摘要： 本文较系统地讨论了显式Bézier三角曲面的Clough-Tocher分割构造方法,并从工程应用角度提出了一种准C′连续的Bézier三角曲面。由这种准C′连续的Bézier三角曲面,通过进一步求解整体C′连续的线性方程组,可在给定的三角形网上构造整体C′连续的Bézier三角曲面。这种C′连续的Bézier三角曲面在解决3D离散数据的曲面插值中取得了较好的应用效果。

关键词: Bézier三角曲面, 准C′连续, 3D离散数据, 曲面插值

Abstract: The construction of explicit trlangular Eezier surface is discussed systematically oft the basis of Clough-Tocher triangle split. A quasi-C' triangular Bezier surface is advanced by the authors. An explicit triangular Bezier surface which is defined over a given triangle meshes can be constructed by solving a overall C' continuous equation. This explicit triangular Bezier surface can be widely used in 3 D scattered data intorpolant.