一种适合于工程应用的准C^1连续Bézier三角曲面及其构造方法

A Quasi-C^1 Triangular Bezier Surface Fit in with Engineering Application and Its Construction

本文比较系统地讨论了Clough-Tocher三角形分割模型在Bézier三角曲面设计中的作用。并从工程应用的角度提出了一种以Clough-Tocher分割为基础,旨在原三角形区域上构造9参数Bézier三角曲面的新方法。这种新的9参数插值不仅能够消除Clough-Tother分割产生的畸变插值区域对插值曲面品质的影响,还能够有效地减轻一般9参数三次Bézier三角曲面片之间的尖端连接。本文将从工程应用的角度把这种插值曲面称为准C^1连续的9参数Bézier三角曲面。在一些实际应用中,这种准C^1连续的插值曲面对3D离散数据的拟合效果是令人满意的。

This article systematically discussed the Clough-Tocher split triangle and its role in designing the triangular Bezier surface. From the angle of application, the authors put forword a new method of constructing quasi-C1 continuous triangular Bezier surface on given triangular meshes. This kind of interpolant surface can not only effectively lighten the sharp connections between two nine-parameter triangular Bezier patches, but also greatly decrease the number of defing triangular Bezier patches. With this quasi-C1 triangular Bezier surf ace, a satisfactory interpolant result to 3D scattered data may be obtained.