G² Spline Curves Based on Lupas q-analogue of Bernstein Operator

To improve the shape control ability of freeform curves, based on the properties of the Lupas q-Bernstein operator, new properties of the Lupas q-Bezier curve are given. Further, additional degrees of freedom are obtained by introducing new shape parameters for given control points, and a G² spline curve is constructed by joining piecewise Lupas q-Bezier curves smoothly. In particular, when the shape parameters are selected specially, the curve degenerates into the Gamma spline curve. Theoretical analysis and calculation examples show that the G² spline curve has more flexibility in shape control than the Gamma spline curve.