Geodesic Distance Computation via Virtual Source Propagation

Abstract

We present a highly practical, efficient, and versatile approach for computing approximate geodesic distances. The method is designed to operate on triangle meshes and a set of point sources on the surface. We also show extensions for all kinds of geometric input including inconsistent triangle soups and point clouds, as well as other source types, such as lines. The algorithm is based on the propagation of virtual sources and hence easy to implement. We extensively evaluate our method on about 10000 meshes taken from the Thingi10k and the Tet Meshing in the Wild data sets. Our approach clearly outperforms previous approximate methods in terms of runtime efficiency and accuracy. Through careful implementation and cache optimization, we achieve runtimes comparable to other elementary mesh operations (e.g. smoothing, curvature estimation) such that geodesic distances become a “first‐class citizen” in the toolbox of geometric operations. Our method can be parallelized and we observe up to 6× speed‐up on the CPU and 20× on the GPU. We present a number of mesh processing tasks easily implemented on the basis of fast geodesic distances. The source code of our method is provided as a C++ library under the MIT license.

Convex Quadratic Programming for Computing Geodesic Distances on Triangle Meshes

“…The key idea is to propagate a dynamic outward wavefront across mesh faces in a Dijkstra-like sweep. Later, the Geodesic Source Propagation (GSP) method [24] is introduced, relying on the propagation of virtual sources. The algorithm distinguishes itself by replacing the traditional priority queue with a dual queue system based on two FIFO queues and adopting an organized cache-coherent mesh layout, thereby enhancing performance.…”

“…Note, that the Geodesic Source Propagation (GSP) method [24] relies on the propagation of virtual sources, distinguishing itself from traditional approximation algorithms. GSP can be considered as a simplified version of exact algorithms.…”

Comparative Analysis of Vincenty and Geodesic Method Approaches in Measuring the Distance Between Subdistrict Offices in Salatiga City

“…Windarni et al's research, entitled Determination of Land Area with the Circle Approach Method Based on Google Earth and GADM for the Semarang Regency Region [9], use Google Earth data and the GADM database to obtain the boundaries of each subdistrict in the form of latitude and longitude coordinates and researchers also study how to obtain the area of a subdistrict in Semarang Regency by applying the circle approach method and the Karney polygon method. Trettner et al's research, entitled Geodesic Distance Computation via Virtual Source Propagation [10], presents a practical, efficient and versatile approach for calculating geodesic distance estimates. The method is designed for triangle meshes, with a set of point sources on the surface.…”