Elastic Tubes: Modeling Elastic Deformation of Hollow Tubes

The Cosserat theory of elastic rods has been used in a wide range of application domains to model and simulate the elastic deformation of thin rods. It is physically accurate and its implementations are efficient for interactive simulation. However, one requirement of using Cosserat rod theory is that the tubular object must have rigid cross‐sections that are small compared to its length. This requirement make it difficult for the approach to model elastic deformation of rods with large, non‐rigid cross‐sections that can change shape during rod deformation, in particular, hollow tubes. Our approach achieves this task using a hybrid model that binds a mesh elastically to a reference Cosserat rod. The mesh represents the surface of the hollow tube while the reference rod models bending, twisting, shearing and stretching of the tube. The cross‐sections of the tube may take on any arbitrary shape. The binding is established by a mapping between mesh vertices and the rod's directors. Deformation of the elastic tube is accomplished in two phases. First, the reference rod is deformed according to Cosserat theory. Next, the mesh is deformed using Laplacian deformation according to its mapping to the rod and its surface elastic energy. This hybrid approach allows the tube to deform in a physically correct manner in relation to the bending, twisting, shearing, and stretching of the reference rod. It also allows the surface to deform realistically and efficiently according to surface elastic energy and the shape of the reference rod. In this way, the deformation of elastic hollow tubes with large, non‐rigid cross‐sections can be simulated accurately and efficiently.     

Cosserat Nets

Cosserat nets are networks of elastic rods that are linked by elastic joints. They allow to represent a large variety of objects such as elastic rings, coarse nets, or truss structures. In this paper, we propose a novel approach to model and dynamically simulate such Cosserat nets. We first derive the static equilibrium of the elastic rod model that supports both bending and twisting deformation modes. We further propose a dynamic model that allows for the efficient simulation of elastic rods. We then focus on the simulation of the Cosserat nets by extending the elastic rod deformation model to branched and looped topologies. To round out the discussion, we evaluate our deformation model. By comparing our deformation model to a reference model, we illustrate both the physical plausibility and the conceptual advantages of the proposed approach.     

A novel framework for physically based sculpting and animation of free-form solids

This paper presents a new, physically based model for performing finite element simulation of deformable objects in which all quantities – strain, stress, displacement, etc. – are computed entirely in local frames of reference. In our framework, subdivision solids with non-homogeneous material properties, such as mass and deformation distributions, can be defined throughout continuous, volumetric domains. This capability enables an animator or virtual sculptor to exert fine-level control over deforming objects and to define a wide variety of physical behaviors. Furthermore, since all quantities pertinent to physical simulation are computed locally, our model facilitates both large-scale and small-scale deformations, as well as rigid or near-rigid transformations. We demonstrate applications of our framework in animation and interactive sculpting and show that interactive simulation of non-trivial, volumetric shapes is possible with our methodologies.     

Direct Position‐Based Solver for Stiff Rods

In this paper, we present a novel direct solver for the efficient simulation of stiff, inextensible elastic rods within the position‐based dynamics (PBD) framework. It is based on the XPBD algorithm, which extends PBD to simulate elastic objects with physically meaningful material parameters. XPBD approximates an implicit Euler integration and solves the system of non‐linear equations using a non‐linear Gauss–Seidel solver. However, this solver requires many iterations to converge for complex models and if convergence is not reached, the material becomes too soft. In contrast, we use Newton iterations in combination with our direct solver to solve the non‐linear equations which significantly improves convergence by solving all constraints of an acyclic structure (tree), simultaneously. Our solver only requires a few Newton iterations to achieve high stiffness and inextensibility. We model inextensible rods and trees using rigid segments connected by constraints. Bending and twisting constraints are derived from the well‐established Cosserat model. The high performance of our solver is demonstrated in highly realistic simulations of rods consisting of multiple 10 000 segments. In summary, our method allows the efficient simulation of stiff rods in the PBD framework with a speedup of two orders of magnitude compared to the original XPBD approach.     

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.     

The application of interactive dynamic virtual surgical simulation visualization method

In this paper, an interactive dynamic simulation method is proposed to solve computational models of soft tissue undergoing large deformation, collision detection, and volume conservation in medical surgical simulation visualization. During the process of implementation of the interactive dynamic simulation method, the point-based method is used to simulate the elastic solids undergoing large deformations and the position-based method is used to simulate the objects collision, friction and volume conservation. Numerical results demonstrate that the proposed method improves the efficiency and stability of the response of heterogeneous soft tissue undergoing contact or even the multi-organs interactions, and it can be extended to interactive biopsy and cutting simulation.

