基于改进弹簧振子模型的软组织形变仿真

研究虚拟手术中软组织形变的特定性优化问题。传统弹簧振子模型由于采用线弹力方程及显示欧拉积分法求解,导致的真实性低、计算复杂、实时性差的问题。为解决形变动特性问题,提出一种改进弹簧振子模型的形变方法,采用四面体网格弹簧振子模型进行建模,并通过定义质点间弹簧的非线性弹力方程以及作用于质点的体积力方程,来减弱超弹性现象的发生,提高真实性。模型求解时,采用一种改进显式欧拉积分的动态局部算法来求解形变方程。实验结果表明,所提算法提高了形变仿真的真实性、实时性和稳定性,可为软组织形变动态仿真系统的设计提供参考。     

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.     

求无约束极小值的变尺度法

在最优化问题中有的不受约束条件限制，称为无约束最优化问题；但大多数最优化问题，往往受到各种因素的制约，称为约束最优化问题。由于约束最优化问题，大都可通过不同途径化为无约束问题来求解，所以，无约束最优化方法，是解决约束最优化问题的基础。无约束最优化方法大体上可分为两类：一类是直接法，即直接由目标函数求最优解的方法，另一类是间接法，即通过使用函数的导数求最优解，有时还要根据海森矩阵（由若干个二阶偏导数按一定排列所组成的矩阵）所提供的信息而构成各种方法，这些方法统称为梯度法。一般来说，无约束最优化问题…     

基于快速建立四面体网格的有限元心脏建模

针对目前通过医学成像技术获得心脏序列图像来提取相关心脏结构参数,判断心脏的功能的三维心脏建模技术的热点问题.提出了一种基于快速建立四面体网格的有限元心脏建模的方法,结合心脏这种形变模型的各种约束条件,模拟心脏的动态形变,利用有限元与生物力学原理构建心脏表面重建的有限元方程,由心脏表面三角网格数据点快速构建一系列不相重叠的四面体网格单元,以满足单元的应力矢量及单元节点位移矢量计算的需要,为模拟重建心脏运动奠定基础.实验结果表明了有效性和可行性.     

多QoS约束网格作业调度问题的多目标演化算法

针对网格计算中的多QoS约束网格作业调度问题,以独立作业为研究对象,将其规约为多目标组合最优化问题．通过深入剖析多目标最优化理论及其演化算法,结合网格作业调度自然特征,提出了一种解决多QoS约束网格作业调度问题的多目标演化算法．该算法求解多个QoS维度效用函数指标的非劣解集,尝试解决多管理域间网格用户、资源管理者等网格实体的多目标协同问题．仿真结果表明,在时间维度、可靠性维度、安全性维度QoS效用值等用户级QoS指标,以及丢弃作业数等系统级指标方面该算法与QoS-Min-min和QoS-Sufferage等同类算法相比具有较好的综合性能．     

含复杂插值曲面实体四面体网格优化方法

复杂插值曲面的几何形态由分布稀疏且不均匀的散乱数据点控制,含这类曲面实体的四面体网格优化在保证边界一致时存在一定的困难,提出一种将网格优化与曲面插值相结合的优化方法,借鉴Balelldtran提出的直接法,将正三角形结点之间的空间关系作为几何规则,以移动结点使四面体的所有侧面尽量趋近于正三角形,实现网格优化,用线性方程纽表示这种几何规则,形成优化约束.将原始采样点及其它控制界面几何形态的数据转化为控制点约束,以保证边界一致性.结合优化约束与控制点约束,作为离散光滑插值(DSI)方程的约束项,实现网格优化与曲面插值的耦合.实例表明,该方法能够在保证复杂插值曲面边界一致性的前提下实现四面体网格优化.     

非结构网格下曲线变形的水平集方法

采用基于非结构网格的水平集方法对曲线变形问题进行了数值模拟。通过度量函数最优化过程得到曲线变形的驱动方程,驱动方程中增加曲线曲率项对度量函数进行优化,空间上采用有限体积法求解水平集方程,时间上采用Runge-kutta显式方法,时间、空间均达到2阶精度。实验结果得到了高质量的过渡曲线,显示复杂几何拓扑形变可以理想地实现。     

从表面重构的体数据实现三维网格剖分

针对有限元分析中网格最优化问题,本文提出一种改进的生成四面体网格的自组织算法。该算法首先应用几何方法将三角形表面模型重新构造成规定大小的分类体数据,同时由该表面模型建立平衡八叉树,计算用以控制网格尺寸的三维数组;然后将体数据转换成邻域内不同等值面的形态一致的边界指示数组;结合改进的自组织算法和相关三维数据的插值函数,达到生成四面体网格的目的。实验对比表明,该方法能够生成更高比例的优质四面体,同时很好地保证了边界的一致。在对封闭的三维表面网格进行有限元建模时,本文算法为其提供了一种有效、可靠的途径。     

