Reconstruction of surfaces from point clouds using a Lagrangian surface evolution model

Abstract

We present a method for reconstruction of surfaces in R 3 from point clouds. Given a set of points, we construct a triangular mesh approximation of a surface that they represent. The triangulation is obtained by a Lagrangian surface evolution model consisting of an advection and a curvature term. To construct them, we compute the distance function d to the given point cloud. Then the advection evolution is driven by ∇d and the curvature term depends on d and the mean curvature of the evolving surface. In order to control the quality of the mesh during the evolution, we perform tangential redistribution of mesh points as the surface evolves.