Giesen, JoachimJohn, Matthias2015-02-162015-02-1620021467-8659https://doi.org/10.1111/1467-8659.00596We 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.10.1111/1467-8659.00596363-371