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1

If the first image, where each point is a small square with certain color, is what you are searching for, you need to build the Delaunay's triangulation.


11

What you want is to produce a dual graph; that is, a graph produced by converting faces to vertices, and connecting them based on adjacent faces in the original graph. Example: The problem, as you can see, is that if you want to keep the same layout of the graph, you'll get some really curvy edges in the dual graph. Also, you'll often end up with a ...


0

There are two questions here: How to assign the fewest number of checkpoints, so that every vertex is within at most T distance from some checkpoint. How to spread those checkpoints as evenly as possible. Question 1 turns out to have a linear-time solution: First, fix some root node arbitrarily. If this is a level, then some start/spawn point makes a ...


0

I propose a recursive pseudo code aproach to use while creating the tree Keep track of placed check points in a listlike structure: stacked_check_point_collection here comes the recursive method: create_node(last_check_point_distance, current_node) //recursive method add current_node to tree; if last_chec_point_distance > T { /*check other ...


3

Looking at your image gives an idea of how this should work. Two points are apparent: Endpoint nodes (those with only one connected neighbour) are the least likely to have checkpoints, since they share with the fewest other nodes; endpoint nodes will in fact only contain a checkpoint iff they are isolated as a degenerate DAG, i.e. they have no neighbours ...



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