Quasi-Bézier Curves with Shape Parameters

The universal form of univariate Quasi-Bézier basis functions with multiple shape parameters and a series of corresponding QuasiBézier curveswere constructed step-by-step in this paper, using themethod of undetermined coefficients.The series ofQuasi-Bézier curves had geometric and affine invariability, convex hull property, symmetry, interpolation at the endpoints and tangent edges at the endpoints, and shape adjustability while maintaining the control points. Various existing Quasi-Bézier curves became special cases in the series. The obvious geometric significance of shape parameters made the adjustment of the geometrical shape easier for the designer. The numerical examples indicated that the algorithm was valid and can easily be applied.