Many applications of geometric modeling in manufacturing or for visualization require tangent plane continuous surfaces to interpolate data. While a number of algorithms exist that guarantee local, analytic smoothness, the resulting surfaces often have undesirable extraneous features when compared to a (nonsmooth) piecewise linear surface. Such features are inflection, sharp changes of curvature, bulging between the data sites, etc. The functional and aesthetic implications of these 'shape defects' on the modeled object can be severe. This project will pinpoint sources and nature of the features for specific surface constructions and devise algorithms to systematically modify data and/or the underlying surface representation in order to reduce or remove the features. In particular, the research will build on the experience with a number of algorithms and will investigate and quantify the effects of: 1. a change of continuity constraints across patch boundaries, in particular, the choice of reparametrization; 2) a perturbation of the location of data sites and normals; 3) a change of the representation of the patches; in particular, changing from a polynomial to a rational representation; 4) a perturbation of the neighborhood relations between the data, such as remeshing by removing or inserting boundaries.
