Triangulation of an elevation surface structured by a sparse 3D grid

This paper proposes a method to triangulate an elevation surface structured in a sparse 3D grid by using a fast search algorithm based on the 2D Delaunay triangulation. After projecting the 3D point clouds onto a natural 2D grid in the x, y plane, we triangulate the surface (actually, we compute a Delaunay triangulation of the 2D point cloud taking advantage of its regular structure). The main novelty of our approach is that the neighboring points of an edge ei are searched in a rectangle supported by the edge ei under consideration. The obtained results show that our method could process very fast, the initial shape of the surface is well preserved, and the topology of the output triangular mesh approximates the input surface of 3D point clouds.