A quadratic Bézier representation withholds a curve segment with free from loops, cusps and inflection points. Furthermore,
this rational form provides extra freedom to generate visually pleasing curves due to the existence of weights. In this
paper, we propose sufficient conditions for rational quadratic Bézier curves to possess monotonic increasing/decreasing
curvatures by means of monotone curvature tests which are based on the derivative of curvature functions. We have
derived a simple interval of the middle weight that assures the construction of a family of rational quadratic Bézier curves
to be planar spirals, which is characterized by the turning angle, end curvatures and the chords of control polygon.
The proposed formulation can be used by CAD systems for aesthetic product design, highway/railway design and robot
trajectory design avoiding unwanted curvature oscillations.