一种二次保形插值参数曲面

1．引言保形插值是工业设计和制造中经常遇到的问题，有关这方面的研究已有许多文献【‘－u1．设n二Fx；，yi，人，川7一0，1，…；n；j＝0；l，…，。；x；＜x；＋1．l＝0，1，…．n—1；yi＜的十；，J二O，L…，。一卫｝是一给定的数据集，Cadson和［ltsch、Beatson和zejerJ－1985年分别提出的方法只保持被插数据集的轴向单调性；Dodd和Roulier等人于1983和1987年提出的方法只保持被插点集网格线上的轴向凸凹性和单调性；Constantini和FOntanella于1990年提出的方法可保持被插点集在所有于区域的边界及共内部的轴向凸凹性和单调性；…

A SHAPE PRESERVING SURFACE INTERPOLATION BY PIECEWISE QUADRATIC PARAMETRIC POLYNOMIALS

A shape preserving surface interpolation scheme to data set without three consecutive collinear data points in both x and y directions is presented, which is a piecewise quadratic parametric polynomials, and is G1 or C1 continuous as desired on the whole domain. The interpolating surface can preserve the convexity, concavity, inflection property and monotonicity of the data set. Futhermore, some parameters (such as the cross boundary tangent vectors of the adjacent sub-surfaces) can be freely chosen within a certain extent to adjust the shape of the interpolating surface or to obtain a better approximation to the original function from which the data come. The shape preserving interpolation to an arbitrary set of data on rectangular grids is also discussed, and an algorithm with generality is described, a special case of which is the algorithm of the above G1 (or C1) shape preserving interpolant. A number of examples of the algorithmsare given.