Cluster-Based Generation of Hierarchical Surface Models

We present a highly efficient, automatic method for the generation of hierarchical surface triangulations. Given a set of scattered points in three-dimensional space, without known connectivity information, our method reconstructs a valid triangulated surface model in a two-step procedure. First, we apply clustering to the set of given points and identify point subsets in locally nearly planar regions. Second, we construct a surface triangulation from the output of the clustering step. The output of the clustering step is a set of 2-manifold tiles, which locally approximate the underlying, unknown surface. We construct the triangulation of the entire surface by triangulating the individual tiles and triangulating the gaps between the tiles. Since we apply point clustering in a hierarchical fashion we can generate model hierarchies by triangulating various levels resulting from the hierarchical clustering step.