     

Physically Based Deformable Models in Computer Graphics

Physically based deformable models have been widely embraced by the Computer Graphics community. Many problems outlined in a previous survey by Gibson and Mirtich have been addressed, thereby making these models interesting and useful for both offline and real‐time applications, such as motion pictures and video games. In this paper, we present the most significant contributions of the past decade, which produce such impressive and perceivably realistic animations and simulations: finite element/difference/volume methods, mass‐spring systems, mesh‐free methods, coupled particle systems and reduced deformable models‐based on modal analysis. For completeness, we also make a connection to the simulation of other continua, such as fluids, gases and melting objects. Since time integration is inherent to all simulated phenomena, the general notion of time discretization is treated separately, while specifics are left to the respective models. Finally, we discuss areas of application, such as elastoplastic deformation and fracture, cloth and hair animation, virtual surgery simulation, interactive entertainment and fluid/smoke animation, and also suggest areas for future research.     

Real-Time Simulation of Thin Shells

This paper proposes a real-time simulation technique for thin shells undergoing large deformation. Shells are thin objects such as leaves and papers that can be abstracted as 2D structures. Development of a satisfactory physical model that runs in real-time but produces visually convincing animation of thin shells has been remaining a challenge in computer graphics. Rather than resorting to shell theory which involves the most complex formulations in continuum mechanics, we adopt the energy functions from the discrete shells proposed by Grinspun et al. [ [GHDS03] ]. For real-time integration of the governing equation, we develop a modal warping technique for shells. This new simulation framework results from making extensions to the original modal warping technique [ [CK05] ] which was developed for the simulation of 3D solids. We report experimental results, which show that the proposed method runs in real-time even for large meshes, and that it can simulate large bending and/or twisting deformations with acceptable realism.     

Animation of fracture by physical modeling

The breaking of solid objects, like glass or pottery, poses a complex problem for computer animation. We present our methods of using physical simulation to drive the animation of breaking objects. Breakage is obtaned in a three-dimensional flexible model as the limit of elastic behavior. This article describes three principal features of the model: a breakage model, a collision-detection/response scheme, and a geometric modeling method. We use networks of point masses connected by springs to represent physical objects that can bend and break. We present effecient collision-detection algorithms, appropriate for simulating the collisions between the various pieces that interact in breakage. The capability of modeling real objects is provided by a technique of building up composite structures from simple lattice models. We applied these methods to animate the breaking of a teapot and other dishware activities in the animationTipsy Turvy shown at Siggraph '89. Animation techniques that rely on physical simulation to control the motion of objects are discussed, and further topics for research are presented.     

Boundary Stabilization of a Cosserat Elastic Body

Boundary stabilization of vibrating three‐dimensional Cosserat elastic solids are studied using mathematical tools, such as operator theory and semigroup techniques. The advantages of the boundary control laws for both boundary stabilization problems are investigated. The boundary stabilization problems are studied using a Lyapunov stability method and LaSalle's invariant set theorem. Numerical simulations are provided to illustrate the effectiveness and performance of the designed control scheme.     

A unified particle model for fluid–solid interactions

We present a new method for the simulation of melting and solidification in a unified particle model. Our technique uses the Smoothed Particle Hydrodynamics (SPH) method for the simulation of liquids, deformable as well as rigid objects, which eliminates the need to define an interface for coupling different models. Using this approach, it is possible to simulate fluids and solids by only changing the attribute values of the underlying particles. We significantly changed a prior elastic particle model to achieve a flexible model for melting and solidification. By using an SPH approach and considering a new definition of a local reference shape, the simulation of merging and splitting of different objects, as may be caused by phase change processes, is made possible. In order to keep the system stable even in regions represented by a sparse set of particles we use a special kernel function for solidification processes. Additionally, we propose a surface reconstruction technique based on considering the movement of the center of mass to reduce rendering errors in concave regions. The results demonstrate new interaction effects concerning the melting and solidification of material, even while being surrounded by liquids. Copyright © 2007 John Wiley & Sons, Ltd.     

