Cylindrical coordinate representations for modeling surfaces of the cornea and contact lenses

The paper develops four alternatives for modeling surfaces of the cornea and contact lenses. The cornea and contact lenses are generally smooth surfaces with possible discontinuities in circumferential or radial patterns. We define surfaces derived from semi-regular tensor product B-spline surfaces over a polar coordinate domain. The semi-regular partition allows finer control over the patch size, which is desirable for adaptive refinement. In geometric space, several patches meet at the origin, potentially resulting in a discontinuity. This is addressed by either imposing a system of constraints or blending the center region into a continuous function. The representations are fit to sampled data from a range of shapes and compared in terms of overall fit and fidelity at the origin. In the cases where constraint equations are used, their effectiveness and consequences on the resulting accuracy are assessed.