A fast propagation scheme for approximate geodesic paths

Geodesic paths on surfaces are indispensable in many research and industrial areas, including architectural and aircraft design, human body animation, robotic path planning, terrain navigation, and reverse engineering. 3D models in these applications are typically large and complex. It is challenging for existing geodesic path algorithms to process large-scale models with millions of vertices. In this paper, we focus on the single-source geodesic path problem, and present a novel framework for efficient and approximate geodesic path computation over triangle meshes. The algorithm finds and propagates paths based on a continuous Dijkstra strategy with a two-stage approach to compute a path for each propagating step. Starting from an initial path for each step, its shape is firstly optimized by solving a sparse linear system and then the output floating path is projected to the surface to obtain the refined one for further propagation. We have extensively evaluated our algorithms on a number of 3D models and also compared their performance against existing algorithms. Such evaluation and comparisons indicate our algorithm is fast and produces acceptable accuracy.