曲率変化の滑らかな曲線の評価基準と創成法

Abstract

This paper describes criteria and generation methods of a curve which has monotonously and smoothly varying curvature under the constraints of tangent directions and curvature values at arbitrary points on the curve. The criteria are represented by the first and second derivatives of curvature and shown as regions of the m-n space whose coordinates are normarized lengths of Bezier edge vectors. The sufficient condition of the criteria is introduced by geometrically determining a control polygon of a Bezier curve with relation to its angles and edge lengths. And these Bezier curves are connected smoothly to satisfy the constraints.