布料仿真中的自适应各向异性应变限制研究

布料仿真技术旨在通过计算机生成逼真的布料动态效果,在虚拟现实、服装动画等领域有着广泛的应用前景. 为了避免仿真过程中布料的过度形变并且提高布料应变的准确性,在布料模拟过程中为布料添加了自适应的各向异性应变限制约束. 首先将布料模型离散化为三角形网格,在每一帧都对布料进行网格重划的基础上,通过定义内积倒数映射,将规定的布料全局应变限制转化为各个三角形形变主轴的局部应变限制,保证了在每次网格重划之后局部应变限制仍然能够和全局应变限制保持一致. 另外在求解过程中,提出了结合罚函数与拉格朗日乘子法的改进方法求解算法得到的约束非线性规划方程. 实验表明,本文所提出的方法有效地提高了应变限制的准确性.     

Interactive thin elastic materials

Despite great strides in past years are being made to generate motions of elastic materials such as cloth and biological skin in virtual world, unfortunately, the computational cost of realistic high‐resolution simulations currently precludes their use in interactive applications. Thin elastic materials such as cloth and biological skin often exhibit complex nonlinear elastic behaviors. However, modeling elastic nonlinearity can be computationally expensive and numerically unstable, imposing significant challenges for their use in interactive applications. This paper presents a novel simulation framework for simulating realistic material behaviors with interactive frame rate. Central to the framework is the use of a constraint‐based multi‐resolution solver for efficient and robust modeling of the material nonlinearity. We extend a strain‐limiting method to work on deformation gradients of triangulated surface models in three‐dimensional space with a novel data structure. The simulation framework utilizes an iterative nonlinear Gauss–Seidel procedure and a multilevel hierarchy structure to achieve computational speedups. As material nonlinearity are generated by enforcing strain‐limiting constraints at a multilevel hierarchy, our simulation system can rapidly accelerate the convergence of the large constraint system with simultaneous enforcement of boundary conditions. The simplicity and efficiency of the framework makes simulations of highly realistic thin elastic materials substantially fast and is applicable of simulations for interactive applications. Copyright © 2015 John Wiley & Sons, Ltd.     

Boundary Handling at Cloth–Fluid Contact

We present a robust and efficient method for the two‐way coupling between particle‐based fluid simulations and infinitesimally thin solids represented by triangular meshes. Our approach is based on a hybrid method that combines a repulsion force approach with a continuous intersection handling to guarantee that no penetration occurs. Moreover, boundary conditions for the tangential component of the fluid's velocity are implemented to model the different slip conditions. The proposed method is particularly useful for dynamic surfaces, like cloth and thin shells. In addition, we demonstrate how standard fluid surface reconstruction algorithms can be modified to prevent the calculated surface from intersecting close objects. For both the two‐way coupling and the surface reconstruction, we take into account that the fluid can wet the cloth. We have implemented our approach for the bidirectional interaction between liquid simulations based on Smoothed Particle Hydrodynamics (SPH) and standard mesh‐based cloth simulation systems.     

A Finite Element Formulation of Baraff-Witkin Cloth

The Baraff-Witkin [BW98] model has been a popular formulation for cloth for 20 years. However, its relationship to the finite element method (FEM) has always been unclear, because the model resists being written as an isotropic, hyperelastic strain energy. In this paper, we show that this is because the Baraff-Witkin model is actually a coupled anisotropic strain energy. We show that its stretching term approximates the isotropic As-Rigid-As-Possible (ARAP) energy, and its shearing term is a cross-fiber coupling energy common in biomechanics. While it has been known empirically for some time that the model can produce indefinite force Jacobians, the conditions under which they occur has never been clear. Our formulation enables a complete eigenanalysis that precisely characterizes exactly when indefiniteness occurs, and leads to fast, analytic, semi-positive-definite projection methods. Finally, our analysis suggests a generalized Baraff-Witkin energy with non-orthogonal warp and weft directions.     

