如何通过两个位置的纬度和经度来计算它们之间的距离?

25

我有一组地点的纬度和经度。

  • 如何找到从该组中一个位置到另一个位置的距离
  • 是否有公式?
12个回答

0
在这个页面上,您可以看到整个代码和公式,了解Android Location类中如何计算位置距离的方法。

android/location/Location.java

编辑: 根据 @Richard 的提示,我将链接函数的代码放入了我的答案中,以避免链接失效:

private static void computeDistanceAndBearing(double lat1, double lon1,
    double lat2, double lon2, BearingDistanceCache results) {
    // Based on http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf
    // using the "Inverse Formula" (section 4)
    int MAXITERS = 20;
    // Convert lat/long to radians
    lat1 *= Math.PI / 180.0;
    lat2 *= Math.PI / 180.0;
    lon1 *= Math.PI / 180.0;
    lon2 *= Math.PI / 180.0;
    double a = 6378137.0; // WGS84 major axis
    double b = 6356752.3142; // WGS84 semi-major axis
    double f = (a - b) / a;
    double aSqMinusBSqOverBSq = (a * a - b * b) / (b * b);
    double L = lon2 - lon1;
    double A = 0.0;
    double U1 = Math.atan((1.0 - f) * Math.tan(lat1));
    double U2 = Math.atan((1.0 - f) * Math.tan(lat2));
    double cosU1 = Math.cos(U1);
    double cosU2 = Math.cos(U2);
    double sinU1 = Math.sin(U1);
    double sinU2 = Math.sin(U2);
    double cosU1cosU2 = cosU1 * cosU2;
    double sinU1sinU2 = sinU1 * sinU2;
    double sigma = 0.0;
    double deltaSigma = 0.0;
    double cosSqAlpha = 0.0;
    double cos2SM = 0.0;
    double cosSigma = 0.0;
    double sinSigma = 0.0;
    double cosLambda = 0.0;
    double sinLambda = 0.0;
    double lambda = L; // initial guess
    for (int iter = 0; iter < MAXITERS; iter++) {
        double lambdaOrig = lambda;
        cosLambda = Math.cos(lambda);
        sinLambda = Math.sin(lambda);
        double t1 = cosU2 * sinLambda;
        double t2 = cosU1 * sinU2 - sinU1 * cosU2 * cosLambda;
        double sinSqSigma = t1 * t1 + t2 * t2; // (14)
        sinSigma = Math.sqrt(sinSqSigma);
        cosSigma = sinU1sinU2 + cosU1cosU2 * cosLambda; // (15)
        sigma = Math.atan2(sinSigma, cosSigma); // (16)
        double sinAlpha = (sinSigma == 0) ? 0.0 :
            cosU1cosU2 * sinLambda / sinSigma; // (17)
        cosSqAlpha = 1.0 - sinAlpha * sinAlpha;
        cos2SM = (cosSqAlpha == 0) ? 0.0 :
            cosSigma - 2.0 * sinU1sinU2 / cosSqAlpha; // (18)
        double uSquared = cosSqAlpha * aSqMinusBSqOverBSq; // defn
        A = 1 + (uSquared / 16384.0) * // (3)
            (4096.0 + uSquared *
             (-768 + uSquared * (320.0 - 175.0 * uSquared)));
        double B = (uSquared / 1024.0) * // (4)
            (256.0 + uSquared *
             (-128.0 + uSquared * (74.0 - 47.0 * uSquared)));
        double C = (f / 16.0) *
            cosSqAlpha *
            (4.0 + f * (4.0 - 3.0 * cosSqAlpha)); // (10)
        double cos2SMSq = cos2SM * cos2SM;
        deltaSigma = B * sinSigma * // (6)
            (cos2SM + (B / 4.0) *
             (cosSigma * (-1.0 + 2.0 * cos2SMSq) -
              (B / 6.0) * cos2SM *
              (-3.0 + 4.0 * sinSigma * sinSigma) *
              (-3.0 + 4.0 * cos2SMSq)));
        lambda = L +
            (1.0 - C) * f * sinAlpha *
            (sigma + C * sinSigma *
             (cos2SM + C * cosSigma *
              (-1.0 + 2.0 * cos2SM * cos2SM))); // (11)
        double delta = (lambda - lambdaOrig) / lambda;
        if (Math.abs(delta) < 1.0e-12) {
            break;
        }
    }
    float distance = (float) (b * A * (sigma - deltaSigma));
    results.mDistance = distance;
    float initialBearing = (float) Math.atan2(cosU2 * sinLambda,
        cosU1 * sinU2 - sinU1 * cosU2 * cosLambda);
    initialBearing *= 180.0 / Math.PI;
    results.mInitialBearing = initialBearing;
    float finalBearing = (float) Math.atan2(cosU1 * sinLambda,
            -sinU1 * cosU2 + cosU1 * sinU2 * cosLambda);
    finalBearing *= 180.0 / Math.PI;
    results.mFinalBearing = finalBearing;
    results.mLat1 = lat1;
    results.mLat2 = lat2;
    results.mLon1 = lon1;
    results.mLon2 = lon2;
}

仅提供链接的答案可能会随着时间的推移而失效,因此不太有用。 - Richard
你是对的,@Richard。我更新了链接并在我的回答中添加了linkt函数代码。 - Radon8472
谢谢!提供更完整的文献引用会很有用,这样大家可以通过其他方式找到它。 - Richard

-3

只需使用距离公式 Sqrt( (x2-x1)^2 + (y2-y1)^2 )


2
不要这样做。它只适用于赤道附近的小距离。远离赤道,即使是小距离也是错误的;在更高的纬度上,经度变化1度只有纬度变化1度的 * cos(latitude) 大小的距离。 - ToolmakerSteve

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