In the image below, the line is a trail and the point is an existing restroom. I would like to find the rough locations of 2 additional restrooms that minimize the maximum distance along trail from anywhere on the trail to the closest of the 3 restrooms.
The trail was GPS-collected in segments and connected with Edit Vertices in ArcMap. The dataset comprises 1 line shp for the trail and 1 point shp for the restroom. I have no idea how to proceed.
I have posted a simplified version of this question in stackoverflow.
Hints will be appreciated as well. Thanks.