A new method for automatically constructing convexity-preserving interpolatory splines

A new method for automatically constructing convexity-preserving interpolatory splines

PAN Yongjuan;WANG Guojin

【期刊名称】《自然科学进展（英文版）》 【年(卷),期】2004(014)006

【摘要】Constructing a convexity-preserving interpolating curve according to the given planar data points is a problem to be solved in computer aided geometric design (CAGD). So far, almost all methods must solve a system of equations or recur to a complicated iterative process, and most of them can only generate some function-form convexity-preserving interpolating curves which are unaccommodated with the parametric curves, commonly used in CAGD systems. In order to overcome these drawbacks, this paper proposes a new method that can automatically generate some parametric convexity-preserving polynomial interpolating curves but dispensing with solving any system of equations or going at any iterative computation. The main idea is to construct a family of interpolating spline curves first with the shape parameter a as its family parameter; then, using the positive conditions of Bernstein polynomial to respectively find a range in which the shape parameter a takes its value for two cases of global convex data points and piecewise convex data points so as to make the corresponding interpolating curves convexity-preserving and C2(or G1) continuous.