四面体网格生成方法的研究与实现

针对四面体网格生成过程中需要人工构造背景网格和指定尺寸信息的问题,提出了一种自动计算网格尺寸的方法。该方法通过按层次推进产生四面体网格,根据周围前沿面的尺寸和法线信息,计算新生成四面体的尺寸,使四面体网格在尺寸上能够均匀分布。在网格生成过程中,无需人工指定相关信息,并能保证新生成四面体的质量。联立直线和平面的参数方程,根据方程组解的情况判断线段和三角形是否相交,并对相交的条件作了详细的分析。使用空间八叉树管理前沿面,降低与前沿面相关操作的复杂度。数值算例表明,该方法能够生成较高质量的四面体网格。     

基于二维轮廓序列的膝关节三维重建

提出了一个基于二维轮廓序列的四面体网格生成方法,用于医学图像三维几何模型重构.该方法首先对各选定的断层图像提取目标轮廓并做分支匹配等处理,然后生成各轮廓内部平面域的三角网格,最后在相邻断层之间根据三角网格连接四面体单元.该方法被应用于人体膝关节虚拟手术系统的三维几何建模,得到的膝部股骨模型包含494个节点和2 046个四面体单元,膝部脂肪模型包含2 854个节点和14011个四面体单元,这些模型被成功地应用于膝关节手术仿真,从而证明了该三维模型重建方法的可行性和有效性.     

虚拟膝关节手术中的实时大范围形变方法

虚拟膝关节手术过程中要求对膝关节3D几何模型进行实时的大范围形变,而形变的特点,包括总体轮廓、细节保持、实时性、平滑性以及拓扑性等都影响到它的真实感。针对膝关节3D模型得到了一种新的形变方法,根据模型的横截面构建出模型的骨架,并利用柱坐标的变换来实现大范围形变,使形变能保持良好的局部细节特征,算法能满足虚拟手术的实时性和真实感的要求。该方法也能推广应用于其他类似的关节弯曲运动的实时变形。     

基于GA和FEM的夹具布局和变夹紧力优化设计

通过夹具布局和夹紧力大小的优化可以提高薄壁件加工精度．建立了夹具布局和变夹紧力分层优化模型．首先,以工件加工变形最小化和变形最均匀化为目标函数,对夹具布局进行优化设计;其次,基于优化的夹具布局对变夹紧力进行设计．采用有限元法计算工件的加工变形,加工变形求解时综合考虑了接触力、摩擦力、切削力、夹紧力和切屑的影响．采用遗传算法求解优化模型,获得优化的夹具布局和变夹紧力．通过实例分析,验证了分层优化设计方法可以进一步减小工件加工变形,提高加工变形均匀度．     

虚拟膝关节手术中基于骨架的实时形变方法

针对带有骨架的3D模型的大范围形变问题,提出一种改进的梯度域方法,通过在容易引起体积失真的部位(如关节)加入虚拟节点构建体图,采用体微分坐标实现保持体积的形变。通过修改能量函数中的权值,实现表面材料相关的形变。实验表明,该方法能够满足虚拟膝关节手术的实时性和真实感要求。     

Topology optimization based on finite strain plasticity

In this paper infinitesimal elasto-plastic based topology optimization is extended to finite strains. The employed model is based on rate-independent isotropic hardening plasticity and to separate the elastic deformation from the plastic deformation, use is made of the multiplicative split of the deformation gradient. The mechanical balance laws are solved using an implicit total Lagrangian formulation. The optimization problem is solved using the method of moving asymptotes and the sensitivity required to form convex separable approximations is derived using a path-dependent adjoint strategy. The optimization problem is regularized using a PDE-type filter. A simple boundary value problem where the plastic work is maximized is used to demonstrate the capability of the presented model. The numerical examples reveal that finite strain plasticity successfully can be combined with topology optimization.     

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.     

