Uniformly inserting points on square grid
We consider the problem of inserting points in a square grid, which has many motivations, including halftoning in reprography and image processing. The points are inserted one at a time. The objective is to distribute the points as uniformly as possible. More specifically, after each insertion, the gap ratio should be as small as possible. We give an insertion strategy with a maximal gap ratio no more than 2 root 2 approximate to 2.828, which is the first result in uniformly inserting points in a grid. Moreover, we show that no online algorithm can achieve the maximal gap ratio strictly less than 2.5 for a 3 x 3 grid. (C) 2011 Elsevier B.V. All rights reserved.
grid algorithms computational geometry point insertion uniformity