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

For polygon shapes with a reasonable number of boundary points such as in a GIS or games application it might be quicker easier to do a series of tests.

For each vertex in the red polygon compute the distance to each vertex in the blue polygons and find the closest (hint, compare distance^2 so you don't need the sqrt() ) Find the closest, then check the vertex on each side of the found red and blue vertex to decide which line segments are closest and then find the closest approach between two line segments.

See http://local.wasp.uwa.edu.au/~pbourke/geometry/lineline3d/ (it's easy to simply for the 2d case)