Combining physically-based simulation of colliding objects with trajectory control

This paper describes a method that facilitates the use of physically-based models by animators. The main point is to give the animator a familiar interface, while providing a simulation module which detects collisions, thus enhancing realism. The user gives a set of key-frames to guide motion, but does not have to address problems such as interpenetration avoidance, deformations due to collisions, or realism of motion. The simulator will correct the trajectories and compute deformations according to each object's physical properties (such as mass, inertia, stiffness) as well as the collisions and contacts automatically detected during motion. To achieve this, objects are provided with actuators capable of generating forces and torques computed via generalized proportional-derivative controllers. When deflected by external actions, actuated objects try to return to their initial path. Speed variations over time are computed during the simulation, and depend on the complexity of the paths, on the objects models, and on the events such as collisions occurring during motion. In addition simulations are generated at interactive rates, even in the case of complex articulated objects. This facilitates the fine tuning of an animation sequence.     

Assembly simulation of multi-branch cables

Cable assembly simulation is a key issue in the computer-aided design (CAD) of products with complex electrical components. In this study, an assembly simulation method is developed to simulate the assembly process of multi-branch cables. First, based on the Cosserat theory of elastic rods, a novel scheme is introduced to model the joints of multi-branch cables. The potential energy of joints is calculated by taking the topology and anatomical features into consideration. Various physical properties are considered. Various constraints, including connectors, collars, and handles are analyzed, based on which the initial conditions of assembly simulation are determined. The configuration of the cable is then calculated by minimizing its potential energy. To increase computational efficiency, GPU acceleration is introduced, which makes the simulation run at interactive rates even for a cable with resolution up to 1000 discrete points. Finally, the proposed algorithm is integrated into the commercial assembly simulation system, DELMIA. Several simulations were performed with our system. It was demonstrated that the proposed method is able to handle cables with complex topologies. In addition, the proposed method is about four times as efficient as a previous method, and it is able to generate realistic configurations of multi-branch cables at interactive rates. Thus, the proposed method is helpful in the assembly process planning of cables.     

Hybrid Geometric — Image Based Rendering

We present a Hybrid Geometric‐Image Based Rendering (HGIBR) system for displaying very complex geometrical models at interactive frame rates. Our approach replaces distant geometry with a combination of image‐based representations and geometry, while rendering nearby objects from geometry. Reference images are computed on demand, which means that no pre‐processing, or additional storage are necessary. We present results for a massive model of a whole offshore gas platform, to demonstrate that interactive frame rates can be maintained using the HGIBR approach. Our implementation runs on a pair of PCs, using commodity graphics hardware for fast 3D warping.     

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.     

基于Cosserat 弹性杆理论的柔性线缆物理建模方法

针对虚拟环境中线缆敷设过程仿真的线缆建模问题,提出一种基于Cosserat 弹性 杆理论的柔性线缆物理建模方法。该方法在线缆离散模型的基础上根据Cosserat 弹性杆理论导 出线缆的总体势能,并通过优化算法得到线缆总体势能最小时的线缆形态,即线缆的平衡状态。 模型考虑到线缆的柔性和连续性,能够模拟线缆的弯曲和扭转变形;通过对线缆进行离散表达, 实现了对线缆总体势能的数值求解;引入罚函数将求解线缆总体势能最小值问题转化为非线性 无约束优化问题;非线性无约束优化问题的求解采用信赖域方法,提高了求解的稳定性。设计 并开发了虚拟环境中的线缆敷设过程仿真原型系统,并进行实例验证,证明该方法的可行性。     

A realistic elastic rod model for real-time simulation of minimally invasive vascular interventions

Simulating intrinsic deformation behaviors of guidewire and catheters for interventional radiology (IR) procedures, such as minimally invasive vascular interventions is a challenging task. Especially real-time simulations for interactive training systems require not only the accuracy of guidewire manipulations, but also the efficiency of computations. The insertion of guidewires and catheters is an essential task for IR procedures and the success of these procedures depends on the accurate navigation of guidewires in complex 3D blood vessel structures to a clinical target, whilst avoiding complications or mistakes of damaging vital tissues and blood vessel walls. In this paper, a novel elastic model for modeling guidewires is presented and evaluated. Our interactive guidewire simulator models the medical instrument as thin flexible elastic rods with arbitrary cross sections, treating the centerline as dynamic and the deformation as quasi-static. Constraints are used to enforce inextensibility of guidewires, providing an efficient computation for bending and twisting modes of the physically-based simulation model. We demonstrate the effectiveness of the new model with a number of simulation examples.     

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.