一类可调控的G^1连续分段三次多项式曲线

A Class of Modifiable G^1-Continuous Piecewise Cubic Polynomial Curve

给出了一类可调控的G1 连续的分段三次多项式曲线,且在每段曲线上有两个局部形控参数,通过分析该曲线与三次Bezier曲线之间的关系,给出了形控参数的几何意义,调整形控参数可灵活方便改变曲线的形状,最后还把该曲线推广到双三次多项式曲面情形,并给出数值例子和应用。

A class of modifiable G^1-continuous piecewise cubic polynomial curves and two local control parameters on every single piece are presented in this paper. By analyzing the relationships between the curves mentioned above and the cubic Bezier curves,the geometric significance of local control parameters is given and the shape of the curves can be flexibly and easily changed by changing the values of the local control parameters.Finally, it popularizes the curves to the case of cubic polynomial surfaces and provides us rations of figures and their usage.