双曲抛物面上的一类G2连续逼近样条

摘要

Over a hyperbolic paraboloid,a type of splines of G2-continuity can be constructed conveniently based on affine coordinate system, in terms of bi-parametrization equipped with an approximation factor, and studying on a family of functions between these two parameters.When control polygon is a parallelogram, and the approximation factor is greater than certain number,spline curves on it are of shape retention.The approximation effect of the type of splines is theoretically analyzed.%在双曲抛物面上,仿射坐标系下,通过带逼近控制因子的双参数化方法,以及研究其参数间的函数关系构造出一类G2连续样条曲线.当控制多边形是平形四边形时,样条曲线段在逼近控制因子大于某个数时具有保形性质.对这类样条曲线段的逼近问题进行了一定的理论分析.