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

C. Lincke and C. A. Wüthrich
Computer Graphics, Visualization, Man-Machine Communication Group
Faculty of Media
Bauhaus University Weimar
99421 Weimar, Germany

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 reflected 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 defining the supercover.