Transfinite interpolation of conic triangles using quadric patches

The use of quadric surface patches to form a continuous approximating surface to given curved surfaces was discussed in a paper by Baart and McLeod. A method was proposed for the construction of continuous patches on a covering mesh of conic segments, where each patch consists of three quadric subpatches, and each conic boundary segment interpolates three points on the given surface. This construction is not unique, and in this paper we investigate the effect of various combinations of the parameters on the resulting quadric patches. We also propose a method that will ensure that, were the given sculptured patch itself quadric, the approximation will be exact.