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Geodesics are essential in many geometry processing applications. However,traditional algorithms for computing geodesic distances and paths on 3D meshmodels are often inefficient and slow. This makes them impractical forscenarios that require extensive querying of arbitrary point-to-pointgeodesics. Although neural implicit representations have emerged as a popularway of representing 3D shape geometries, there is still no research onrepresenting geodesics with deep implicit functions. To bridge this gap, thispaper presents the first attempt to represent geodesics on 3D mesh models usingneural implicit functions. Specifically, we introduce neural geodesic fields(NeuroGFs), which are learned to represent the all-pairs geodesics of a givenmesh. By using NeuroGFs, we can efficiently and accurately answer queries ofarbitrary point-to-point geodesic distances and paths, overcoming thelimitations of traditional algorithms. Evaluations on common 3D models showthat NeuroGFs exhibit exceptional performance in solving the single-sourceall-destination (SSAD) and point-to-point geodesics, and achieve high accuracyconsistently. Besides, NeuroGFs also offer the unique advantage of encodingboth 3D geometry and geodesics in a unified representation. Moreover, wefurther extend generalizable learning frameworks of NeuroGFs by adding shapefeature encoders, which also show satisfactory performances for unseen shapesand categories. Code is made available athttps://github.com/keeganhk/NeuroGF/tree/master.

NeuroGF: A Neural Representation for Fast Geodesic Distance and Path Queries