Sectional-curvature preserving skinning surfaces

Abstract

In this work we develop a method for constructing sectional-curvature preserving (scp) C 2-continuous surfaces, which interpolate point-sets lying on parallel planes. The working function space consists of skinning surfaces, whose skeletal lines and blending functions are polynomial splines of nonuniform degree. The asymptotic behaviour of these surfaces and their sectional curvature, as the segment degrees tend to infinity globally or semilocally, is thoroughly studied. This study provides sufficient geometrical conditions on the given data ensuring that, it the segment degrees increase semilocally then the surface will eventually become scp in the corresponding parameter subdomain. Based on the obtained asymptotic results, an automatic algorithm for constructing scp interpolatory surfaces is developed and numerically tested.