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A method of computer-aided contact lens design and fabrication uses spline-based mathematical surfaces without restrictions of rotational symmetry. The spline encompasses any piecewise function with any associated constraints of smoothness or continuity. The method comprises some or all of the following steps: data acquisition, three-dimcisional mathematical surface model construction, posterior surface description, ray tracing for anterior surface, and peripheral edge system (PES) design. The result is a mathematical or algorithmic description of a contact lens. Based on the more powerful mathematical representation of splines, these contact lenses can have posterior surfaces that provide a good fit to corneas having complicated shapes. This enables the design and fabrication of lenses (including soft lenses) with good optics for irrcgularly shapcd corncas.