縮閉線に基づく曲率変化の滑らかな曲線，曲面の生成 （第５報） 滑らかなハイライト線を持つ曲面の生成

Abstract

This research proposes a surface generation method which satisfies the designer's intention to the surfaces and smoothness of the reflected images on them. The method directly determines the curvature distribution of a surface, which is represented by a locus of the evolute of the generatrix moved along the directrices. In this report, the evolute surface formed by the locus is modified according to a criterion of the hilight lines which are silhouette pattern of the given surface. The criterion is the square of projected curvature of highlight lines per unit length. To obtain the surafaces which satisfy the criterion, the evolutes of their sections along the direction of highlight lines are determined to change smoothly. They are represented with two segments of the second-degree rational Bézier curves, whose parameters are determined to minimize the criterion. The method is extended to determine a surface when a highlight line is given by a designer. Some examples of boundary curves with various patterns of curvature variation are shown to be generated as smooth surfaces.