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- Surface Reconstruction From 3D Point CloudsPublication . Leitão, Gonçalo Nuno Paula de Campos Vinhas; Gomes, Abel João PadrãoThe triangulation of a point cloud of a 3D object is a complex problem, since it depends on the complexity of the shape of such object, as well as on the density of points generated by a specific scanner. In the literature, there are essentially two approaches to the reconstruction of surfaces from point clouds: interpolation and approximation. In general, interpolation approaches are associated with simplicial methods; that is, methods that directly generate a triangle mesh from a point cloud. On the other hand, approximation approaches generate a global implicit function — that represents an implicit surface — from local shape functions, then generating a triangulation of such implicit surface. The simplicial methods are divided into two families: Delaunay and mesh growing. Bearing in mind that the first of the methods presented in this dissertation falls under the category of mesh growing methods, let us focus our attention for now on these methods. One of the biggest problems with these methods is that, in general, they are based on the establishment of dihedral angle bounds between adjacent triangles, as needed to make the decision on which triangle to add to the expansion mesh front. Typically, other bounds are also used for the internal angles of each triangle. In the course of this dissertation, we will see how this problem was solved. The second algorithm introduced in this dissertation is also a simplicial method but does not fit into any of the two families mentioned above, which makes us think that we are in the presence of a new family: triangulation based on the atlas of charts or triangle stars. This algorithm generates an atlas of the surface that consists of overlapping stars of triangles, that is, one produces a total surface coverage, thus solving one of the common problems of this family of direct triangulation methods, which is the appearance of holes or incomplete triangulation of the surface. The third algorithm refers to an implicit method, but, unlike other implicit methods, it uses an interpolation approach. That is, the local shape functions interpolate the points of the cloud. It is, perhaps, one of a few implicit methods that we can find in the literature that interpolates all points of the cloud. Therefore, one of the biggest problems of the implicit methods is solved, which has to do with the smoothing of the surface sharp features resulting from the blending of the local functions into the global function. What is common to the three methods is the interpolation approach, either in simple or implicit methods, that is, the linearization of the surface subject to reconstruction. As will be seen, the linearization of the neighborhood of each point allows us to solve several problems posed to the surface reconstruction algorithms, namely: point sub‐sampling, non‐uniform sampling, as well as sharp features.