2D and 3D visibility in discrete geometry: an application to discrete geodesic paths

Abstract

In this article, we present a discrete definition of the classical visibility in computational geometry based on digital straight lines. We present efficient algorithms to compute the set of pixels in a non-convex domain that are visible from a source pixel. Based on these definitions, we define discrete geodesic paths in discrete domain with obstacles. This allows us to introduce a new geodesic metric in discrete geometry.