Global Structure Optimization of Quadrilateral Meshes

We introduce a fully automatic algorithm which optimizes the high‐level structure of a given quadrilateral mesh to achieve a coarser quadrangular base complex. Such a topological optimization is highly desirable, since state‐of‐the‐art quadrangulation techniques lead to meshes which have an appropriate singularity distribution and an anisotropic element alignment, but usually they are still far away from the high‐level structure which is typical for carefully designed meshes manually created by specialists and used e.g. in animation or simulation. In this paper we show that the quality of the high‐level structure is negatively affected by helical configurations within the quadrilateral mesh. Consequently we present an algorithm which detects helices and is able to remove most of them by applying a novel grid preserving simplification operator (GP‐operator) which is guaranteed to maintain an all‐quadrilateral mesh. Additionally it preserves the given singularity distribution and in particular does not introduce new singularities. For each helix we construct a directed graph in which cycles through the start vertex encode operations to remove the corresponding helix. Therefore a simple graph search algorithm can be performed iteratively to remove as many helices as possible and thus improve the high‐level structure in a greedy fashion. We demonstrate the usefulness of our automatic structure optimization technique by showing several examples with varying complexity.     

基于机器学习合成高分辨率布料褶皱

为了精化布料网格得到逼真的布料模拟效果,提出了一种基于机器学习的方法合成高分辨率布料褶皱。首先模拟真实的布料运动,获取布料运动的帧数据信息,将布料运动的帧数据信息转换为图像信息的形式进行存储。然后将图像信息作为输入,输入到卷积神经网络(CNN)中进行训练,通过将卷积神经网络与缩小网络相结合,最终得到高分辨率布料图像。最后将高分辨率布料图像转换为高分辨率布料网格,对布料进行模拟。实验结果表明,与初始的低分辨率布料网格对比,合成的高分辨率布料网格模拟出的布料有着大量且细微的褶皱,并且能够模拟出真实的布料效果,与真实场景中的布料模拟效果相似。该方法在不同的场景中都可以模拟出高质量的布料动画效果,而且减少了仿真速度,验证了该方法的有效性。     

边界简化与多目标优化相结合的高质量四边形网格生成

目的 高质量四边形网格生成是计算机辅助设计、等几何分析与图形学领域中一个富有挑战性的重要问题。针对这一问题,提出一种基于边界简化与多目标优化的高质量四边形网格生成新框架。方法 首先针对亏格非零的平面区域,提出一种将多连通区域转化为单连通区域的方法,可生成高质量的插入边界;其次,提出"可简化角度"和"可简化面积比率"两个阈值概念,从顶点夹角和顶点三角形面积入手,将给定的多边形边界简化为粗糙多边形;然后对边界简化得到的粗糙多边形进行子域分解,并确定每个子域内的网格顶点连接信息;最后提出四边形网格的均匀性和正交性度量目标函数,并通过多目标非线性优化技术确定网格内部顶点的几何位置。结果 在同样的离散边界下,本文方法与现有方法所生成的四边网格相比,所生成的四边网格顶点和单元总数目较少,网格单元质量基本类似,计算时间成本大致相同,但奇异点数目可减少70% 80%,衡量网格单元质量的比例雅克比值等相关指标均有所提高。结论 本文所提出的四边形网格生成方法能够有效减少网格中的奇异点数目,并可生成具有良好光滑性、均匀性和正交性的高质量四边形网格,非常适用于工程分析和动画仿真。     

The Matchstick Model for Anisotropic Friction Cones

Inspired by frictional behaviour that is observed when sliding matchsticks against one another at different angles, we propose a phenomenological anisotropic friction model for structured surfaces. Our model interpolates isotropic and anisotropic elliptical Coulomb friction parameters for a pair of surfaces with perpendicular and parallel structure directions (e.g. the wood grain direction). We view our model as a special case of an abstract friction model that produces a cone based on state information, specifically the relationship between structure directions. We show how our model can be integrated into LCP and NCP-based simulators using different solvers with both explicit and fully implicit time-integration. The focus of our work is on symmetric friction cones, and we therefore demonstrate a variety of simulation scenarios where the friction structure directions play an important part in the resulting motions. Consequently, authoring of friction using our model is intuitive and we demonstrate that our model is compatible with standard authoring practices, such as texture mapping.     

