In this paper, motion planning of snake robots is considered. In particular, we develop a mapping from a continuous 3D curve to the position and shape of a snake robot. The snake robot's position is the x, y, z coordinates of its center of mass; its shape is defined by a series of angles representing the rotation of each joint relative the the inertial reference frame. Smooth curves are often easier to use in path planning and design of gait patterns, but snake robots are non-smooth. A mapping is therefore necessary. The mapping is optimal in the least squares sense. The optimal configuration is found by explicitly differentiating the cost function, and finding the equilibria. The method is compared to two other methods in literature, and has lower mean square error than both these other methods.