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    Terrain smoothing?

    So I have this program... it creates (or I create) a set of "High points", which end up being the only predefined locations on the map. The program then goes through every other point on the map and determines what that point's height should be based on its' distance to the high points. Right now, it uses a simple quadratic formula to smooth from the high point down, but this gets ugly the lower the altitude is. The goal is simple: smooth the slopes from between the points, making them "aware" of each other. I've tried a couple simple methods but have yielded no real results. Anyone have any ideas what the best way to do this would be?

    This is the current output of my program:
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