点C与大圆上弧AB的不正确距离

Question

我得到的CD长度不正确，其中D标记了弧AB上第三点C的投影：

输入以上代码：：

startX,STARTY-弧的起始点坐标-->(48.1388,11.54988)

    private static void pointToArcDistance(double thirdX, double thirdY, double startX, double startY, 
        double endX, double endY) {
        double R = 6371000; 
        double φ1 = startX * Math.PI / 180; 
        double φ2 = endX * Math.PI / 180;
        double Δφ = (endX - startX) * Math.PI / 180;
        double Δλ = (endY - startY) * Math.PI / 180;
        double a = Math.sin(Δφ / 2) * Math.sin(Δφ / 2) +
        Math.cos(φ1) * Math.cos(φ2) *
        Math.sin(Δλ / 2) * Math.sin(Δλ / 2);
        double c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1 - a));
        double d13 = R * c; // distance between start & endPoint in meters
        double brng12 = bearing(startX, startY, endX, endY);
        double brng13 = bearing(startX, startY, thirdX, thirdY);
        double δ13 = d13 / R;
        double dXt = Math.asin(Math.sin(δ13) * Math.sin(brng13 - brng12)) * R;
        System.out.println("tangent distance(CD)::" + dXt);
    }
    
    private static double bearing(double lat1, double long1, double lat2, double long2) {
        double y = Math.sin(long2 - long1) * Math.cos(lat2);
        double x = Math.cos(lat1) * Math.sin(lat2) -
        Math.sin(lat1) * Math.cos(lat2) * Math.cos(long2 - long1);
        double polarDegrees = toDegrees(Math.atan2(y, x));
        return polarDegrees 

Answer 1

求点到弧的距离：

1. 首先，找到圆弧所暗示的椭圆的中心
2. 使用ATAN2
查找到点的角度
3. 使用cos（角度）*r1,sin（角度）*r2
找到椭圆的x、y截距
4. 使用从x、y截距到点的距离公式