On manifolds with metrics, minimizing geodesics, or shortest paths, are minimum-length curves connecting points. Various real-world tasks can be reduced to the generation of geodesics on manifolds. Examples include time-optimal path planning on sloping ground [Matsumoto, 1989], robot motion planning under various constraints [LaValle, 2006, Ratliff et al., 2015], physical systems [Pfeifer, 2019], the Wasserstein distance [Agueh, 2012], and image morphing [Michelis and Becker, 2021, Effland et al., 2021]. Typically, metrics are only known infinitesimally (a form of a Riemannian or Finsler metric), and their distance functions are not known beforehand. Computation of geodesics by solving optimization problems or differential equations is generally computationally costly and requires an explicit form of the metric, or at least, values of its differentials.