Extension of the quadratic Bézier curves based on the linear combination of basic functions

Based on the idea of the linear combination of basic functions, the quadratic Bézier curves is extended, and the nature of the expansion curve is also discussed in this paper. The extension of the quadratic Bézier curves expresses simple and contains the basic form of the original curve. Not only enhances the shape-control capability of the quadratic Bézier curves, but also keeps the same degree of original one. It is easy to find that the curve can be reshaped by adjusting the shape factor.