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Subject: 计算机应用::计算机图形学
Title:
基于有限元方法的气球变形模拟
Author: 王清云
Issued Date: 2015-05-24
Supervisor: 刘学慧
Major: 计算机应用技术
Degree Grantor: 中国科学院研究生院
Place of Degree Grantor: 北京
Degree Level: 硕士
Keyword: 有限元方法 ; 基于物理的模拟 ; 薄壳模型 ; 保体积算法 ; 气球变形动画
Abstract:
基于物理的变形动画是计算机图形学中的重要课题,近年来成为研究热点。薄壳模型是变形体中一类特殊的模型,在生活中随处可见,比如树叶、帽子、气球等。由于这类物体的常见性,薄壳模型的变形在动画、影视、仿真等领域有广泛的应用。薄壳模型与其他模型相比具有独特的特点,这种模型的厚度远远小于其他两个维度,这一点与薄板模型相同,但是薄壳模型初始状态是曲面的,而薄板模型是平面的。

在变形体模拟方法中,有限元方法是连续体模型,相对于质点弹簧模型等离散模型有更好的精度及收敛性,还可以实现不可压等体积方面的效果。近年来,有限元方法在变形动画中取得很大进展,本文也采用有限元方法实现气球的充气变形动画。

气球与其他薄壳模型相比,具有独特的特性:拉伸变形大、弯曲及错切变形小、保体积(厚度随拉伸变化)。之前基于有限元的算法大多针对三维模型或者布料一类的薄板模型,少有的针对薄板模型的算法或者太过复杂,或者没有符合薄壳模型特别是气球材料的特性,无法应用在气球变形中。

本文提出了基于有限元方法的薄壳模型的简单变形算法,并将之应用在气球的充气变形动画中。基于气球的特性,本文增加了保体积算法以及气体模型,使其更贴合真实效果。本文在三角形单元的基础上稍作更改,形成简单的三棱柱模型,忽略弯曲变形、错切变形,并结合保体积算法,实现气球材料的保体积特性。气球充气过程中,由于气球的流动相对于气球的膨胀影响较小,因此本文采用简单的均匀气体模型,忽略气体的流动,尽可能地简化算法,而又不影响模拟效果。本文的最后将本文的算法应用在不同的气球模型中,并与其他算法进行了比较,效果上有很大的改进。

English Abstract:
Physically based deformation animation is an important topic in computer graphics, which has become a research focus. Thin shell is a special model of deformable models, such as hats, leaves, balloons and so on, which can be found anywhere in our life. As a result, thin shell deformation is widely used in animations, movies and simulation systems. However, thin shell model has different nature from other models. Its thickness is small compared to its other dimensions. This nature is similar to thin plate model. Thin shell model has a curved rest configuration, not a flat one of thin plate model.

Among the deformation methods, finite element method is based on continuum mechanics, which is more accurate and convergent than discrete models like mass spring system. Besides, finite element method can capture volumetric effects such as volume preservation. In recent years, deformation simulations based on finite element method have made great progress, and this is also used in our system.

Different from other thin shells, balloons have special nature: more stretching, less bending and shearing, incompressible. Previously deformation methods often focus on 3d models or thin plate models such as cloth. The rest thin shell methods are complex or ignore the special nature of thin shells especially balloons.

In this paper, a simple thin shell deformation algorithm using finite element method is introduced, which is used to simulate the deformation of balloons inflating animation. Considering the nature of balloons, volume preservation algorithm and gas model are added. The triangle element is modified to simple three-prism element, ignoring bending and shearing, and volume preservation algorithm is used to match the incompressible nature of balloons. During inflating, the movement of gas is very small compared with the stretching of rubber, so the gas model is very simple, ignoring the movement of gas. In this way, the algorithm is very simple with an acceptable accuracy. In the end of this paper, this method is tested on different balloon examples including comparison with other methods.

Content Type: 学位论文
URI: http://ir.iscas.ac.cn/handle/311060/17150
Appears in Collections:计算机科学国家重点实验室 _学位论文

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Recommended Citation:
王清云. 基于有限元方法的气球变形模拟[D]. 北京. 中国科学院研究生院. 2015-05-24.
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