Fracture Patterns Design for Anisotropic Models with the Material Point Method

Physically plausible fracture animation is a challenging topic in computer graphics. Most of the existing approaches focus on the fracture of isotropic materials. We proposed a frame-field method for the design of anisotropic brittle fracture patterns. In this case, the material anisotropy is determined by two parts: anisotropic elastic deformation and anisotropic damage mechanics. For the elastic deformation, we reformulate the constitutive model of hyperelastic materials to achieve anisotropy by adding additional energy density functions in particular directions. For the damage evolution, we propose an improved phase-field fracture method to simulate the anisotropy by designing a deformation-aware second-order structural tensor. These two parts can present elastic anisotropy and fractured anisotropy independently, or they can be well coupled together to exhibit rich crack effects. To ensure the flexibility of simulation, we further introduce a frame-field concept to assist in setting local anisotropy, similar to the fiber orientation of textiles. For the discretization of the deformable object, we adopt a novel Material Point Method(MPM) according to its fracture-friendly nature. We also give some design criteria for anisotropic models through comparative analysis. Experiments show that our anisotropic method is able to be well integrated with the MPM scheme for simulating the dynamic fracture behavior of anisotropic materials.     

Minimal Sampling for Effective Acquisition of Anisotropic BRDFs

BRDFs are commonly used for material appearance representation in applications ranging from gaming and the movie industry, to product design and specification. Most applications rely on isotropic BRDFs due to their better availability as a result of their easier acquisition process. On the other hand, anisotropic BRDF due to their structure‐dependent anisotropic highlights, are more challenging to measure and process. This paper thus leverages the measurement process of anisotropic BRDF by representing such BRDF by the collection of isotropic BRDFs. Our method relies on an anisotropic BRDF database decomposition into training isotropic slices forming a linear basis, where appropriate sparse samples are identified using numerical optimization. When an unknown anisotropic BRDF is measured, these samples are repeatably captured in a small set of azimuthal directions. All collected samples are then used for an entire measured BRDF reconstruction from a linear isotropic basis. Typically, below 100 samples are sufficient for the capturing of main visual features of complex anisotropic materials, and we provide a minimal directional samples to be regularly measured at each sample rotation. We conclude, that even simple setups relying on five bidirectional samples (maximum of five stationary sensors/lights) in combination with eight rotations (rotation stage for specimen) can yield a promising reconstruction of anisotropic behavior. Next, we outline extension of the proposed approach to adaptive sampling of anisotropic BRDF to gain even better performance. Finally, we show that our method allows using standard geometries, including industrial multi‐angle reflectometers, for the fast measurement of anisotropic BRDFs.     

On the implementation of rate-independent standard dissipative solids at finite strain – Variational constitutive updates

This paper is concerned with an efficient, variationally consistent, implementation for rate-independent dissipative solids at finite strain. More precisely, focus is on finite strain plasticity theory based on a multiplicative decomposition of the deformation gradient. Adopting the formalism of standard dissipative solids which allows to describe constitutive models by means of only two potentials being the Helmholtz energy and the yield function (or equivalently, a dissipation functional), finite strain plasticity is recast into an equivalent minimization problem. In contrast to previous models, the presented framework covers isotropic and kinematic hardening as well as isotropic and anisotropic elasticity and yield functions. Based on this approach a novel numerical implementation representing the main contribution of the paper is given. In sharp contrast to by now classical approaches such as the return-mapping algorithm and analogously to the theoretical part, the numerical formulation is variationally consistent, i.e., all unknown variables follow naturally from minimizing the energy of the considered system. Consequently, several different numerically efficient and robust optimization schemes can be directly employed for solving the resulting minimization problem. Extending previously published works on variational constitutive updates, the advocated model does not rely on any material symmetry and therefore, it can be applied to a broad range of different plasticity theories. As two examples, an anisotropic Hill-type and a Barlat-type model are implemented. Numerical examples demonstrate the applicability and the performance of the proposed implementation.     

The use of incomplete LU decomposition in modeling convection-diffusion processes in an anisotropic medium

The three-dimensional stationary convection-diffusion problem with mixed derivatives, describing the convection-diffusion processes in an anisotropic medium, is considered. The solution of this problem in an anisotropic medium is of significant interest for various models. A finite-difference upwind approximation of this problem is performed on a thirteen-point stencil. Sufficient conditions for the matrix of the system of linear algebraic equations (SLAE) obtained after natural ordering of the grid domain to be an M-matrix are proved. The SLAE is numerically solved by the method of incomplete LU decomposition, which converges for M-matrices. Numerical experiments were performed, which showed the efficiency of this method for solving the convection-diffusion problem both in isotropic and anisotropic media. A drawback of the method is the restriction on the coefficients multiplying mixed derivatives, which enters into the set of sufficient conditions for the matrix of the operator to be an M-matrix.     

