Rational h-Bézier Curve and Its Representation of Conic Section

The h-Bézier curves are a one-parameter family of generalized Bézier curves.In order to extend the modeling ability of h-Bézier curves and represent conic sections accurately,rational h-Bézier curves are constructed by adding positive real numbers as weights.Firstly,we define rational h-Bézier curves and analyze some basic properties of rational h-Bézier curves.The degree elevation algorithm and de Casteljau algorithm of rational h-Bézier curve are then derived,and an alternative expression of a quadratic rational Bézier curve as a quadratic rational h-Bézier curve is obtained.Moreover,we discuss the classification of conic sections represented by quadratic rational h-Bézier curves from the perspective of algebra and geometry,respectively.In addition,we also give the modeling examples of fountain and arch.Numerical examples show that rational h-Bézier curves have more modeling superiority and flexibility than h-Bézier curves and classical rational Bézier curves.