The differential geometry of surfaces describes both intrinsic and extrinsic properties: the intrinsic ones, such as the metric, are inherent, whereas extrinsic ones describe shape relative to 3D space, such as the distribution of surface normal vectors. This paper describes how the surface normals of a non-rotationally-symmetric illumination lens are generated, via Snell's law in vector form, from (1) the distribution of light from a sources, and (2) a desired directional distribution of light exiting the lens. These two distributions are expressed as grids with cells of variable size but constant photometric flux, on the Gaussian sphere of directions. The grids must be sufficiently fine so as to generate enough surface normal vectors for accurate numerical generation of the requisite surface. The grids must have the same number of cells, and the same topology (i.e., rectangular vs. polar). The source-intensity grid must be adjusted to account for Fresnel reflection losses. For an unfaceted (smooth-surfaced) lens, the array of surface normal vectors must be adjusted for equality of the crossed partial derivatives. This class of lenses has only recently become producible due to the advent of electric- discharge machining for the shaping of non-rotationally symmetric injection molds for plastic lenses.