Why it matters

Visibility graph optimal for polygon obstacles. Understanding shapes 2D planning.

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The architecture

Add start + goal to polygon corners.

Edges between visible pairs.

Shortest path via Dijkstra.

Visibility graphCorners + start + goalverticesVisibility edgesno polygon crossesDijkstrashortest pathOptimal in 2D polygon world; O(n^2 log n) to build; use for known maps
Visibility graph.
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How it works end to end

O(n^2) edges worst case.

Visibility test: no polygon segment crosses.

Rotational sweep for efficient construction.