質問の緯度経度であらわされる２点の間の地点を求めるプログラムをJavaで作ってみた。

　質問の緯度経度であらわされる２点の間の地点を求めるプログラムをJavaで作ってみました。(^_^;
　実行結果のr=0.5のとこと値を比べてみると、あってるみたいです。o(^-^)o

 0.5 :  54°21′44″, -4°31′50″

Midpoint: 54°21′44″N, 004°31′50″W

※参考URL
http://www.movable-type.co.uk/scripts/latlong.html

$\phi_1 = toRadians(lat_1) = lat_1 \time \frac {\pi}{180.0}$
$\phi_2 = toRadians(lat_2)$
$\lambda_1 = toRadians(lng_1)$
$\lambda_2 = toRadians(lng_2)$
$\Delta\phi= \phi_2 - \phi_1$
$\Delta\lambda= \lambda_2 - \lambda_1$
Haversine formula:
$R = 6371 (km)$
$a = \sin^2(\frac{\Delta\phi}{2}) + \cos\phi_1\cdot\cos\phi_2\cdot\sin^2(\frac {\Delta\lambda}{2})$
$d = 2R \cdot \tan^{-1}(\frac{\sqrt{a}}{\sqrt{1-a}})$
$\theta = \tan^{-1}(\frac{\sin\Delta\lambda}{\cos\phi_1\cdot\tan\phi_2-\sin\phi_1\cdot\cos\Delta\lambda} )$
$\phi_r = \sin^{-1}( \sin\phi_1\cdot\cos(\frac{r\cdot d}{R}) + \cos\phi_1\cdot\sin(\frac{r\cdot d}{R})\cdot\cos\theta )$
$\lambda_r = \lambda_1 + \tan^{-1}( \frac{\sin\theta\cdot\sin(\frac{r\cdot d}{R})\cdot\cos\phi_1}{\cos(\frac{r\cdot d}{R})-\sin\phi_1\cdot\sin\phi_r} )$
$lat_r = toDegrees(\phi_r) = \phi_r\time\frac {180.0} {\pi}$
$lng_r = toDegrees(\lambda_r)$

● Haversine1.java

/* 
 * Haversine1.java
 */

import static java.lang.Math.*;

class Haversine1 {
    static final int R = 6371; // km

    public static void main(String[] args) {
        double lat1 =  dmsToDec(50.0,  3.0, 59.0);
        double lon1 = -dmsToDec( 5.0, 42.0, 53.0);
        double lat2 =  dmsToDec(58.0, 38.0, 38.0);
        double lon2 = -dmsToDec( 3.0,  4.0, 12.0);
        double d = getDistance(lat1,lon1,lat2,lon2);
        double b = getDirection(lat1,lon1,lat2,lon2);
        
        System.out.printf("%4.1f [km]\n",d);
        System.out.println(decToDms(b));
        System.out.println();
        for(int i=0; i<= 10; i++){
            double r = 0.1*i;
            System.out.printf(" %2.1f : %s, %s\n",r,
                decToDms(getLatitude(lat1, r*d, b)),
                decToDms(getLongitude(lat1, lon1, r*d, b)));
        }
    }
    
    public static double getDistance(double lat1, double lon1, double lat2, double lon2) {
        double dLat = toRadians(lat2-lat1);
        double dLon = toRadians(lon2-lon1);
        lat1 = toRadians(lat1); lat2 = toRadians(lat2);
        double a = sin(dLat/2) * sin(dLat/2) + sin(dLon/2) * sin(dLon/2) * cos(lat1) * cos(lat2);
        double c = 2 * atan2(sqrt(a), sqrt(1-a));
        double distance = R * c;
        return distance;
    }

    public static double getDirection(double lat1, double lon1, double lat2, double lon2) {
        lat1 = toRadians(lat1); lat2 = toRadians(lat2);
        lon1 = toRadians(lon1); lon2 = toRadians(lon2);
        double dLon = lon2 - lon1;
        double y = sin(dLon);
        double x = cos(lat1)*tan(lat2)-sin(lat1)*cos(dLon);
        double brng = toDegrees(atan2(y, x));
        return (brng>=0.0) ? brng : brng + 360.0;
    }
    
    public static double getLatitude(double lat1, double d, double brng) {
        lat1 = toRadians(lat1); brng = toRadians(brng);
        double lat2 = asin( sin(lat1)*cos(d/R) + cos(lat1)*sin(d/R)*cos(brng) );
        return toDegrees(lat2);
    }
    
    public static double getLongitude(double lat1, double lon1, double d, double brng) {
        lat1 = toRadians(lat1); lon1 = toRadians(lon1); brng = toRadians(brng);
        double lat2 = asin( sin(lat1)*cos(d/R) + cos(lat1)*sin(d/R)*cos(brng) );
        double lon2 = lon1 + atan2(sin(brng)*sin(d/R)*cos(lat1), cos(d/R)-sin(lat1)*sin(lat2));
        return toDegrees(lon2);
    }
    
    public static double dmsToDec(double h, double m, double s) {
        return (h + m / 60.0 + s / 3600.0);
    }
    
    public static String decToDms(double x) {
        String sign = " ";
        double hh, mm, ss;
        
        if(x< 0){ sign="-"; x*=-1; }
        ss = x;
        hh = floor(ss);
        ss = (ss - hh) * 60.0;
        mm = floor(ss);
        ss = (ss - mm) * 60.0;
        return String.format("%s%.0f°%02.0f′%02.0f″",sign,hh,mm,ss);
    }
}

●実行結果

968.9 [km]
 9° 7′11″

 0.0 :  50°03′59″, -5°42′53″
 0.1 :  50°55′35″, -5°29′44″
 0.2 :  51°47′10″, -5°16′06″
 0.3 :  52°38′43″, -5°01′56″
 0.4 :  53°30′15″, -4°47′11″
 0.5 :  54°21′44″, -4°31′50″
 0.6 :  55°13′12″, -4°15′50″
 0.7 :  56°04′37″, -3°59′08″
 0.8 :  56°55′60″, -3°41′40″
 0.9 :  57°47′20″, -3°23′23″
 1.0 :  58°38′38″, -3°04′12″