Given is spherical optical power, cylindrical optical power in diopters and cylindrical angle in degrees. Also given is the base curve in millimeters, and the contact lens diameter in millimeters. Also given is the refractive index of the lens (and the outside medium). How do I figure out the shape of the lens from this?

My best guess so far, is that the base curve is the radius of curvature of the inner surface of the lens, shaped like a sphere. My other guess is that the outer surface of the lens is taken from a torus, that has been tilted according to the angle (like holding a donut in front of you and changing its roll).

I am not sure how to relate the optical powers to geometry. I think they might be deltas between the diopters of the two surfaces? Or maybe they are not in units of diopters, but "keratometer readings"(?)?

I am nearsighted so am mostly interested in that case. Would be interesting to understand my prescription in full detail :-)

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