Interactive Control of Curve Segments of Monotone Curvature

Abstract

In this paper, we propose Quasi-Aesthetic Curves and a method for interactively controlling typical class A Bezier curves.Quasi-Aesthetic Curves are curve in the form of rational cubic Bezier curves with approximately linear Logarithmic Curvature Histograms. To verify the monotonicity of curvature of Quasi-Aesthetic Curves, we derive the monotonicity curvature condition of rational cubic Bezier curves.Typical class A Bezier curves are polynomial Bezier curves of monotone curvature. Since typical class A Bezier curves lack interactive control, we develop a method for interactively controlling the curves by specifying two endpoints and their tangents.We show that as the degree of a class A Bezier curve converges to infinity, the curve converges to a logarithmic spiral, which is included in Aesthetic Curves as α=1. Finally, we summarize interactive control method of curves of monotone curvatures and discuss the future directions of research.