Surface Reconstruction from Unorganized Points

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This project concerns the problem of reconstructing a two- dimensional surface, such as the outside of a real object, from a collection of sample points. The problem is important for building models in computer graphics, and in other areas of science and engineering. A new algorithm has been developed which is provably correct and efficient, based on the Delaunay triangulation of the samples. An innovative aspect of the algorithm is that the samples do not have to be evenly distributed over the object - detailed areas can be sampled densely and smooth areas can be sampled sparsely. The basic algorithm will be tested in various applications, each requiring different extensions or modifications, and the application of the theory to other problems in geometric modeling will be studied.