We describe a numerical technique to generate logically rectangular body-fitted interior and exterior grids. The technique is based on solving a Hamilton-Jacobi-type equation for a propagating level set function, using techniques borrowed from hyperbolic conservation laws. Coordinate grid lines are kept smooth through curvature terms which regularize the equation of motion, and upwind difference schemes which satisfy the correct entropy conditions of front propagation. The resulting algorithm can be used to generate two- and three-dimensional interior and exterior grids around reasonably complex bodies which may contain sharp corners and significant variations in curvature. The technique may also be easily extended to problems of boundary-fitted moving grids.