GIS算法總結（求經緯度，求距離，求方位角）

公司項目中用到的一些GIS算法，記錄一下。所有經緯度都是基於WGS-84標準，爲Google Earth上的經緯度。
1.已知兩個點的經緯度，求它們的直線距離

python代碼實現

from math import *
def getDistance(latA, lonA, latB, lonB):
    ra = 6378140  # radius of equator: meter
    rb = 6356755  # radius of polar: meter
    flatten = (ra - rb) / ra  # Partial rate of the earth
    # change angle to radians
    radLatA = radians(latA)
    radLonA = radians(lonA)
    radLatB = radians(latB)
    radLonB = radians(lonB)
 
    pA = atan(rb / ra * tan(radLatA))
    pB = atan(rb / ra * tan(radLatB))
    x = acos(sin(pA) * sin(pB) + cos(pA) * cos(pB) * cos(radLonA - radLonB))
    c1 = (sin(x) - x) * (sin(pA) + sin(pB))**2 / cos(x / 2)**2
    c2 = (sin(x) + x) * (sin(pA) - sin(pB))**2 / sin(x / 2)**2
    dr = flatten / 8 * (c1 - c2)
    distance = ra * (x + dr)
    return distance
    
distance = getDistance(30.25482684590,120.01375138640,30.25582684590,120.01375138640)
print(distance, '米')

2.已知兩個點的經緯度，求它們的方位角

python代碼實現

def getDegree(latA, lonA, latB, lonB):
    """
    Args:
        point p1(latA, lonA)
        point p2(latB, lonB)
    Returns:
        bearing between the two GPS points,
        default: the basis of heading direction is north
    """
    radLatA = radians(latA)
    radLonA = radians(lonA)
    radLatB = radians(latB)
    radLonB = radians(lonB)
    dLon = radLonB - radLonA
    y = sin(dLon) * cos(radLatB)
    x = cos(radLatA) * sin(radLatB) - sin(radLatA) * cos(radLatB) * cos(dLon)
    brng = degrees(atan2(y, x))
    brng = (brng + 360) % 360
    return brng
    
brng = getDegree(30.25482684590,120.01375138640,30.25582684590,120.01375138640)
print(brng)

3.已知一個點的經緯度，方位角，距離，求另一點的經緯度

python代碼實現

from math import *


def rad(d):
    return d * pi / 180.0


def deg(x):
    return x * 180 / pi


def getLonAndLat(lat, lng, brng, dist):
    a = 6378137
    b = 6356752.3142
    f = 1.0 / 298.257223563

    lon1 = lng * 1
    lat1 = lat * 1
    s = dist
    alpha1 = rad(brng)
    sinAlpha1 = sin(alpha1)
    cosAlpha1 = cos(alpha1)

    tanU1 = (1 - f) * tan(rad(lat1))
    cosU1 = 1 / sqrt((1 + tanU1 * tanU1))
    sinU1 = tanU1 * cosU1
    sigma1 = atan2(tanU1, cosAlpha1)
    sinAlpha = cosU1 * sinAlpha1
    cosSqAlpha = 1 - sinAlpha * sinAlpha
    uSq = cosSqAlpha * (a * a - b * b) / (b * b)
    A = 1 + uSq / 16384 * (4096 + uSq * (-768 + uSq * (320 - 175 * uSq)))
    B = uSq / 1024 * (256 + uSq * (-128 + uSq * (74 - 47 * uSq)))

    sigma = s / (b * A)
    sigmaP = 2 * pi
    while abs(sigma - sigmaP) > 1e-12:
        cos2SigmaM = cos(2 * sigma1 + sigma)
        sinSigma = sin(sigma)
        cosSigma = cos(sigma)
        deltaSigma = B * sinSigma * (cos2SigmaM + B / 4 * (cosSigma * (-1 + 2 * cos2SigmaM * cos2SigmaM) -
                                                           B / 6 * cos2SigmaM * (-3 + 4 * sinSigma * sinSigma) * (
                                                                   -3 + 4 * cos2SigmaM * cos2SigmaM)))
        sigmaP = sigma
        sigma = s / (b * A) + deltaSigma

