Automatic Reconstruction of Triangular Meshes from Point Sets

Constructing polygons or polyhedra with well-defined properties from a set of general points has been an active area of research since the inception of computational geometry. Some examples include convex hull shape characterizing polygons bounding boxes convex and non-convex k-gons k-holes optimal area and perimeter polygonizations. This book delineates algorithms theory and the experimental results on constructing constrained triangular meshes from point clouds. In particular two geometric reconstruction problems have been covered. 1. Shape reconstruction and 2. Polygonization with optimal area. Both these problems have been discussed in three dimensions where one of the problems focuses on reconstructing closed water-tight surfaces from three dimensional point sets and the other addresses the polyhedronization of point sets with volume constraint. Discussed problems are relevant with numerous applications in computer graphics computer vision pattern recognition geographical information science (GIS)4D printing and surface lofting among others.