  An arbitrary order finite difference method for curved boundary domains with
Cartesian grid is proposed. The technique handles in a universal manner
Dirichlet, Neumann or Robin condition. We introduce the Reconstruction Off-site
Data (ROD) method, that transfers in polynomial functions the information
located on the physical boundary. Three major advantages are: (1) a simple
description of the physical boundary with Robin condition using a collection of
points; (2) no analytical expression (implicit or explicit) is required,
particularly the ghost cell centroids' projection are not needed; (3) we split
up into two independent machineries the boundary treatment and the resolution
of the interior problem, coupled by the the ghost cell values. Numerical
evidences based on the simple 2D convection-diffusion operators are presented
to prove the ability of the method to reach at least the 6th-order with
arbitrary smooth domains.
