Scaling of plane figures that assures faithful digitization

Abstract

In this paper we propose a method for obtaining a faithful digitization of certain broad classes of plane figures, so that the original continuous object and its digitization feature analogous geometric properties. The approach is based on an appropriate scaling of a given figure so that the obtained one admits digitization satisfying some desirable conditions. Informally speaking, we show that from certain point on, a continuous object and its digitization are in a sense equivalent. In terms of computational complexity, the scaling factor is easily computable. As a corollary of the presented theory we prove the strong NP-hardness of the problem of obtaining a polyhedron reconstruction in which the facets are trapezoids or triangles. © 2008 Springer-Verlag Berlin Heidelberg.