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Bringing order to a vertex soup

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Consider this: I have an array of vertexes, each with 2 coordinates (2d: x and y) and I want to make a surface out of them, uniting them as (many) triangles without of course, covering other vertexes. Is there any algorithm able to do this? I was thinking of adapting the rendering algorithm used in the SOAR terrain engine, which provides with a surface just like what I need (thought the triangle count on my surface would be a lot smaller).

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