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Given Voronoi diagram, how to locate which polygon contains query point q? What if q is one of the Voronoi sites, would it make any difference?

Do we walk through each polygon and check point-in-polygon? It is too expensive and slow to do that.

Coder
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  • So if I have a Voronoi diagram with over 1 million cells I have to have some sort of spatial index on top of it? – Coder Aug 23 '17 at 15:49

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This is a well-studied topic. Search for "point location within a convex subdivision." Here is one paper that can lead you to others:

Cheng, Siu-Wing, and Man-Kit Lau. "Adaptive point location in planar convex subdivisions." International Symposium on Algorithms and Computation. Springer, Berlin, Heidelberg, 2015. (Journal link.)

Or maybe this presentation is easier to penetrate:

Subhash Suri, "Point Location." (PDF download.)

Joseph O'Rourke
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