Optimal point set projections onto regular grids

Abstract

The problem of determining nice (regular, simple, minimum crossing, monotonic) and non-degenerate (with distinct x-coordinate, non-collinear, non-cocircular, non-parallel) orthogonal and perspective images of a set of points or a set of disjoint line segments has been studied extensively in the literature for the theoretical case of infinite resolution images. In this paper we propose to extend the study of this type of problems to the case where the images have finite resolution. Applications dealing with such images are common in practice, in fields such as computer graphics and computer vision. We derive algorithms that solve the simplest problem of obtaining an optimal orthogonal image of a two-dimensional or three-dimensional point set. Due to the high cost of the proposed algorithms we also present algorithms that provide approximate solutions to the problems with better complexity. © Springer-Verlag Berlin Heidelberg 2003.