Eulerian approximate ray tracing and applications to grid generation

We introduce a scheme to compute the viscosity solution of the Riemannian Eikonal equation, on a regular grid or triangular mesh and which uses the order given by the Sweeping algorithm, to update the points. We also compute the bicharacteristic curves of the viscosity solution in a domain Omega in Eulerian way: instead of solving a system of ODE for every source point belongs to partial derivativeOmega, we label each ray by a parameter theta and thus we compute a function theta = theta(s, t), theta : Omega subset of R-2 --> R, whose level sets are the rays. We then present some numerical results