Harmonic parameterization by electrostatics

Abstract

In this article, we introduce a method to apply ideas from electrostatics to parameterize the open space around an object. By simulating the object as a virtually charged conductor, we can define an object-centric coordinate system which we call Electric Coordinates. It parameterizes the outer space of a reference object in a way analogous to polar coordinates. We also introduce a measure that quantifies the extent to which an object is wrapped by a surface. This measure can be computed as the electric flux through the wrapping surface due to the electric field around the charged conductor. The electrostatic parameters, which comprise the Electric Coordinates and flux, have several applications in computer graphics, including: texturing, morphing, meshing, path planning relative to a target object, mesh parameterization, designing deformable objects, and computing coverage. Our method works for objects of arbitrary geometry and topology, and thus is applicable in a wide variety of scenarios.