Quadratic rational h-Bézier curve with monotonic curvature

The h-Bézier curve is a kind of generalized Bézier curve. The rational h-Bézier curve obtained by adding a positive real number weight factor can accurately represent the conic section. In order to obtain conic curve segments with monotone curvature, this paper studies the curvature distribution of standard quadratic rational h-Bézier curves. By discussing the curvature extremum of quadratic rational h-Bézier curves, a necessary and sufficient condition for monotonicity of curve curvature is obtained. From the geometric point of view, for the curve with the first and last control vertices determined, in order to obtain hyperbolic segments and elliptic segments with monotonous curvature, only the middle control vertices need to be on or within the curvature critical circle. Thus, by selecting appropriate intermediate control vertex positions, weight factors w, and shape parameter h, a curvature monotonic quadratic rational h-Bézier curve can be constructed. This method includes the construction methods of quadratic h-Bézier curves with monotonic curvature and quadratic rational Bézier curves, and is more flexible in curve modeling.