Java 已知两个点的坐标经纬度以及方向角，判断两点是否相交，若相交求交点经纬度

可以通过以下步骤来判断两个点是否相交并求出交点经纬度：

1. 将经纬度转换为平面坐标系中的直角坐标系，如墨卡托投影坐标系或UTM坐标系；
2. 根据方向角计算出两个点所在直线的解析式；
3. 判断两条直线是否相交，可以通过判断它们的斜率是否相等来判断；
4. 若两条直线相交，则求出它们的交点坐标；
5. 将交点坐标转换为经纬度坐标。

下面是 Java 代码示例：

import java.awt.geom.Point2D;

public class Intersection {
    // 计算两个点之间的距离
    public static double distance(double lon1, double lat1, double lon2, double lat2) {
        double R = 6371.0; // 地球半径，单位为千米
        double radLat1 = Math.toRadians(lat1);
        double radLat2 = Math.toRadians(lat2);
        double a = radLat1 - radLat2;
        double b = Math.toRadians(lon1) - Math.toRadians(lon2);
        double s = 2 * Math.asin(Math.sqrt(Math.pow(Math.sin(a/2),2) +
                Math.cos(radLat1)*Math.cos(radLat2)*Math.pow(Math.sin(b/2),2)));
        s = s * R;
        return s;
    }

    // 将经纬度转换为平面坐标系中的墨卡托投影坐标系
    public static Point2D.Double mercator(double lon, double lat) {
        double x = Math.toRadians(lon * 20037508.34 / 180);
        double y = Math.log(Math.tan((90 + lat) * Math.PI / 360)) / (Math.PI / 180);
        y = y * 20037508.34 / 180;
        return new Point2D.Double(x, y);
    }

    // 计算两点连线的方向角
    public static double direction(double lon1, double lat1, double lon2, double lat2) {
        double dx = lon2 - lon1;
        double dy = lat2 - lat1;
        double angle = Math.atan2(dy, dx);
        return angle;
    }

    // 判断两条直线是否相交
    public static boolean isIntersect(double lon1, double lat1, double dir1, double lon2, double lat2, double dir2) {
        double k1 = Math.tan(dir1);
        double k2 = Math.tan(dir2);
        if (k1 == k2) { // 两条直线平行
            return false;
        } else {
            double x1 = mercator(lon1, lat1).x;
            double y1 = mercator(lon1, lat1).y;
            double x2 = mercator(lon2, lat2).x;
            double y2 = mercator(lon2, lat2).y;
            double x = (k1*x1 - k2*x2 + y2 - y1) / (k1 - k2);
            double y = k1 * (x - x1) + y1;
            return true;
        }
    }

    // 求两条直线的交点坐标
    public static Point2D.Double intersection(double lon1, double lat1, double dir1, double lon2, double lat2, double dir2) {
        double k1 = Math.tan(dir1);
        double k2 = Math.tan(dir2);
        double x1 = mercator(lon1, lat1).x;
        double y1 = mercator(lon1, lat1).y;
        double x2 = mercator(lon2, lat2).x;
        double y2 = mercator(lon2, lat2).y;
        double x = (k1*x1 - k2*x2 + y2 - y1) / (k1 - k2);
        double y = k1 * (x - x1) + y1;
        double lon = Math.toDegrees(x / 20037508.34 * 180);
        double lat = Math.toDegrees(Math.atan(Math.exp(y / 20037508.34 * 180 * Math.PI / 180)) * 2 - Math.PI / 2);
        return new Point2D.Double(lon, lat);
    }

    public static void main(String[] args) {
        double lon1 = 116.3688;
        double lat1 = 39.9155;
        double lon2 = 116.4444;
        double lat2 = 39.9318;
        double dir1 = Math.toRadians(60);
        double dir2 = Math.toRadians(150);

        if (isIntersect(lon1, lat1, dir1, lon2, lat2, dir2)) {
            Point2D.Double point = intersection(lon1, lat1, dir1, lon2, lat2, dir2);
            System.out.println("交点经度：" + point.x);
            System.out.println("交点纬度：" + point.y);
        } else {
            System.out.println("两条直线不相交");
        }
    }
}