Aesthetic Placement of Points Using Generalized Lloyd Relaxation

Abstract

In this paper we describe a computational method for producing aesthetically pleasing distributions of disks on a canvas. The positions of the disks are initially given at random and are moved into interesting configurations by means of a local optimization routine. The configurations are computed by a Voronoi-cell based optimization algorithm (Lloyd's relaxation method). We extend this method in a way that not only evenly spaced but also clustered point sets can be produced. This is done by inverting the iterative step of the optimization algorithm. We define an energy term and show that for a certain amount of energy interesting configurations appear. This is evaluated in a small user study.