一种基于Hermite插值的离散点构造曲面的新算法

A NEW METHOD OF SCULPTURED SURFACE STRUCTURED WITH SCATTERED DATA BASED ON HERMITE ALGORITHM

摘要: 提出了一种通过矩形作用域划分、迭加来构造曲面的新思想.在此基础之上,对实际测量的三维离散点进行特殊的Hermite插值构造曲面,并通过重叠的矩形作用域的迭加以形成一张新曲面.文中证明了这种方法的完备性,并严格证明了所构造曲面对实际测量点的依赖性,而不会因为迭加出现奇异点.

Abstract: A new method for reconstruction of a sculptured surface from division and accumulation of a rectangle is proposed．This method consists of accumulations of several overlapped rectangles，followed by a piecewise bicubic Hermite interpolation to three-dimensional scattered data．The completion of this method and the geometric property of the new structured surface which is dependent on data points are certified．