如何从球面上的当前点（纬度/经度）找到线段上最近的点

Question

例如： 比方说，我们在地球地图上有某种直墙，我们知道它的起点和终点的纬度/经度坐标：

wall.start.lat, wall.start.lon
wall.end.lat, wall.end.lon

我们还有一些对象：

object.lat
object.lon

如果我要从那个物体走到表面上的墙壁，我需要找到距离这个物体最近的墙壁点。

在飞机上很容易解决，但我一直坚持使用球体。

Answer 1

您可以在this latlong page使用越野距离部分

 I’ve sometimes been asked about distance of a point from a great-circle path (sometimes called cross track error).

Formula:    dxt = asin( sin(δ13) ⋅ sin(θ13−θ12) ) ⋅ R
where   δ13 is (angular) distance from start point to third point
θ13 is (initial) bearing from start point to third point
θ12 is (initial) bearing from start point to end point
R is the earth’s radius
JavaScript: 
var δ13 = d13 / R;
var dXt = Math.asin(Math.sin(δ13)*Math.sin(θ13-θ12)) * R;
Here, the great-circle path is identified by a start point and an end point – depending on what initial data you’re working from, you can use the formulas above to obtain the relevant distance and bearings. The sign of dxt tells you which side of the path the third point is on.

The along-track distance, from the start point to the closest point on the path to the third point, is

Formula:    dat = acos( cos(δ13) / cos(δxt) ) ⋅ R
where   δ13 is (angular) distance from start point to third point
δxt is (angular) cross-track distance
R is the earth’s radius
JavaScript: 
var δ13 = d13 / R;
var dAt = Math.acos(Math.cos(δ13)/Math.cos(dXt/R)) * R;

并应用目标点给定距离和距起点的方位方法来获取点坐标

Answer 2

我愿意：

1. 假设一个单位球体，计算从中心到线段端点的向量
2. 叉积以获得包含线段的平面的法线
3. 用对象点标准化长度和点积，以获得它与平面的距离
4. asin() 将其转换为沿曲面到线段大圆路径的距离
5. 乘以实际半径得到合适的单位

您还需要对象点和线段端点之间的距离，以防它们变得更近。