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The aim is to demonstrate an effective pathfinding method within a specific triangulation of points in a plane.

January 1, 1986

There is a planar graph almost as good as the complete graph

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The aim is to demonstrate an effective pathfinding method within a specific triangulation of points in a plane.
Defined a triangulation from a set of points in the plane.
Analyzed the path length in relation to the straight-line distance between points.
Developed an O(n) data structure for finding paths in the presence of obstacles.
A path within the triangulation is less than √10 times the straight-line distance between endpoints.
Shortest path is less than 3 times the corresponding straight-line distance.
An efficient O(n log n) time algorithm for pathfinding was produced.

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Randomized trial demonstrates efficient pathfinding in a planar graph, suggesting improved navigation in the presence of obstacles.

Paul Chew (1986) studied this question.

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