中文摘要：

提高运动流体的可视化效果与效率是近年来科学研究、工程项目、电脑游戏、影视作品、视觉仿真等领域最热门、最具挑战性的课题之一。提出一种将非线性的Catmull．Rom插值样条应用于四边形网格细分的单元剖分改进算法，对二维波面图像进行可视化模拟。针对流体表面由于网格细分引起的波面图像拐点多、不光滑以及计算复杂的问题，在保证计算效率的基础上，得到光滑的图像。用基于St．Andrew的单元剖分算法解决二义性问题，在可视化过程中，跟踪波面的走向从而减少网格的计算与判断。最后以库埃特流体运动为例，实现其二维波面图像的可视化。

英文摘要：

It is one of the most popular and challenging subjects in recently years to improve visualization and efficiency of moving fluid in scientific researches, engineering projects, computer games, film-video works, and visual simulation. This thesis proposes a kind of betterment algorithm that applies the spline interpolation called Catmull- Rom in cell subdivision of squares, so as to conduct visual simulation in 2D-wave surface images. Such problems as roughness, too many bend points and complicated computation caused by cell subdivision of moving fluid surface can be solved by the algorithms to get smooth images on the premise of ensuring computation efficiency. The problem of ambiguity can get resolution by virtue of St Andrew＇s cell subdivision, and then in the process of visualization, the algorithm can track the trend of wave surface to reduce cell computation and judgment. Finally, an example is given in which Couette movement reaches visualization of 2D-wave surface image.