo.prototype.distanceToLineSegMtrs=函数（geo1，geo2）
{            
//位于原点上方且垂直于geo1、geo2平面的单位球体上的点
//可能是飞机的两边
var p2=geo1.交叉规范化（geo2）；
// Code to find the distance in metres between a lat/lng point and a polyline of lat/lng points
// All in WGS84. Free for any use.
//
// Bill Chadwick 2007
// updated to Google Maps API v3, Lawrence Ross 2014

        // Construct a bdccGeo from its latitude and longitude in degrees
        function bdccGeo(lat, lon) 
        {
            var theta = (lon * Math.PI / 180.0);
            var rlat = bdccGeoGeocentricLatitude(lat * Math.PI / 180.0);
            var c = Math.cos(rlat); 
            this.x = c * Math.cos(theta);
            this.y = c * Math.sin(theta);
            this.z = Math.sin(rlat);        
        }
        bdccGeo.prototype = new bdccGeo();

        // internal helper functions =========================================

        // Convert from geographic to geocentric latitude (radians).
        function bdccGeoGeocentricLatitude(geographicLatitude) 
        {
            var flattening = 1.0 / 298.257223563;//WGS84
            var f = (1.0 - flattening) * (1.0 - flattening);
            return Math.atan((Math.tan(geographicLatitude) * f));
        }

         // Returns the two antipodal points of intersection of two great
         // circles defined by the arcs geo1 to geo2 and
         // geo3 to geo4. Returns a point as a Geo, use .antipode to get the other point
        function bdccGeoGetIntersection( geo1,  geo2,  geo3,  geo4) 
        {
            var geoCross1 = geo1.crossNormalize(geo2);
            var geoCross2 = geo3.crossNormalize(geo4);
            return geoCross1.crossNormalize(geoCross2);
        }

        //from Radians to Meters
        function bdccGeoRadiansToMeters(rad)
        {
            return rad * 6378137.0; // WGS84 Equatorial Radius in Meters
        }

        //from Meters to Radians
        function bdccGeoMetersToRadians(m)
        {
            return m / 6378137.0; // WGS84 Equatorial Radius in Meters
        }

        // properties =================================================


        bdccGeo.prototype.getLatitudeRadians = function() 
        {
            return (bdccGeoGeographicLatitude(Math.atan2(this.z,
                Math.sqrt((this.x * this.x) + (this.y * this.y)))));
        }

        bdccGeo.prototype.getLongitudeRadians = function() 
        {
            return (Math.atan2(this.y, this.x));
        }

        bdccGeo.prototype.getLatitude = function() 
        {
            return this.getLatitudeRadians()  * 180.0 / Math.PI;
        }

        bdccGeo.prototype.getLongitude = function() 
        {
            return this.getLongitudeRadians()  * 180.0 / Math.PI ;
        }

        // Methods =================================================

        //Maths
        bdccGeo.prototype.dot = function( b) 
        {
            return ((this.x * b.x) + (this.y * b.y) + (this.z * b.z));
        }

        //More Maths
        bdccGeo.prototype.crossLength = function( b) 
        {
            var x = (this.y * b.z) - (this.z * b.y);
            var y = (this.z * b.x) - (this.x * b.z);
            var z = (this.x * b.y) - (this.y * b.x);
            return Math.sqrt((x * x) + (y * y) + (z * z));
        }

      //More Maths
        bdccGeo.prototype.scale = function( s) 
        {
            var r = new bdccGeo(0,0);
            r.x = this.x * s;
            r.y = this.y * s;
            r.z = this.z * s;
            return r;
        }

        // More Maths
        bdccGeo.prototype.crossNormalize = function( b) 
        {
            var x = (this.y * b.z) - (this.z * b.y);
            var y = (this.z * b.x) - (this.x * b.z);
            var z = (this.x * b.y) - (this.y * b.x);
            var L = Math.sqrt((x * x) + (y * y) + (z * z));
            var r = new bdccGeo(0,0);
            r.x = x / L;
            r.y = y / L;
            r.z = z / L;
            return r;
        }

      // point on opposite side of the world to this point
        bdccGeo.prototype.antipode = function() 
        {
            return this.scale(-1.0);
        }






        //distance in radians from this point to point v2
        bdccGeo.prototype.distance = function( v2) 
        {
            return Math.atan2(v2.crossLength(this), v2.dot(this));
        }

      //returns in meters the minimum of the perpendicular distance of this point from the line segment geo1-geo2
      //and the distance from this point to the line segment ends in geo1 and geo2 
        bdccGeo.prototype.distanceToLineSegMtrs = function(geo1, geo2)
        {            

            //point on unit sphere above origin and normal to plane of geo1,geo2
            //could be either side of the plane
            var p2 = geo1.crossNormalize(geo2); 

