What is the quickest way to find the shortest cartesian distance between two polygons

Question

I have 1 red polygon say and 50 randomly placed blue polygons - they are situated in geographical 2D space. What is the quick

Answer 1

As others have mentioned using bounding areas (boxes, circles) may allow you to discard some polygon-polygon interactions. There are several strategies for this, e.g.

1. Pick any blue polygon and find the distance from the red one. Now pick any other polygon. If the minimum distance between the bounding areas is greater than the already found distance you can ignore this polygon. Continue for all polygons.
2. Find the minimum distance/centroid distance between the red polygon and all the blue polygons. Sort the distances and consider the smallest distance first. Calculate the actual minimum distance and continue through the sorted list until the maximum distance between the polygons is greater than the minimum distance found so far.

Your choice of circles/axially aligned boxes, or oriented boxes can have a great affect on performance of the algorithm, dependent on the actual layout of the input polygons.

For the actual minimum distance calculation you could use Yang et al's 'A new fast algorithm for computing the distance between two disjoint convex polygons based on Voronoi diagram' which is O(log n + log m).