基于几何测量和变形的真实感织物模拟

提出一种有效、直观的基于几何测量和网格变形的织物模拟方法,可以获得具有不同面料属性的织物真实感形态.织物几何测量方法能够度量反映面料几何属性的3个关键特征,包括复原性、拉伸性和弯曲性.对应这3个几何属性度量,建立包括顶点位置、边长和二面角约束能量项的基于微分网格变形的泛函能量优化模型.3个变形能量项各自对应的权重是从每种真实面料测量数据中量化统计得到.该变形能量函数可以统一在最小二乘数值优化中求解,通过过程优化和权重设置,即可模拟到真实织物行为.实验结果表明,该方法可以有效地仿真到不同面料材质的织物真实感效果.     

Freeform surface flattening based on fitting a woven mesh model

This paper presents a robust and efficient surface flattening approach based on fitting a woven-like mesh model on a 3D freeform surface. The fitting algorithm is based on tendon node mapping (TNM) and diagonal node mapping (DNM), where TNM determines the position of a new node on the surface along the warp or weft direction and DNM locates a node along the diagonal direction. During the 3D fitting process, strain energy of the woven model is released by a diffusion process that minimizes the deformation between the resultant 2D pattern and the given surface. Nodes mapping and movement in the proposed approach are based on the discrete geodesic curve generation algorithm, so no parametric surface or pre-parameterization is required. After fitting the woven model onto the given surface, a continuous planar coordinate mapping is established between the 3D surface and its counterpart in the plane, based on the idea of geodesic interpolation of the mappings of the nodes in the woven model. The proposed approach accommodates surfaces with darts, which are commonly utilized in clothing industry to reduce the stretch of surface forming and flattening. Both isotropic and anisotropic materials are supported.     

A Data‐Driven Approach for Real‐Time Clothes Simulation†

A data‐driven approach for the real‐time processing of clothes, particularly suitable for simulating dresses worn by virtual characters, is proposed. It starts, prior to real‐time simulation, by analyzing cloth behavior in relation to the underlying skeleton movement from a presimulated sequence of the cloth obtained using any high‐quality off‐line simulators. The idea is to use this analysis to find an optimal combination of physics‐based simulation and geometric approximation of the simulator; potentially colliding regions are defined on the cloth such that they will hold true for the skeleton movement that closely matches that of presimulated sequence. At runtime, using these analyses, our simulation process provides both visually pleasing results and performance, as long as the motion of the character remains sufficiently close to the original sequence used for the precomputation. The key contributions of this paper are (1) efficient collision handling that prunes out potentially colliding objects by using the off‐line simulation sequence as examples; (2) data‐driven fix‐up process for the coarse mesh simulation that deduces the gross behavior of the cloth; and (3) geometric approximation of the fine mesh deformation, responsible for details in the shape of the cloth such as wrinkles.     

Retiling scheme: a novel approach of direct anisotropic quad-dominant remeshing

Remeshing has been an active research topic in Digital Geometry Processing. In this paper, a novel approach of direct anisotropic quad-dominant remeshing is proposed. We apply the retiling method to the particular problem of quad-dominant remeshing. Compared with other methods, this method can simply partition the surface of an original triangular mesh into connected quads with the mesh edges aligning to the principal directions. The first step in this method is to estimate and smooth the curvature tensor field of the surface at the vertices, and then the quad-dominant mesh is obtained by retiling the quad surface so that quadrilateral edges are parallel to the local principal curvature directions. In addition, to preserve the sharp feature information during remeshing processes, the feature lines can be extracted using mesh segmentation method, and the intersections between the feature lines and the orthogonal planes can be found during the process of retiling. A feature fusion process is presented to join the feature edges and feature points into the quad-dominant mesh. The experiment results show that this new remeshing method is simple and easy to implement. The resolution of the quadrilateral mesh can be controlled during the remeshing. It is applicable to arbitrary genus meshes and can generate high-quality quad-dominant mesh.     

