Necessary and Sufficient Conditions for Expressing Quadratic Rational Bezier Curves

Quadratic rational Bezier curve transformation is widely used in the field of computational geometry. In this paper, we offer several important characteristics of the quadratic rational Bezier curve. More precisely, on the basis of proving its monotonicity, the necessary and sufficient conditions for transforming a quadratic rational Bezier curve into a point, line segment, parabola, elliptic arc, circular arc, and hyperbola are proved, respectively.