A fast skeletonisation of 2D objects using a generalised double-layer potential and the H-matrix method

Abstract

This paper proposes a fast numerical method to calculate the so-called topological skeleton of two-dimensional objects. The proposed method is based on a generalised double-layer potential that provides a smoothed singed distance field for an object given in a surface format and is thus considered CAD-friendly. To efficiently evaluate the skeleton, we here incorporate the H-matrix method to calculate the potential. Numerical experiments show that, although sometimes the H-matrix method might become unstable, the skeleton can be calculated with sufficient accuracy within acceptable computational time in many practical cases.