基于平均曲率的布料模拟弯曲模型

通过对布料特性及内部结构的研究与分析,针对布料的弯曲特性提出一种非线性弯曲近似模型。首先对实际布料的弯曲属性值进行测量,获得布料的弯曲属性参数;然后,在此基础上建立基于平均曲率的弯曲近似模型来表示弯曲力。其次,利用曲面的平均曲率与高斯曲率对布料的三角网格模型进行分区划分。最后,根据子区域平均曲率的变化对弯曲力进行更新。仿真实验中,在不影响布料模拟质量的前提下,与Volino弯曲模型相比在弯腰时关键帧的速度平均提高了2.7%,抬臂时关键帧的速度平均提高了4.1%。实验结果表明,该模型对弯曲力的计算兼顾了简单性和精确性,能充分表现衣服褶皱细节,生成的衣服褶皱较真实。     

服装动态效果的仿真技术

真实性和实时性一直是服装动态效果仿真所追求的目标.为了对服装的动态效果进行真实的仿真,就必须对织物的所有主要参数进行精确的模拟,如弹力和粘力.实时服装动画的一个难点就是对服装褶皱的模拟,以及相应的碰撞检测问题.对服装动态效果仿真技术的现状进行了介绍,并对未来的发展提出了一些看法.     

布料上污渍效果的真实感模拟

布料上的污渍效果是计算机游戏和影视制作中有待模拟的细节之一.提出一种基于物理的布料上污渍效果的真实感模拟的方法--采用多层模型对布料进行建模.对于污渍在布料上的渗透和扩散运动,提出了NSEAM(Navier-Stokes equations for anisotropie media)模型,它可以模拟污渍和布料之间的相互作用,如扩散作用、蒸发作用、渗透作用等.最后,采用硬件加速的方法对上述过程进行了真实感绘制.实验结果表明,文中方法可以生成不同结构的布料上较为逼真的污渍效果,其绘制效果令人满意.     

布料仿真技术在游戏中的设计和实现

近几年来,布料仿真技术广泛应用于游戏开发中,本文针对游戏在实时性和交互性方面的特殊需求,结合“网络游戏公共技术平台关键技术研究”项目,对布料的物理模型、模型求解以及碰撞检测和处理等方面进行了分析和设计,并在此基础上实现了几种布料动画的模拟。     

极大熵条件下的动态搜索优化图象重建方法

提出一种满足多种准则的动态搜索优化图象重建方法。从图象场的本质出发，设立了３个准则函数。熵函数的导数是非线性的，本文将其变换为近似的线性公式以获得迭代公路。动态搜索则尽可能避免很多算法在迭代过程中对图象校正过量或不足的问题。     

Anisotropic quadrilateral mesh generation: An indirect approach

In this paper a new indirect approach is presented for anisotropic quadrilateral mesh generation based on discrete surfaces. The ability to generate grids automatically had a pervasive influence on many application areas in particularly in the field of Computational Fluid Dynamics. In spite of considerable advances in automatic grid generation there is still potential for better performance and higher element quality. The aim is to generate meshes with less elements which fit some anisotropy criterion to satisfy numerical accuracy while reducing processing times remarkably. The generation of high quality volume meshes using an advancing front algorithm relies heavily on a well designed surface mesh. For this reason this paper presents a new technique for the generation of high quality surface meshes containing a significantly reduced number of elements. This is achieved by creating quadrilateral meshes that include anisotropic elements along a source of anisotropy.     

Improvements in the membrane behaviour of the three node rotation-free BST shell triangle using an assumed strain approach

In this paper an assumed strain approach is presented in order to improve the membrane behaviour of a thin shell triangular element. The so called Basic Shell Triangle (BST) has three nodes with only translational degrees of freedom and is based on a Total Lagrangian Formulation. As in the original BST element the curvatures are computed resorting to the surrounding elements (patch of four elements). Membrane strains are now also computed from the same patch of elements which leads to a non-conforming membrane behaviour. Despite this non-conformity the element passes the patch test. Large strain plasticity is considered using a logarithmic strain–stress pair. A plane stress behaviour with an additive decomposition of elastic and plastic strains is assumed. A hyperplastic law is considered for the elastic part while for the plastic part an anisotropic quadratic (Hill) yield function with non-linear isotropic hardening is adopted. The element, termed EBST, has been implemented in an explicit (hydro-)code adequate to simulate sheet-stamping processes and in an implicit static/dynamic code. Several examples are given showing the good performance of the enhanced rotation-free shell triangle.