The kinetic 3D voronoi diagram: A tool for simulating environmental processes

Abstract

Simulations of environmental processes are usually modelled by partial differential equations that are approximated with numerical methods, based on regular grids. An attractive alternative for simulating a fluid flow is the Free-Lagrange Method (FLM). In this paper, I discuss the use of the FLM-based on the Voronoi diagram (VD)-for the modelling of fluid flow in three dimensions (e.g. the movement of underground water or of pollution plumes in the ocean). Such a technique requires the kinetic three-dimensional VD, which is a VD for which the points are allowed to move freely in space. I present a new algorithm for the movement of points in a three-dimensional VD, and show that it can be relatively easy to implement as it is the extension of a simple two-dimensional algorithm.