Surface reconstruction based on a dynamical system †

We present an efficient algorithm that computes a manifold triangular mesh from a set of unorganized sample points in . The algorithm builds on the observation made by several researchers that the Gabriel graph of the sample points provides a good surface description. However, this surface description is only one‐dimensional. We associate the edges of the Gabriel graph with index 1 critical points of a dynamical system induced by the sample points. Exploiting also the information contained in the critical points of index 2 provides a two‐dimensional surface description which can be easily turned into a manifold.

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