Simulation Of Deformable Objects Research Articles

An Algorithm for the Fast Simulation of Multicomponent Object Deformation

In this paper, a fast algorithm for the simulation of deformable objects composed of multiple components made of different materials is introduced. By using the boundary element method and considering individual components and their interfaces separately, a relationship between the unknown and known displacements is established. Based on this expression, a component-based condensation method can be applied. This reduces the size of the matrix to be inverted to depend only on the number of unknown displacements of the components with changing boundary condition. To speed up the construction of the required matrices, a maximal matrix method is proposed. By categorizing the changes in boundary conditions, three fast update strategies on matrix inverse are introduced. Based on the maximal matrix method and the matrix inverse update strategy, we define eight easily formed characteristic matrices, which enhance the computation speed further. The efficiency of the proposed method is demonstrated by a set of experimental results.

MSRS: A fast linear solver for the real-time simulation of deformable objects

Nowadays many interactive computer graphics applications deal with soft-bodies. These applications are always demanding higher and higher levels of realism, increasing the complexity of the animated scenarios. Therefore, the techniques used to animate the objects should be very efficient to grant interactivity. Most often, an accurate answer is not needed and a visually plausible one is enough. One of the most important issues in physically based simulations is to keep the model stable under all simulation conditions. In this paper we present a technique called matrix system reduction solver (MSRS) to highly accelerate the real-time simulation of a finite element-based technique. Our method is fast, visually plausible and robust. In the first stage of the algorithm an initial solution is estimated. Then, only those equations showing a large error are solved using a more precise technique. In the final stage the linear and angular momenta are corrected. Experimental results show the feasibility of this new approach from the point of view of performance compared to the results provided by the stiffness warping method.

Mesh Ensemble Motion Graphs

We explore the use of space-time cuts to smoothly transition between stochastic mesh animation clips involving numerous deformable mesh groups while subject to physical constraints. These transitions are used to construct Mesh Ensemble Motion Graphs for interactive data-driven animation of high-dimensional mesh animation datasets, such as those arising from expensive physical simulations of deformable objects blowing in the wind. We formulate the transition computation as an integer programming problem, and introduce a novel randomized algorithm to compute transitions subject to geometric nonpenetration constraints. We present examples for several physically based motion datasets, with real-time display and optional interactive control over wind intensity via transitions between wind levels. We discuss challenges and opportunities for future work and practical application.

Geometrically exact dynamic splines

In this paper, we propose a complete model handling the physical simulation of deformable 1D objects. We formulate continuous expressions for stretching, bending and twisting energies. These expressions are mechanically rigorous and geometrically exact. Both elastic and plastic deformations are handled to simulate a wide range of materials. We validate the proposed model in several classical test configurations. The use of geometrical exact energies with dynamic splines provides very accurate results as well as interactive simulation times, which shows the suitability of the proposed model for constrained CAD applications. We illustrate the application potential of the proposed model by describing a virtual system for cable positioning, which can be used to test compatibility between planned fixing clip positions, and mechanical cable properties.

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.

Modelling 3D semi-deformable tubes in real time

Numerical simulation of deformable objects is an important problem in biomechanical engineering and computational science. A significant class of problems in this area requires that the simulation results are presented both haptically and graphically in real time (an example being a medical training simulator based on virtual reality). In such cases various types of trade-offs between accuracy and efficiency are implemented. Numerical procedures for modelling deformable objects, with respect to their efficiency, mainly belong to the following two classes: interactive methods (that are fast but have moderate accuracy), and continuum mechanics based methods (that are accurate, but generally not fully interactive). In this paper we present a numerical method based on oriented splines for the numerical simulation of semi-deformable tubes. The numerical results demonstrate both the accuracy and the interactivity of the proposed method, making it a suitable component of complex systems for interactive virtual reality simulations of biomechanical systems.

A Cellular Neural Network Methodology for Deformable Object Simulation

This paper presents a new methodology to simulate soft object deformation by drawing an analogy between a cellular neural network (CNN) and elastic deformation. The potential energy stored in an elastic body as a result of a deformation caused by an external force is propagated among mass points by a nonlinear CNN. The novelty of the methodology is that: 1) CNN techniques are established to describe the potential energy distribution of the deformation for extrapolating internal forces and 2) nonlinear materials are modeled with nonlinear CNNs rather than geometric nonlinearity. Integration with a haptic device has been achieved for deformable object simulation with force feedback. The proposed methodology not only predicts the typical behaviors of living tissues, but it also accommodates isotropic, anisotropic, and inhomogeneous materials, as well as local and large-range deformation.