Fast Corotated FEM using Operator Splitting

In this paper we present a novel operator splitting approach for corotated FEM simulations. The deformation energy of the corotated linear material model consists of two additive terms. The first term models stretching in the individual spatial directions and the second term describes resistance to volume changes. By formulating the backward Euler time integration scheme as an optimization problem, we show that the first term is invariant to rotations. This allows us to use an operator splitting approach and to solve both terms individually with different numerical methods. The stretching part is solved accurately with an optimization integrator, which can be done very efficiently because the system matrix is constant over time such that its Cholesky factorization can be precomputed. The volume term is solved approximately by using the compliant constraints method and Gauss‐Seidel iterations. Further, we introduce the analytic polar decomposition which allows us to speed up the extraction of the rotational part of the deformation gradient and to recover inverted elements. Finally, this results in an extremely fast and robust simulation method with high visual quality that outperforms standard corotated FEMs by more than two orders of magnitude and even the fast but inaccurate PBD and shape matching methods by more than one order of magnitude without having their typical drawbacks. This enables a very efficient simulation of complex scenes containing more than a million elements.     

Modeling and Estimation of Energy‐Based Hyperelastic Objects

In this paper, we present a method to model hyperelasticity that is well suited for representing the nonlinearity of real‐world objects, as well as for estimating it from deformation examples. Previous approaches suffer several limitations, such as lack of integrability of elastic forces, failure to enforce energy convexity, lack of robustness of parameter estimation, or difficulty to model cross‐modal effects. Our method avoids these problems by relying on a general energy‐based definition of elastic properties. The accuracy of the resulting elastic model is maximized by defining an additive model of separable energy terms, which allow progressive parameter estimation. In addition, our method supports efficient modeling of extreme nonlinearities thanks to energy‐limiting constraints. We combine our energy‐based model with an optimization method to estimate model parameters from force‐deformation examples, and we show successful modeling of diverse deformable objects, including cloth, human finger skin, and internal human anatomy in a medical imaging application.     

Fast optimization-based elasticity parameter estimation using reduced models

Elasticity parameters are central to physically-based animation and medical image analysis. We present an accelerated method to automatically estimate these parameters for a deformation simulator using an iterative optimization framework, given the desired (target) output surface/shape. During the optimization, the input model is deformed by the simulator, and the distance between the deformed surface and the target surface is minimized numerically. To accelerate the optimization process, we introduce a dimension reduction technique to allow a trade-off between the computational efficiency and desired accuracy. The reduced model is constructed using statistical training with a set of example deformations. To demonstrate this approach, we apply the computational framework to 2D animations of elastic bodies simulated with a linear finite element method. We also present a 3D elastography example, which is simulated with a reduced-dimension finite element model to improve the performance of the optimizer.     

Spindle configuration analysis and optimization considering the deformation in robotic machining applications

Robotic machining is an increasing application due to various advantages of robots such as flexibility, maneuverability and competitive cost. For robotic machining, the machining accuracy is the major concern of current researches. And particular attention is paid to the proper modeling of manipulator stiffness properties, the cutting force estimation and the robot posture optimization. However, through our research, the results demonstrate the spindle configuration largely affects the deformation of the robot end-effector (EE). And it may even account for approximately half of the total deformation for machining applications with the force acting perpendicular to the tool. Furthermore, the closer distance between the tool tip and the EE does not mean that the deformation tends to be smaller. Thus, it is reasonable to consider optimizing the spindle configuration based on the optimal robot posture, thereby exhausting advantages of the robot and further reducing machining errors. In this paper, a spindle configuration analysis and optimization method is presented, aiming at confirming the great influence of the spindle configuration on the deformation of the robot EE and minimizing it. First, a deformation model based on the spindle configuration (SC-based deformation model) is presented, which establishes a mapping between the spindle configuration and the deformation of the robot EE. And it confirms the large effect of the spindle configuration on the deformation of the EE. Then, a complementary stiffness evaluation index (CSEI) is proposed. And it adopts matrix norms to evaluate the influence of the spindle configuration on the complementary stiffness matrix in the SC-based deformation model. Using this index, the proposed SC-based deformation model is simplified for the ODG-JLRB20 robot adopted in this paper. Finally, a spindle configuration optimization model is derived to minimize the simplified SC-based deformation model using an iterative procedure. With this model, the optimal spindle configuration with respect to the EE can be obtained for a specific machining trajectory. Experimental results conducted on the ODG-JLRB20 robot demonstrate the correctness and effectiveness of the present method.     

Gradient Domain Mesh Deformation - A Survey

This survey reviews the recent development of gradient domain mesh deformation method. Different to other deformation methods, the gradient domain deformation method is a surface-based, variational optimization method. It directly encodes the geometric details in differential coordinates, which are also called Laplacian coordinates in literature. By preserving the Laplacian coordinates, the mesh details can be well preserved during deformation. Due to the locality of the Laplacian coordinates, the variat...