什么是初始轴承和最终轴承 [英] What is initial bearing and final bearing

问题描述

我正在尝试计算此链接.我看到我们最初使用下面的方程式获得的方位角是初始方位角.

 公共静态double GetBearing(双纬1，双经1，双纬2，双经2){var lat1 = ToRadians(latitude1);var lat2 = ToRadians(latitude2);var longdiff = ToRadians(longitude1-longitude2);var X = Math.Cos(lat2)* Math.Sin(longdiff);var Y = Math.Cos(lat1)* Math.Sin(lat2)-Math.Sin(lat1)* Math.Cos(lat2)* Math.Cos(longdiff);var bearing = ToDegrees(Math.Atan2(X，Y));回报率(轴承+360)％360;} 

假设

对于最终轴承，只需将初始轴承从端点移至起点并将其反转(使用θ=(θ+ 180)％360).

我对初始轴承和最终轴承之间的差异感到困惑.什么是初始轴承和最终轴承?对于两点之间的轴承，我们应该采用哪种轴承作为最终答案.

解决方案

方位角是沿到达目的地的最短路径的方向与向北的方向之间的夹角.我们拥有最初和最后一个的原因是我们生活在球体上，因此最短的路径是测地线.它是地球上的一条直线，如果在平面地图上绘制它会有点-它将是一条曲线.

有两种方法可以考虑它.在平面地图上思考:当您从A到B行驶时，该曲线的方向会略有变化，因此该线与North之间的角度也会发生变化，即方位角也会发生变化.

或者您可以考虑球体，然后考虑三角形A-B-北极.方位角是AB与适当子午线之间的角度.初始方位是AB与子午线A之间的夹角.最后一个方位是AB与子午线B之间的夹角.

单个最终答案"仅当A和B之间的距离较短时，才有意义.那么地球的曲率并不重要，初始轴承和最终轴承彼此非常接近，因此可以根据所需的精度来谈论单个轴承.

I am trying to calculate bearing between two lat/lon points as given in this link. I see that the bearing we get initially using the below equation is initial bearing.

    public static double GetBearing(double latitude1, double longitude1, double latitude2, double longitude2)
        {
            var lat1 = ToRadians(latitude1);
            var lat2 = ToRadians(latitude2);
            var longdiff = ToRadians(longitude1 - longitude2);
            var X = Math.Cos(lat2) * Math.Sin(longdiff);
            var Y = Math.Cos(lat1) * Math.Sin(lat2) - Math.Sin(lat1) * Math.Cos(lat2) * Math.Cos(longdiff);
            var bearing =ToDegrees(Math.Atan2(X, Y));
            return (bearing+360)%360;
        }

It is given that

For final bearing, simply take the initial bearing from the end point to the start point and reverse it (using θ = (θ+180) % 360).

I am confused about the difference between initial bearing and final bearing. What is this initial and final bearing and which bearing should we take as the final answer for bearing between two points.

解决方案

The bearing is the angle between direction along the shortest path to destination and direction to North. The reason we have initial and final one is that we live on sphere, so the shortest path is geodesic line. It is a straight line on globe, bit if you draw it on flat map - it will be a curve.

There are two ways to think about it. Thinking on flat map: as you travel from A to B, this curve changes direction slightly, so the angle between this line and North changes, i.e. bearing changes.

Or you can think on sphere, and then think about triangle A - B - North Pole. The bearing is angle between between AB and appropriate meridian. Initial bearing is angle between AB and meridian crossing A. Final one is angle between AB and meridian crossing B. They are different.

The single "final answer" bearing only makes sense when distance between A and B is short. Then the curvature of Earth does not matter much, and the initial and final bearings are very close to each other, so depending on precision needed one can talk about single bearing.

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