The Constructions and Applications of Generalized Bézier Curves with A Control Parameter

A new scheme of parameter curves-generalized Bezier curves by trigonometric polynomial with a control parameter is constructed, which inherits advantages of Bezier curves. The trigonometric polynomial curves can be adjusted by the control parameter when the control points are fixed. Specially, the constructed curves merge into the Bezier curves when λ=0. The generalized Bezier curves can be used to represent straight lines precisely and some remarkable transcendental curves precisely, such as circular arc, ellipse and cardioids etc.