  We study the variational problem of finding the fastest path between two
points that belong to different anisotropic media, each with a prescribed speed
profile and a common interface. The optimal curves are Finsler geodesics that
are refracted -- broken -- as they pass through the interface, due to the
discontinuity of their velocities. This "breaking" must satisfy a specific
condition in terms of the Finsler metrics defined by the speed profiles, thus
establishing the generalized Snell's law. In the same way, optimal paths
bouncing off the interface -- without crossing into the second domain --
provide the generalized law of reflection. The classical Snell's and reflection
laws are recovered in this setting when the velocities are isotropic. If one
considers a wave that propagates in all directions from a given ignition point,
the trajectories that globally minimize the traveltime generate the wavefront
at each instant of time. We study in detail the global properties of such
wavefronts in the Euclidean plane with anisotropic speed profiles. Like the
individual rays, they break when they encounter the discontinuity interface.
But they are also broken due to the formation of cut loci -- stemming from the
self-intersection of the wavefronts -- which typically appear when they
approach a high-speed profile domain from a low-speed profile.
