Smoothing of curves and surfaces
This paper is concerned with the representation of surfaces with a desired shape. When using Bézier or B-splines techniques for interpolation or approximation of curves or surfaces, undesired inflexion points or changes of sign in the Gaussian curvatures may occur. A procedure is described that permits to detect such points by inspecting the associated orthotomic curve or surface. If we consider a point P, not in the surface X, as a light source, the orthotomic surface can be thought as the wave front reflected by X. It turns out that changes in sign in the Gaussian curvatures of X correspond to cusps in the orthotomic surface (caustics), that can be made much more apparent than the changes of curvature in the original surface, as is shown graphically in various examples. It is also indicated how to smooth interactively such undesirable features on Bézier curves by collapsing two of these changes of curvature into a flat point; this is done by finding the zeroes of an appropriate Bézout determinant. This smoothing procedure does not look too practical for surfaces, since fairly high degree polynomials arise in the computation.
scientific article; zbMATH DE number 3921799
scientific article