Distance between point and polygon

Question

Task

Calculate the distance d in meters between a query-point q and a polygon P.

The query-point q is defined as tuple (latitude_q, longitude_q), the polygon P as ordered list of tuples [(latitude₁, longitude₁), ..., (latitude_n, longitude_n)].

Problem

I can't handle latitude and longitude as if they were x- and y-coordinates of a plane as this leads to huge errors if the polygon is not small and not near (0, 0).

Tools

I know how to calculate the distance between two points given each points latitude and longitude. I do also know how to calculate the distance between a point and a great circle. But for this task I'd need to know how to calculate the distance dist(q, 1—2) between a point q and and part of a great-circle 1—2. The distance of q would be simply min(dist(q, a—b)) ∀ a—b in P.

Question

Can you provide me a formula how to calculate the distance between a query-point q defined by a tuple (latitude_q, longitude_q) and a great-circle-arc defined by pair of latitude-longitude-tuples [(latitude₁, longitude₁),(latitude₂, longitude₂)]?

Example

Answer 1

如果你有代码来计算一个点 x 和一个测地线之间的距离 分段 s ，你可以为你的测地多边形的每个边重复这个。

让 s =（ a ， b ）。 s 是一个大圆弧。旋转球体，使其 s 位于赤道上， x 跟随球体旋转。 然后 x 的纬度基本上告诉你到 s 的距离：它要么是 从 x 到 a 或 x 到 b 的距离，或者，如果 x 位于 s 上方/下方的扇区中，它是纬度的一个简单因子（2πr）。