On Formulation and Display for Visualizing Features and Evaluating Quality of Free-form Surfaces

Abstract

For evaluating quality of free-form surfaces and visualizing their features, various curves on a surface, which characterize its properties, are defined and their equations are deduced. Newly introduced curves include those of equi-gradient, silhouette, highlight and a locus of points of extremum gradient on contour curves, loci of points of extremum principal curvature on lines of curvature. The objectives of these curves and their uses are described. Other curves such as contour curves, its orthogonal ones, loci of points of zero curvatures, and lines of curvature as well as umbilics are also treated. Displays of these curves are shown.