基于物理模型的水波动画  

Water Wave Animation Based on the Physical Model

作　　者：秦培煜[1] 陈传波[1] 解洪涛[2] 夏晖[1] 吕泽华[1] 

机构地区：[1]华中科技大学计算机学院,武汉430074 [2]华中科技大学经济学院,武汉430074

出　　处：《计算机科学》2007年第10期238-240,共3页Computer Science

基　　金：本文研究得到国家863项目(编号:2004AA420100)资助。

摘　　要：近年来,自然景物的模拟一直是计算机图形学中最具挑战性的问题之一。关于山、水、云、烟、火焰等自然景物的模拟,在计算机游戏、影视、广告等各种领域中有着广泛的用途。作为自然景物模拟的重要内容,对流水、波浪的模拟正日益引起人们的关注。本文基于二维浅水波方程模型,给出了一种实现水波动画的数值模拟方法。和以往的方法不同的是,本文既没有去特意构造具体的波形函数,也没有去求解复杂的Navier-Stokes方程,而是基于二维浅水波方程模型,采用隐式半拉格朗日积分方法进行求解,在保证稳定性的同时,可以允许大时间步长。实践证明,用该算法模拟水波,效果比较真实,而且在普通的PC平台上即可满足一般动画的实时需求。In recent years, simulating natural phemomena has always been one of the most challeging tasks in compute graphics. Simulating natural phenomena, such as hills, water, cloud, smoke, fire and so on, has been widely used in computer game, movie production, and advertisement, etc. As one of its most important parts, simulating water wave has been given more and more attention. This paper presents a new method for water wave animation based on the twodimensional shallow water equations. Unlike traditional methods, the paper neither constructs special functions to model the shape of water wave individually, nor solves the complex Navie-Stokes equations. Instead, the two-dimensional shallow water equations are integrated by a novel numerical method-the imphcit semi-Lagrangian integration scheme-which allows large timesteps while maintaining stability. Our results show that our models and mehtods are effective and efficient. They can even satisfy the requirements of real time animation under generic PC.

关 键 词：水波动画 浅水波方程 半拉格朗日方法 隐式积分 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]