Curvature of planar aesthetic curves

Farin proposed a method for designing Bezier curves with monotonic curvature and torsion. Such are relevant in design due to their aesthetic shape. The relies on applying matrix M the first edge of control polygon curve order obtain by iteration remaining edges. With this method, sufficient conditions $M$ provided, which lead definition Class A curves, generalising previous result Mineur et al plane being composition dilatation rotation. However, Cao Wang have shown counterexamples such conditions. In paper, we revisit Farin's idea using subdivision algorithm relate at every point initial produce closed formula planar terms eigenvalues seed vector curve, polygon. Moreover, give new curvature. main difference is that do not require our be preserved under curve. This facilitates giving unified derivation existing results more general case.