摘要
一、引言给定插值数据点集{（x<sub>i</sub>,y<sub>i</sub>）}<sub>i-0</sub><sup>n</sup>,在许多实际应用中（VLSI,CAD/CAM等）,要求插值曲线除满足一定的光滑性条件外,还必须反映插值点集的整体几何性质。例如,通常要求单调（凸）数据产生的插值曲线是单调（凸）的。
An important problem in CAGD is to pass a smooth curve throgh a set oftwo--or three-dimensional points. Hermite scheme is used widely in CAGD. But the shapeof the interpolatory curve largely depends on the moduli of tangent vectors as well as theparametric knots, and the shape--adjusting can not be implemented interactively by meansof geometric approaches. This article studies the problem of rational interpolation, providesan approach for contruction C^1 shape--preserving rational cubic interpolatory curves. andwith the shape parameters. the shape of the curve can be adjusted locally by means ofgeometric methods. The shape parameters contained in rational curves have the function oftension parameters. Furtherrnore, this paper presemts an algorithm that combinesinteractive techniques with interpolatory methods to allow user intervention.
出处
《纯粹数学与应用数学》
CSCD
1992年第1期89-96,共8页
Pure and Applied Mathematics
