A note on Class A Bézier curves

The Class A Bézier curves presented in Farin (2006) were constructed by so-called Class A matrix, which are special matrices satisfying two appropriate conditions. The speciality of the Class A matrix causes the Class A Bézier to possess two properties, which are sufficient conditions for the proof of the curvature and torsion monotonicity. In this paper, we discover that, in Farin (2006), the conditions Class A matrix satisfied cannot guarantee one of the two properties of the Class A Bézier curves, then the proof of the curvature and torsion monotonicity becomes incomplete. Furthermore, we modified the conditions for the Class A matrices to complete the proof.