三维散乱点的c^1曲面插值及应用

C1 Interpolation to 3D Arbitrary Points and Its Application

本文介绍了一种对三维散乱点插值的二次Bernstein-Bezier c^1曲面构造方法。首先,不规则分布的3D数据点{(x_i,y_i,z_i),i=1,2,3,…,N}被投影到X-Y平面上,并按本文提出的能够处理任意区域内不规则分布点的三角化算法,自动形成平面三角形插值网络。然后按照所形成的三角形网络和网络结点处的函数值,分别估计出每一数据点上的一阶导数值。最后本文给出了用二次多项式表示的三角形网络上的Bernstein-Bezier c^1曲面插值公式,并指出了这一曲面插值模型在某些应用领域的广阔前景。

This article introduces a method of constructing the c1 quadratic Bernstein-Bezier surface of 3D arbitrary points. Firstly these points {( xiyizi)i = 1,2,3,...,N} are cast onto the X-Y plane and automatically triangulated according to a new algorithm designed by the authors. Secondly, by the function value and the triangular mesh,the derivativas on each point can be approximatelly calculated. Finally,an optimal c1 Bernstein-Bezier interpolation formula on the triangular mesh is put forward by the authors and some application prospects for this cl surface model are described.