一类双参数类四次三角Bézier曲线及其扩展

摘要

A class of quasi-quartic trigonometric polynomial Bézier curves with double parameters and its extension are defined. The properties of the class of the curves and its extension are obtained, and the necessary and sufficient conditions for G1(C1)、G2(C2) continuously joining with two segments of quasi-quartic trigonometric polynomial Bézier curves and two extensions are given. The applications of them are discussed. Experimental examples show that the class of the curves and its extensions have stronger abilities in curve designing, especially in designing of non-symmetry figures.%给出了一类双参数的类四次三角Bézier曲线及其扩展曲线的定义，得到了该类曲线及其扩展曲线的性质，给出了两段双参数的类四次三角Bézier曲线G1(C1)、G2(C2)及两段扩展曲线G1(C1)、G2(C2)光滑拼接的充要条件，并讨论了这两类曲线的应用。算例表明，该类曲线及其扩展曲线在曲线造型，特别是在非对称图形的造型中，具有很强的描述能力。