  A geometric model for the computation of the firefront of a forest wildfire
which takes into account several effects (possibly time-dependent wind,
anisotropies and slope of the ground) is introduced. It relies on a general
theoretical framework, which reduces the hyperbolic PDE system of any wave to
an ODE in a Lorentz-Finsler framework. The wind induces a sort of double
semi-elliptical fire growth, while the influence of the slope is modeled by
means of a term which comes from the Matsumoto metric (i.e., the standard
non-reversible Finsler metric that measures the time when going up and down a
hill). These contributions make a significant difference from previous models
because, now, the infinitesimal wavefronts are not restricted to be elliptical.
Even though this is a technical complication, the wavefronts remain computable
in real time. Some simulations of evolution are shown, paying special attention
to possible crossovers of the fire.
