Towards a unifed approach between digitizations of linear objects and discrete analytical objects

Abstract

This paper compares the traditional digitization method as used in Computer Graphics with the arithmetical geometry approach. Digitizations are interpreted as the set of grid points contained in the dilation of a continuous object and a re ected basic domain. We investigate the supercover and derive its analytical description for analytical objects. We prove that the supercover of a convex linear object is a discrete analytical object and provide methods to determine the inequalities de ning the supercover.