Reconstructing Surface Discontinuities by Intersecting Tangent Planes of Advancing Mesh Frontiers

Reconstruction of surface discontinuities from unorganized 3D points is a difficult problem. Both the polygonization and surface fitting approaches to surface reconstruction face the same chicken-and-egg problem: to correctly reconstruct surface discontinuities, the points that lie on the same side of the discontinuities should be used to reconstruct the surfaces to form the discontinuities. However, to know whether the points lie on the same or different sides, the algorithm needs to know the locations and orientations of edge discontinuities, which are not directly available in the unorganized point set. This paper presents an elegant method of overcoming the above problem. The method reconstructs an object’s surface by constructing meshes at flat surfaces and advancing the mesh frontiers towards predicted surface discontinuities. As the frontiers of two or more meshes approach a discontinuity from its different sides, tangent planes at the mesh frontiers are estimated using the points within the frontiers, thus eliminating the problem of accidentally using points on different sides of the discontinuity to estimate a single tangent plane. Then, the tangent planes are intersected to form the discontinuity. Quantitative evaluation shows that this method can estimate the tangent planes very accurately, and can reconstruct surface discontinuities even when 3D points are not sampled at the discontinuities.