Nonimaging optics are usually designed as 2-D profiles that are then extruded to form a trough-like optic, or rotated to generate a rotational optic, or crossed to form a square cross-section optic. These optics are usually not ideal in 3-D geometry. The Miñano design method using Poisson brackets utilizes an extra degree of freedom to design ideal 3-D optics: a variable refractive index inside the optic. This enables, for example, the design of an ideal 3-D concentrator with flat entrance and exit apertures, acceptance angle θ, and maximum concentration.