Programmable smooth junctions are provided for lenses and molds therefor, particularly for toric lens designs, which enable a numerically controlled (NC) machine to be programmed to machine smooth junctions or transitions between adjacent regions of a lens which have different thicknesses or radii of curvature. First and second mathematical functions f(a) and f(b) are defined which specify the curves of first and second segments of a lens surface. The slope dy/dx is derived of the first and second mathematical functions f(a) and f(b) at the transition between the first and second segments of the lens surface. A mathematical function is defined which describes a desired transition between the first and second segments of the lens. The first and second mathematical functions f(a) and f(b), the derived slopes dy/dx of the first and second mathematical functions f(a) and f(b), and the mathematical function describing the desired transition are then utilized to program a numerically controlled machine to machine the first and second segments of the lens surface and the desired transition between the first and second segments.