Optimized linear FEM for modeling deformable objects

AbstractThe main contribution of our work is a technique to accelerate the real‐time simulation of deformable objects using a stable finite element method. Our purpose is to construct a preconditioner matrix for the coefficient matrix of the implicit integration scheme based on the global rotation matrix of the object. We describe some required steps to compute an optimal preconditioner in an off‐line step. Our technique can be used to accelerate the element stiffness warping method and could be used to solve the system directly for objects with small deformations or for objects that appear outside of the users' interest zone. Copyright © 2006 John Wiley & Sons, Ltd.

An autowave based methodology for deformable object simulation

This paper presents a new methodology for deformable object simulation by drawing an analogy between autowaves and elastic deformation. The potential energy stored in an elastic body as a result of a deformation caused by an external force is propagated among mass points by non-linear autowaves. The novelty of the methodology is that autowave techniques are established to describe the potential energy distribution of a deformation for extrapolating internal elastic forces, and non-linear material properties are modelled with non-linear autowaves other than geometric non-linearity. A haptic virtual reality system has been developed for deformation simulation with force feedback. The proposed methodology not only deals with large-range deformations, but also accommodates isotropic, anisotropic and inhomogeneous materials by simply modifying diffusion coefficients.

Interactive cutting of deformable objects using force propagation approach and digital design analogy

Interactive cutting simulation of deformable objects is primarily achieved by modifying the mesh topology of the objects in real time. As cutting proceeds arbitrarily, it results in many possible cases of topological changes that make the design of generic cutting algorithms a tedious bookkeeping task. This paper presents an interactive cutting simulation approach based on mass–spring system. By the analogy of digital design, a systematic method is proposed to trace and manage the topology changes during interactive cutting. The dynamics of deformable objects and the cutting-induced deformation are simulated by the force propagation among the mass-points. In the meantime, adaptive mesh refinements by three processes—redistribution, remeshing and relaxation—are carried out in the process of interactive topology modification. The proposed method is scalable by controlling the extent of localized simulation. It is suitable for cutting simulation in virtual surgery and applications involving the cutting of soft deformable objects.

An Accelerated BEM Approach for the Simulation of Deformable Objects

AbstractThis paper introduces an approach for speeding up the simulation on deformable objects with the boundary element method (BEM). According to the relationship between a matrix and its inverse, the inverse operation on an objective matrix can be completed by calculating the inverse of another matrix with smaller dimension. An update procedure on inverse calculation for three cases is analyzed to avoid directly computing the matrix inverse every time when the boundary condition changes. Besides, a fast matrix-matrix multiplication (MMM) method is conducted to further improve the computational speed.

Discrete multiscale vector field decomposition

While 2D and 3D vector fields are ubiquitous in computational sciences, their use in graphics is often limited to regular grids, where computations are easily handled through finite-difference methods. In this paper, we propose a set of simple and accurate tools for the analysis of 3D discrete vector fields on arbitrary tetrahedral grids. We introduce a variational, multiscale decomposition of vector fields into three intuitive components: a divergence-free part, a curl-free part, and a harmonic part. We show how our discrete approach matches its well-known smooth analog, called the Helmotz-Hodge decomposition, and that the resulting computational tools have very intuitive geometric interpretation. We demonstrate the versatility of these tools in a series of applications, ranging from data visualization to fluid and deformable object simulation.

A boundary element method for simulation of deformable objects

In this paper, a boundary element method is first applied to real-time animation of deformable objects and to simplify data preparation. Next, the visible external surface of the object in deforming process is represented by B-spline surface, whose control points are embedded in dynamic equations of BEM. Finally, the above method is applied to anatomical simulation. A pituitary model in human brain, which is reconstructed from a set of anatomical sections, is selected to be the deformable object under action of virtual tool such as scalpel or probe. It produces fair graphic realism and high speed performance. The results show that BEM not only has less computational expense than FEM, but also is convenient to combine with the 3D reconstruction and surface modeling as it enables the reduction of the dimensionality of the problem by one.