Abstract: Specialty contact lenses can be designed using approximations of one or both surfaces using mathematical representations. The approximations can be configured to optimize the lens manufacturing process. Constraints can be applied to the approximation to achieve the targeted results. The constraints can be assigned based at least in part on labels applied to measurements of the eye. Lens fit parameters can also be applied to control the degree to which the approximation approaches perfectly matching a targeted shape (e.g., the topography of the patient's eye). For example, the lens fit parameter can be related to the order of the mathematical representation used in the approximation. The contact lenses designed and manufactured using the methods and systems disclosed herein can be of any suitable type including, but not limited to, scleral lenses.