How to build a route from an area?

Question

Google Maps

We set the task to implement the construction of the shortest route from a pre-marked area.
I tried it on Yandex - they marked all the exit points from the required area. By choosing a point outside the area, we got its coordinates, then the 3 nearest points on the area were taken in a straight line, and a route was built from them. As you understand, it turns out that in some cases the nearest points along a straight line are not the points of the shortest route. Is it possible to implement the correct calculation using any service (free). Do not offer to increase the number of used points from the area - it increases the load.

Answer 1

The following decision was made: to reduce the number of points as much as possible, the traces that are combined were designated by 1 point, because route 1 will be the same. Next, they took out the number of points from the territory of the Moscow Ring Road that were taken to calculate the route into a separate constant - experimentally set 10, the maximum accuracy. The time for one point is 30 seconds, but for us it turned out not fundamentally. the process is in the background and does not interfere with work.