A second-order PDE technique to construct distance functions with more accurate derivatives

In this paper we demonstrate the use of an anisotropic PDE to improve the behavior of first and second derivatives of a distance function. We begin by deriving a property of these derivatives and showing a natural relationship between this property and the antigeometric heat flow. We then construct a PDE that combines a known first-order PDE with the antigeometric flow and then demonstrate its effectiveness with a discrete simulation.