Generation of Curves and Surfaces with Smoothly Varying Curvature Based on Evolutes (3rd Report)

Generation of Surfaces from Four Boundary Curves

Abstract

This report presents a generation method for surfaces which have four boundary curves and smoothly varying curvature for obtaining smooth highlight lines or reflected images. This method directly interpolates curvature variation as an evolute of a generatrix which moves along directrices. The evolute is represented as a rational Bézier curve and interpolated using its polygons for the boundary curves. Then, it is located to the position on the directrices whose code length and slope vary with the movement. The surface to be generated is a locus of the involute corresponding to the evolute.