Reducing Search Regions for Fast Detection of Exact Point-to-Point Geodesic Paths on Meshes

Fast detection of exact point-to-point geodesic paths on meshes is still challenging with existing methods. For this, we present a method to reduce the region to be investigated on the mesh for efficiency. It is by our observation that a mesh and its simplified one are very alike so that the geodesic path between two defined points on the mesh and the geodesic path between their corresponding two points on the simplified mesh are very near to each other in the 3D Euclidean space. Thus, with the geodesic path on the simplified mesh, we can generate a region on the original mesh that contains the geodesic path on the mesh, called the search region, by which existing methods can reduce the search scope in detecting geodesic paths, and so obtaining acceleration. We demonstrate the rationale behind our proposed method. Experimental results show that we can promote existing methods well, e.g., the global exact method VTP (vertex-oriented triangle propagation) can be sped up by even over 200 times when handling large meshes. Our search region can also speed up path initialization using the Dijkstra algorithm to promote local methods, e.g., obtaining an acceleration of at least two times in our tests.