What is the algorithm for determining the nearest segment of the path to a point?

Question

Cartography

Given a path on the map as an ordered set of points.
There is a point that moves along this path, but with some error.
It is necessary to determine the nearest section of the path (segment, edge) to a given point.
The task at first seemed simple, but then pitfalls surfaced. I think that there is already an existing algorithm, but which one? Voronoi diagrams? Delaunay triangulation?

Answer 1

Seems to have found the answer.
You need to use a BSP tree https://en.wikipedia.org/wiki/Binary_space_partitioning
stackoverflow.com/questions/3423852/algorithm-to-f...
and more options to choose from:
https://gist.github.com/ mbostock/8027637
stackoverflow.com/questions/18900642/get-point-on-...

Answer 2

Find distances to all points, adjacent segments to the closest point and a perpendicular to one of them. If one exists, the answer is the length of this perpendicular, otherwise, the distance to the nearest point

Answer 3

normal to a line (or projection of a point onto a line): the line segment from a point to the intersection with a line at an angle of 90 degrees to that line.