2020•Frontiers in PhysicsOpen access

Necessary and Sufficient Conditions for Expressing Quadratic Rational Bézier Curves

Chaoyu Yang, Jie Yang, Ying Liu, Xianya Geng

Abstract

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

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Key concepts: Hyperbola, Bézier curve, Mathematics, Quadratic equation, Parabola, Transformation (genetics), Arc (geometry), Monotonic function