Generating straight outlines of 2D point sets and holes using dominant directions or orthogonal projections

Representing the shape of finite point sets in 2D by simple polygons becomes a challenge if the resulting outline needs to be non-convex and straight with only few, distinct edges and angles. Such outlines are usually sought in order to border point sets that originate from man-made objects, e.g., for the purpose of building reconstruction from LIDAR data. Algorithms for computing hulls of point sets obtained from such structures usually yield polygons having too many edges and angles and may thus not capture the actual shape very well. Furthermore, many existing approaches cannot handle empty domains within the boundaries of a point set (holes). In this paper, we present methods that create straight, non-convex outlines of finite 2D point sets and of possibly contained holes. The resulting polygons feature fewer vertices and angles than hulls and can thus faithfully represent objects of angular shapes.