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I have a 3D surface given as a set of triples (x_i, y_i, z_i), where x_i and y_i are roughly on a grid, and each (x_i, y_i) has a single associated z_i value. The typical grid is 20x20

I need to find which points belong to the convex hull of the surface, within a given tolerance. I'm looking for an efficient algorithm to perform the computation (my customer has provided an O(n³) version, which takes ~10s on a 400 point dataset...)

gurney alex
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There's quite a lot out there, didn't you search?

Here are a couple with O(n log h) runtime, where n is number of input points and h is number of vertices of the result:

http://en.wikipedia.org/wiki/Chan%27s_algorithm

http://en.wikipedia.org/wiki/Kirkpatrick-Seidel_algorithm

Here is a demonstration of four methods, with links to the algorithms:

http://www.cse.unsw.edu.au/~lambert/java/3d/hull.html

Tom Zych
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The O(n^3) version is probably Jarvis algorithm for 3d Hull. Look at this algorithm, I think is well described:

Mariy
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  • [Link only answers](http://meta.stackexchange.com/questions/8231) aren't ideal, but this one would be hard to summarize. If the link fails, paste it into wayback; it was archived when I checked today. If that fails, google for `jason yang convex hull`. – Tom Zych Nov 09 '15 at 09:16