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mike74

donut-like closed surface

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I'm becoming more and more interested in the idea of picking a bunch of points on a theoretical surface (such as a torus) and then creating a surface of triangles from those points. In many cases, you can do this by finding the convex hull of the points. However, what if your surface is like a torus? If you find the convex hull, the surface will be like a donut without a hole. Any ideas on an algorithm for finding the donut with the hole if you pick a lot of points on a torus? Mike C. http://www.coolgroups.com/

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Well, in terms of figuring out a contour for an arbitrary object like that based on point clouds, google for "marching cubes algorithm". A more exact treatment of the problem of extending the notion of a convex hull to a compact non-euclidean manifold embedded in euclidean space is firmly in the realm of topology and computational geometry, and is outside my area of expertise.

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