Fast approximation of geodesic distances on manifold meshes is important for many applications. In the past, methods have been presented to approximate geodesics using various techniques such as heat propagation. We use wave propagation to estimate geodesic distances that are comparable with exact geodesics as well as other approximate geodesic computations (SNH14).
[SNH14] A Sinha, M Kazhdan. “Geodesics using Waves: Computing Distances using Wave Propagation”, Submitted as Master's project, The Johns Hopkins University, Baltimore, MD (May 21, 2014)