计算沿点相交的纬线长矢量的距离

Question

由于我还没有评论，因为我没有足够的声誉，所以我不得不问另一个问题。 有了这篇出色的文章Distance from Lat/Lng point to Minor Arc segment，我已经用C＃和C实现了代码。 现在，对于情况2.1，我需要知道：相对方位角是锐角，并且p4落在我们的圆弧上，如何计算点相交沿线段的距离（以米为单位！）。 不幸的是，我不是数学天才，所以对我来说，使用实变量名的代码示例将是一个优势。 MatLab示例很容易转换为C＃和C-我在下面包括了C代码：

// GeoSpatial.h Header file containing....
typedef enum _calculationResultType
{
    Undefined,
    Obtuse,
    BeyondArc,
    CrossTrack
} CalculationResultType;

typedef struct  _coordinate
{
    //int Id;
    int FeatureId;
    double Latitude;
    double Longitude;
    int SpeedLimit;
} CoordinateObject, * Coordinate;

double GeoSpatial_Bearing(double latA, double lonA, double latB, double lonB);
double GeoSpatial_Calculate(Coordinate c1, Coordinate c2, Coordinate c3, CalculationResultType * resultType);
double GeoSpatial_Distance(double latA, double lonA, double latB, double lonB);
double GeoSpatial_ToRadians(double degrees);

// C Module....
#include <math.h>
#include "GeoSpatial.h"

const double EarthRadius = 6371000.0L;
const double PI = 3.14159265358979L;

double
GeoSpatial_Bearing(double latA, double lonA, double latB, double lonB)
{
    return atan2(sin(lonB - lonA) * cos(latB), cos(latA) * sin(latB) - sin(latA) * cos(latB) * cos(lonB - lonA));
}

double
GeoSpatial_Calculate(Coordinate c1, Coordinate c2, Coordinate c3, CalculationResultType * resultType)
{
    double lat1 = GeoSpatial_ToRadians(c1->Latitude);
    double lat2 = GeoSpatial_ToRadians(c2->Latitude);
    double lat3 = GeoSpatial_ToRadians(c3->Latitude);
    double lon1 = GeoSpatial_ToRadians(c1->Longitude);
    double lon2 = GeoSpatial_ToRadians(c2->Longitude);
    double lon3 = GeoSpatial_ToRadians(c3->Longitude);

    // Earth's radius in meters

    // Prerequisites for the formulas
    double bearingC1C2 = GeoSpatial_Bearing(lat1, lon1, lat2, lon2);
    double bearingC1C3 = GeoSpatial_Bearing(lat1, lon1, lat3, lon3);
    double distanceC1C3 = GeoSpatial_Distance(lat1, lon1, lat3, lon3);

    // Is relative bearing obtuse?
    if (fabs(bearingC1C3 - bearingC1C2) > (PI / 2))
    {
        double distanceC2C3 = GeoSpatial_Distance(lat2, lon2, lat3, lon3);
        *resultType = Obtuse;
        return distanceC1C3 < distanceC2C3 ? distanceC1C3 : distanceC2C3;
    }

    // Find the cross-track distance.
    double distanceCrossTrack = asin(sin(distanceC1C3 / EarthRadius) * sin(bearingC1C3 - bearingC1C2)) * EarthRadius;

    // Is p4 beyond the arc?
    double distanceC1C2 = GeoSpatial_Distance(lat1, lon1, lat2, lon2);
    double distanceC1C4 = acos(cos(distanceC1C3 / EarthRadius) / cos(distanceCrossTrack / EarthRadius)) * EarthRadius;

    if (distanceC1C4 > distanceC1C2)
    {
        // Distance C2 - C3
        *resultType = BeyondArc;
        return GeoSpatial_Distance(lat2, lon2, lat3, lon3);
    }

    *resultType = CrossTrack;
    return fabs(distanceCrossTrack);
}

double
GeoSpatial_Distance(double latA, double lonA, double latB, double lonB)
{
    return acos(sin(latA) * sin(latB) + cos(latA) * cos(latB) * cos(lonB - lonA)) * EarthRadius;
}

double
GeoSpatial_ToRadians(double degrees)
{
    return degrees * (acos(-1) / 180);
}