Enhanced Heat Method for Computation of Geodesic Distance on Triangular Meshes

We have proposed a method based on the heat method for computing geodesic distance on triangular meshes. The heat method is a very efficient and robust method for computing geodesics on many surfaces. The heat method develops a vector unit field having a gradient the same as that of the distance function and integrates this vector field over the surface by solving a Poisson equation which is required to solve two linear sparse equations. The original heat method uses the direct method to solve those linear equations. The proposed method uses a solver consisting of the algebraic multigrid preconditioned conjugate gradient for solving the linear equations to get the geodesic distance. We observed that using an iterative solver reduces the memory footprint and gives us the option to trade-off between performance and accuracy. The result shows that the proposed method needs less time to compute the geodesic distance for bigger mesh and has significantly reduced memory usage for considered mesh data.