            // intersection of GC normal to geo1/geo2 passing through p with GC geo1/geo2
            var ip = bdccGeoGetIntersection(geo1,geo2,this,p2); 

            //need to check that ip or its antipode is between p1 and p2
            var d = geo1.distance(geo2);
            var d1p = geo1.distance(ip);
            var d2p = geo2.distance(ip);
            //window.status = d + ", " + d1p + ", " + d2p;
            if ((d >= d1p) && (d >= d2p)) 
                return bdccGeoRadiansToMeters(this.distance(ip));
            else
            {
                ip = ip.antipode(); 
                d1p = geo1.distance(ip);
                d2p = geo2.distance(ip);
            }
            if ((d >= d1p) && (d >= d2p)) 
                return bdccGeoRadiansToMeters(this.distance(ip)); 
            else 
                return bdccGeoRadiansToMeters(Math.min(geo1.distance(this),geo2.distance(this))); 
        }

        // distance in meters from GLatLng point to GPolyline or GPolygon poly
        function bdccGeoDistanceToPolyMtrs(poly, point)
        {
            var d = 999999999;
            var i;
            var p = new bdccGeo(point.lat(),point.lng());
            for(i=0; i<(poly.getPath().getLength()-1); i++)
                 {
                    var p1 = poly.getPath().getAt(i);
                    var l1 = new bdccGeo(p1.lat(),p1.lng());
                    var p2 = poly.getPath().getAt(i+1);
                    var l2 = new bdccGeo(p2.lat(),p2.lng());
                    var dp = p.distanceToLineSegMtrs(l1,l2);
                    if(dp < d)
                        d = dp;    
                 }
             return d;
        }

        // get a new GLatLng distanceMeters away on the compass bearing azimuthDegrees
        // from the GLatLng point - accurate to better than 200m in 140km (20m in 14km) in the UK

        function bdccGeoPointAtRangeAndBearing (point, distanceMeters, azimuthDegrees) 
        {
             var latr = point.lat() * Math.PI / 180.0;
             var lonr = point.lng() * Math.PI / 180.0;

             var coslat = Math.cos(latr); 
             var sinlat = Math.sin(latr); 
             var az = azimuthDegrees* Math.PI / 180.0;
             var cosaz = Math.cos(az); 
             var sinaz = Math.sin(az); 
             var dr = distanceMeters / 6378137.0; // distance in radians using WGS84 Equatorial Radius
             var sind = Math.sin(dr); 
             var cosd = Math.cos(dr);

            return new google.maps.LatLng(Math.asin((sinlat * cosd) + (coslat * sind * cosaz)) * 180.0 / Math.PI,
            (Math.atan2((sind * sinaz), (coslat * cosd) - (sinlat * sind * cosaz)) + lonr) * 180.0 / Math.PI); 
        }

function closest(llng, listData) {
    var arr     = listData;
    var pnt     = llng;
    var distArr = [];
    var dist    = google.maps.geometry.spherical.computeDistanceBetween;


    for (index in arr)
        distArr.push([arr[index], dist(pnt, arr[index])]);

    return distArr.sort(function(a,b){
        return a[1]-b[1];
    })[0][0];
}

/**
*   Snap marker to closest point on a line.
*
*   Based on Distance to line example by 
*   Marcelo, maps.forum.nu - http://maps.forum.nu/gm_mouse_dist_to_line.html 
*   Then 
*   @ work of Björn Brala - Swis BV who wrapped the algorithm in a class operating on GMap Objects
*   And now 
*   Bill Chadwick, who factored the basic algorithm out of the class (removing much intermediate storage of results)
*       and added distance along line to nearest point calculation
*   Followed by
*   Robert Crowe, who ported it to v3 of the Google Maps API and factored out the marker to make it more general.
*
*   Usage:
*
*   Create the class
*       var oSnap = new cSnapToRoute();
*
*   Initialize the subjects
*       oSnap.init(oMap, oPolyline);
*
**/

function cSnapToRoute() {

    this.routePoints = Array();
    this.routePixels = Array();
    this._oMap;
    this._oPolyline;

    /**
    *   @desc Initialize the objects.
    *   @param Map object
    *   @param GPolyline object - the 'route'
    **/
    this.init = function (oMap, oPolyline) {
        this._oMap = oMap;
        this._oPolyline = oPolyline;

        this.loadRouteData();   // Load needed data for point calculations
    }

    /**
    *   @desc internal use only, Load route points into RoutePixel array for calculations, do this whenever zoom changes 
    **/
    this.loadRouteData = function () {
        this.routePixels = new Array();
        var proj = this._oMap.getProjection();
        for (var i = 0; i < this._oPolyline.getPath().getLength(); i++) {
            var Px = proj.fromLatLngToPoint(this._oPolyline.getPath().getAt(i));
            this.routePixels.push(Px);
        }
    }

