2D Typical curves (Mineur et al., 1998) are a class of special Bézier 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 Bézier 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 Bézier 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.

2D典型曲线（Mineur等人，1998）是一类具有单调曲率的特殊Bézier曲线，它们在为汽车工业设计美观的表面方面起着关键作用。为了处理3D典型曲线，Farin（2006）引入了更通用的A类贝塞尔曲线概念。这些曲线由所谓的A类矩阵定义，该矩阵应满足一些适当的条件，以保证曲率和扭转的单调性。在本文中，我们首先提出A类贝塞尔曲线的新条件，这些条件完成了Farin（2006）中的证明。然后使用这些条件，为3D典型曲线提出一个新的充分条件。此外，我们发现Farin在3D典型曲线上的主张（Farin，2006）是不正确的。提供了数值示例来验证我们定理的正确性。