Study of Curvature Monotony Condition for the Quadratic Rational Bèzier Curves

The curvature monotony condition for the quadratic rational Bézier curve is derived,which possesses more degree of freedom than the non-rational one.The result shows that for arbitrary three control points,a cluster of curves with monotone curvature are always available if the angle between two control edges is not less than 90degree.By using different weight factors,we can get not only a parabola with monotone curvature,but also an ellipse and hyperbola.