    /**
    *   @desc Get closest point on route to test point
    *   @param GLatLng() the test point
    *   @return new GLatLng();
    **/
    this.getClosestLatLng = function (latlng) {
        var r = this.distanceToLines(latlng);
        var proj = this._oMap.getProjection();
        return proj.fromPointToLatLng(new google.maps.Point(r.x, r.y));
    }

    /**
    *   @desc Get distance along route in meters of closest point on route to test point
    *   @param GLatLng() the test point
    *   @return distance in meters;
    **/
    this.getDistAlongRoute = function (latlng) {
        var r = this.distanceToLines(latlng);
        return this.getDistToLine(r.i, r.fTo);
    }

    /**
    *   @desc internal use only, gets test point xy and then calls fundamental algorithm
    **/
    this.distanceToLines = function (thisLatLng) {
        var tm = this._oMap;
        var proj = this._oMap.getProjection();
        var thisPx = proj.fromLatLngToPoint(thisLatLng);
        var routePixels = this.routePixels;
        return getClosestPointOnLines(thisPx, routePixels);
    }

    /**
    *   @desc internal use only, find distance along route to point nearest test point
    **/
    this.getDistToLine = function (iLine, fTo) {

        var routeOverlay = this._oPolyline;
        var d = 0;
        for (var n = 1 ; n < iLine ; n++) {
            d += routeOverlay.getPath().getAt(n - 1).distanceFrom(routeOverlay.getPath().getAt(n));
        }
        d += routeOverlay.getPath().getAt(iLine - 1).distanceFrom(routeOverlay.getPath().getAt(iLine)) * fTo;

        return d;
    }


}

/* desc Static function. Find point on lines nearest test point
   test point pXy with properties .x and .y
   lines defined by array aXys with nodes having properties .x and .y 
   return is object with .x and .y properties and property i indicating nearest segment in aXys 
   and property fFrom the fractional distance of the returned point from aXy[i-1]
   and property fTo the fractional distance of the returned point from aXy[i]   */


function getClosestPointOnLines(pXy, aXys) {

    var minDist;
    var fTo;
    var fFrom;
    var x;
    var y;
    var i;
    var dist;

    if (aXys.length > 1) {

        for (var n = 1 ; n < aXys.length ; n++) {

            if (aXys[n].x != aXys[n - 1].x) {
                var a = (aXys[n].y - aXys[n - 1].y) / (aXys[n].x - aXys[n - 1].x);
                var b = aXys[n].y - a * aXys[n].x;
                dist = Math.abs(a * pXy.x + b - pXy.y) / Math.sqrt(a * a + 1);
            }
            else
                dist = Math.abs(pXy.x - aXys[n].x)

            // length^2 of line segment 
            var rl2 = Math.pow(aXys[n].y - aXys[n - 1].y, 2) + Math.pow(aXys[n].x - aXys[n - 1].x, 2);

            // distance^2 of pt to end line segment
            var ln2 = Math.pow(aXys[n].y - pXy.y, 2) + Math.pow(aXys[n].x - pXy.x, 2);

            // distance^2 of pt to begin line segment
            var lnm12 = Math.pow(aXys[n - 1].y - pXy.y, 2) + Math.pow(aXys[n - 1].x - pXy.x, 2);

            // minimum distance^2 of pt to infinite line
            var dist2 = Math.pow(dist, 2);

            // calculated length^2 of line segment
            var calcrl2 = ln2 - dist2 + lnm12 - dist2;

            // redefine minimum distance to line segment (not infinite line) if necessary
            if (calcrl2 > rl2)
                dist = Math.sqrt(Math.min(ln2, lnm12));

            if ((minDist == null) || (minDist > dist)) {
                if (calcrl2 > rl2) {
                    if (lnm12 < ln2) {
                        fTo = 0;//nearer to previous point
                        fFrom = 1;
                    }
                    else {
                        fFrom = 0;//nearer to current point
                        fTo = 1;
                    }
                }
                else {
                    // perpendicular from point intersects line segment
                    fTo = ((Math.sqrt(lnm12 - dist2)) / Math.sqrt(rl2));
                    fFrom = ((Math.sqrt(ln2 - dist2)) / Math.sqrt(rl2));
                }
                minDist = dist;
                i = n;
            }
        }

        var dx = aXys[i - 1].x - aXys[i].x;
        var dy = aXys[i - 1].y - aXys[i].y;

        x = aXys[i - 1].x - (dx * fTo);
        y = aXys[i - 1].y - (dy * fTo);

    }

    return { 'x': x, 'y': y, 'i': i, 'fTo': fTo, 'fFrom': fFrom };
}