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We have a small task to determine the best place to locate a new business (e.g. a bakery). The best location will be as farthest as possible from current bakeries, and within residential areas. We know the places of the current businesses (with their lat/long values), and we know the residential areas (as polygon shapes, defined by points of lat/long).
By defining the the current businesses as points, we need to find the point(s) the farthest from the current ones, and in the same time, within city areas (nobody needs a bakery in the middle of nowhere :) )
a .NET library (or a a library accessible by .NET), that takes a list of points (representing the current businesses locations), and a set of polygons (each presented by points as well) that defines the city areas, and optionally take an integer for maximum number of results to be found.
The library should (quickly) calculate the new points, and order them, with the farthest points first.
This library must be to handle points ranging from 2, to 100,000+ as efficient as possible
You are free to write this library the way you like, but it has to be quick enough..
Some options include:
Voronoi Diagrams, Density Estimation.. You can build these tools using c/c++ or MatLab or any other language as long as it is possible to call them from .NET
Note: I’ve found a ready library for Vonoroi diagrams, but it is extremely slow (takes minutes to handle 10k+ points! Please test your code first!