    tmp = sinU1 * sinSigma - cosU1 * cosSigma * cosAlpha1
    lat2 = atan2(sinU1 * cosSigma + cosU1 * sinSigma * cosAlpha1,
                 (1 - f) * sqrt(sinAlpha * sinAlpha + tmp * tmp))
    lambdA = atan2(sinSigma * sinAlpha1, cosU1*cosSigma - sinU1 * sinSigma * cosAlpha1)
    C = f / 16 * cosSqAlpha * (4 + f * (4 - 3 * cosSqAlpha))
    L = lambdA - (1-C) * f * sinAlpha * (sigma + C * sinSigma * (cos2SigmaM+C * cosSigma * (-1+2 * cos2SigmaM * cos2SigmaM)))
    revAz = atan2(sinAlpha, -tmp)
    lngLatObj = {'latitude': deg(lat2), 'longitude': lon1 + deg(L), }
    return lngLatObj


print(getLonAndLat(30.2548268459,120.0137513864,0,110.85670061685299))

JavaScript代碼實現

            /**
             * 度換成弧度
             * @param  {Float} d  度
             * @return {[Float}   弧度
             */
            function rad (d){
                return d * Math.PI / 180.0;
            };
            /**
             * 弧度換成度
             * @param  {Float} x 弧度
             * @return {Float}   度
             */
            function deg (x){
                return x*180/Math.PI;
            };
            /**
             * 
             * @param {*} lng 經度 113.3960698
             * @param {*} lat 緯度 22.941386
             * @param {*} brng 方位角 45   ---- 正北方：000°或360°  正東方：090° 正南方：180°  正西方：270°
             * @param {*} dist 距離 9000
             * 
            */
            function getLonAndLat (lat,lng,brng,dist){
                //大地座標系資料WGS-84 長半徑a=6378137 短半徑b=6356752.3142 扁率f=1/298.2572236
                var a=6378137; 
                var b=6356752.3142; 
                var f=1/298.257223563;

                var lon1 = lng*1;
                var lat1 = lat*1;
                var s = dist;
                var alpha1 = rad(brng);
                var sinAlpha1 = Math.sin(alpha1);
                var cosAlpha1 = Math.cos(alpha1);

                var tanU1 = (1-f) * Math.tan(rad(lat1));
                var cosU1 = 1 / Math.sqrt((1 + tanU1*tanU1)), sinU1 = tanU1*cosU1;
                var sigma1 = Math.atan2(tanU1, cosAlpha1);
                var sinAlpha = cosU1 * sinAlpha1;
                var cosSqAlpha = 1 - sinAlpha*sinAlpha;
                var uSq = cosSqAlpha * (a*a - b*b) / (b*b);
                var A = 1 + uSq/16384*(4096+uSq*(-768+uSq*(320-175*uSq)));
                var B = uSq/1024 * (256+uSq*(-128+uSq*(74-47*uSq)));

                var sigma = s / (b*A), sigmaP = 2*Math.PI;
                while (Math.abs(sigma-sigmaP) > 1e-12) {
                    var cos2SigmaM = Math.cos(2*sigma1 + sigma);
                    var sinSigma = Math.sin(sigma);
                    var cosSigma = Math.cos(sigma);
                    var deltaSigma = B*sinSigma*(cos2SigmaM+B/4*(cosSigma*(-1+2*cos2SigmaM*cos2SigmaM)-
                        B/6*cos2SigmaM*(-3+4*sinSigma*sinSigma)*(-3+4*cos2SigmaM*cos2SigmaM)));
                    sigmaP = sigma;
                    sigma = s / (b*A) + deltaSigma;
                }

                var tmp = sinU1*sinSigma - cosU1*cosSigma*cosAlpha1;
                var lat2 = Math.atan2(sinU1*cosSigma + cosU1*sinSigma*cosAlpha1,
                    (1-f)*Math.sqrt(sinAlpha*sinAlpha + tmp*tmp));
                var lambda = Math.atan2(sinSigma*sinAlpha1, cosU1*cosSigma - sinU1*sinSigma*cosAlpha1);
                var C = f/16*cosSqAlpha*(4+f*(4-3*cosSqAlpha));
                var L = lambda - (1-C) * f * sinAlpha *
                    (sigma + C*sinSigma*(cos2SigmaM+C*cosSigma*(-1+2*cos2SigmaM*cos2SigmaM)));

                var revAz = Math.atan2(sinAlpha, -tmp);  // final bearing
                
                var lngLatObj = {latitude:deg(lat2),longitude:lon1+deg(L),}
                return lngLatObj;
            }
            //調用
            console.log(getLonAndLat(30.2548268459,120.0137513864,0,110.85670061685299));