We introduce the heat method for solving the single-or multiple-source shortest path
problem on both flat and curved domains. A key insight is that distance computation can be …

Numerical computation of shortest paths or geodesics on curved domains, as well as the
associated geodesic distance, arises in a broad range of applications across digital …

This paper introduces a new approach to computing geodesics on polyhedral surfaces---the
basic idea is to iteratively perform edge flips, in the same spirit as the classic Delaunay flip …

Computing discrete geodesic distance over triangle meshes is one of the fundamental
problems in computational geometry and computer graphics. In this problem, an effective …

This paper presents the Saddle Vertex Graph (SVG), a novel solution to the discrete
geodesic problem. The SVG is a sparse undirected graph that encodes complete geodesic …

We present a highly efficient approach to compute continuous shortest path vector fields on
arbitrarily shaped 3D triangular meshes for robot navigation in complex real-world outdoor …

This article presents a new method to optimally partition a geometric domain with capacity
constraints on the partitioned regions. It is an important problem in many fields, ranging from …

Centroidal Voronoi tessellation (CVT) is a special type of Voronoi diagram such that the
generating point of each Voronoi cell is also its center of mass. The CVT has broad …

Computing geodesic distances on triangle meshes is a fundamental problem in
computational geometry and computer graphics. To date, two notable classes of algorithms …

We present GEGNN, a learning-based method for computing the approximate geodesic
distance between two arbitrary points on discrete polyhedra surfaces with constant time …