A sufficient condition for 3D typical curves

2D Typical curves (Mineur et al., 1998) are a class of special Bezier curves with monotone curvature, which play a key role in designing aesthetically pleasing surfaces for the automotive industry. To deal with 3D typical curves, Farin (2006) introduces the more general concept of Class A Bezier curves. These curves are defined by so-called Class A matrix that oughts to satisfy some appropriate conditions for guaranteeing the monotonicity of curvature and torsion. In this paper, we first present new conditions for Class A Bezier curves which complete the proof in Farin (2006). Then using these conditions, we propose a new sufficient condition for 3D typical curves. More, we discover that Farin's claim (Farin, 2006) on 3D typical curves is incorrect. Numerical examples are provided to validate the correctness of our theorems. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This paper introduces new conditions for Class A Bezier curves and proposes a new sufficient condition for 3D typical curves. It corrects previous claims and validates the correctness of new theorems through numerical examples.