  We develop a single pass method for approximating the solution to an
anisotropic eikonal equation related to the anisotropic min-time optimal
trajectory problem. Ordered Upwind Method (OUM) solves this equation, which is
a single-pass method with an asymptotic complexity. OUM uses the search along
the accepted front (SAAF) to update the value at considered nodes. Our
technique, which we refer to as "Neighbor-Gradient Single-Pass Method", uses
the minimizer of the Hamiltonian, in which the gradient is substituted with
neighbor gradient information, to avoid SAAF. Our technique is considered in
the context of control-theoretic problem. We begin by discussing SAAF of OUM.
We then prove some properties of the value function and its gradient, which
provide the key motivation for constructing our method. Based on these
discussions, we present a new single-pass method, which is fast since it does
not require SAAF. We test this method with several anisotropic eikonal
equations to observe that it works well while significantly reducing the
computational cost.
