等几何连续介质弹性模型的带厚度布料仿真方法  

Simulation of cloth with thickness based on isogeometric continuum elastic model

作　　者：任靖雯 戴俊飞 蔺宏伟[1,2] Ren Jingwen;Dai Junfei;Lin Hongwei(School of Mathematical Sciences,Zhejiang University,Hangzhou 310058,China;State Key Laboratory of CAD&CG,Zhejiang University,Hangzhou 310058,China)

机构地区：[1]浙江大学数学科学学院,杭州310058 [2]浙江大学计算机辅助设计与图形学全国重点实验室,杭州310058

出　　处：《中国图象图形学报》2024年第1期243-255,共13页Journal of Image and Graphics

基　　金：国家自然科学基金项目(62272406,61775001,61728503);国家重点研发计划资助(2020YFB1708900)。

摘　　要：目的布料仿真是计算机动画领域的一个研究热点和难点,基于粒子系统的模型快速高效却难以准确描述布料真实的物理特性,这些物理属性可以由连续介质的弹性模型利用有限元方法来实现,但所需网格单元较多,求解复杂且耗时。现有方法通常将布料建模为曲面和壳模型,对较厚布料的仿真能力较弱。针对这些常用模型在几何建模、物理真实性和仿真速度上难以兼顾的问题,提出了一种带厚度的布料仿真模型,能够更真实地表达不同厚度布料的形变行为,并利用等几何分析方法进行基于物理的快速动态仿真模拟。方法将有厚度的布料建模为三变量B样条体表示的薄板模型,利用等几何—伽辽金方法,推导出在给定边界条件下三维连续介质线弹性力学方程的弱形式,将B样条体的控制网格作为计算网格进行仿真分析,最后在隐式动力系统框架下对线性方程组直接求解。结果对本文布料模型进行了多方面的讨论和分析。首先,与几种主流的离散模型下的模拟效果进行了光滑度的对比,本文方法的NURBS(nonuniform rational B-splines)建模有着明显的光滑性优势;并在不同自由度下比较了与经典有限元连续介质模型的计算时间,结果表明模拟结果的平方根误差(root mean squared error,RMSE)小于0.04时,本文方法至多能减少90.23%的自由度和99.43%的计算时间;与同厚度面料的连续介质壳模型相比,计算时间减少约30%。其次,对于经典场景如悬布、旗帜和接触问题,实现了逼真快速的动态模拟效果。此外,还展示和讨论了控制网格的密度、基函数的阶数和物理参数等的选择对模拟效果的影响,验证了通过适当的几何参数和物理参数,使用更高分辨率的控制网格或更高阶的基函数将会促进更多的模拟细节效果。结论本文提出的等几何方法模拟的厚布料模型是同时满足仿真效果和速度基本要求的�Objective Cloth simulation is a research hotspot and difficulty in the field of computer animation.Cloth simulation can be seen in a variety of topics such as visual effects,game development,industrial design,and interactive virtual environments.With the demand for high-quality experience from users today,various models have been proposed to improve simulation performance.Although the models based on the particle system are fast and efficient,they have difficulty accurately capturing the behaviors in accordance with the real physical properties of cloth.These physical properties can be described by the elastic model of continuum employing finite element method(FEM).However,solving with FEM in cloth simulation requires a number of degrees of freedom(or elements),and it is much more complex and timeconsuming.Therefore,existing methods usually model cloth as a surface or a shell,which leads to weak simulation ability of thick cloth.To ease the awkwardness of compromising the geometric modeling,physical authenticity,and computation speed in these models,a new cloth simulation model with thickness is proposed,which describes the deformation behavior of the cloth with different thicknesses more appropriately,and a fast dynamic physically based cloth simulation algorithm is carried out by isogeometric analysis(IGA).IGA treats the physical domain(the geometry)as the computational field,avoiding the mesh generation that has approximating error and is timeconsuming in classical FEM.IGA uses the nonuniform rational B-splines(NURBS)basis functions for the physical domain and the solution field,which has the merit of higherorder continuous solution compared with the traditional linear basis.The direct computation on the control mesh of the physical domain makes solving the physical problems more accurate and faster.Method The thick cloth is initially modeled as a very thin plate expressed by a trivariate B-spline solid.The weft direction and the warp direction of the fabric are free to design,while the basis for the thickness

关 键 词：等几何分析(IGA) 有限元方法(FEM) 弹性力学 物理仿真 布料仿真 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术] O29[自动化与计算机技术—计算机科学与技术]