3. Basic notions of the differential geometry of surfaces

This chapter assembles the most important definitions and formulas of differential geometry, which are necessary for the calculation of an aspherical, asymmetrical design.

So for a parametric C2 surface the first and second fundamental form are derived and the formulas for the principal curvatures and the principal directions of the surface are calculated. For a simple and complete description of the surface we derive finally the terms for the mean and Gauss curvature, the mean power and surface astigmatism.