Material interpolation schemes for unified topology and multi-material optimization

This paper presents two multi-material interpolation schemes as direct generalizations of the well-known SIMP and RAMP material interpolation schemes originally developed for isotropic mixtures of two isotropic material phases. The new interpolation schemes provide generally applicable interpolation schemes between an arbitrary number of pre-defined materials with given (anisotropic) properties. The method relies on a large number of sparse linear constraints to enforce the selection of at most one material in each design subdomain. Topology and multi-material optimization is formulated within a unified parametrization.     

Interactive rendering of globally illuminated scenes including anisotropic and inhomogeneous participating media

Although new graphics hardware has accelerated the rendering process, the realistic simulation of scenes including participating media remains a difficult problem. Interactive results have been achieved for isotropic media as well as for single scattering. In this paper, we present an interactive global illumination algorithm for the simulation of scenes that include participating media, even anisotropic and/or inhomogeneous media. The position of the observer is important in order to render inhomogeneous media according to the transport equation. Previous work normally needed to be ray-based in order to compute this equation properly. Our approach is capable of achieving real time using two 3D textures on a simple desktop PC. For anisotropic participating media we combine density estimation techniques and graphics hardware capabilities.     

A new range-free localization method using quadratic programming

In this paper, we propose a new range-free localization algorithm called optimal proximity distance map using quadratic programming (OPDMQP). First, the relationship between geographical distances and proximity among sensor nodes in the given wireless sensor network is mathematically built. Then, the characteristics of the given network is represented as a set of constraints on the given network topology and the localization problem is formulated into a quadratic programming problem. Finally, the proposed method is applied to two anisotropic networks the topologies of which are very similar to those of the real-world applications. Unlike the most of previous localization methods which work well in the isotropic networks but not in the anisotropic networks, it is shown that the proposed method exhibits excellent and robust performances not only in the isotropic networks but also in the anisotropic networks.     

Two-dimensional multi-pixel anisotropic Gaussian filter for edge-line segment (ELS) detection

In order to further improve the performance of the existing anisotropic Gaussian filters and more fully take advantage of structural information of a boundary, we heuristically develop a new multi-pixel anisotropic Gaussian filter to detect edges or edge-line segments directly from low signal-to-noise ratio images. To significantly increase computational efficiency, the classical isotropic Gaussian filters are first used for quickly estimating an approximate direction along an edge; then our filter is applied to more accurately search edge-line segment direction by a few directional filter masks only near such approximate direction. By comparing the proposed filter with the isotropic Gaussian filters, we analyze two improvement factors associated with the localization and SNR of the proposed filter. Experimental results show that the proposed detector can achieve better performance than several existing edge-detection methods in the sense of noise reduction, good localization, and high edge continuity.     

A high-resolution method for the depth-integrated solute transport equation based on an unstructured mesh

This paper presents a high-resolution numerical method for solving mass transport problems involving advection and anisotropic diffusion in shallow water based on unstructured mesh. An alternating operator-splitting technique is adopted to advance the numerical solution with advection and diffusion terms solved separately in two steps. By introducing a new r-factor into the Total Variation Diminishing (TVD) limiter, an improved finite-volume method is developed to solve the advection term with significant reduction of numerical diffusion and oscillation errors. In addition, a coordinate transformation is introduced to simplify the diffusion term with the Green-Gauss theorem used to deal with the anisotropic effect based on unstructured mesh. The new scheme is validated against three benchmark cases with separated and combined advection and diffusion transport processes involved. Results show that the scheme performs better than existing methods in predicting the advective transport, particularly when a sharp concentration front is in presence. The model also provides a sound solution for the anisotropic diffusion phenomenon. Anisotropic diffusion has been largely neglected by existing flow models based on unstructured mesh, which usually treat the diffusion process as being isotropic for simplicity. Based on the flow field provided by the ELCIRC model, the developed transport model was successfully applied to simulate the transport of a hypothetical conservative tracer in a bay under the influence of tides.     

基于典型相关回归的多跳非测距定位方法

多跳非测距定位方法是一种有效的、简单的节点定位方法,然而其一般仅适用于各向同性,节点密集网络。针对在各向异性网络中,多跳非测距定位方法定位性能低的问题,提出了基于典型相关回归非测距定位方法。该方法通过典型相关回归获得节点间跳数与欧氏距离精确的映射模型,并利用该映射获得未知节点到已知节点估计距离。仿真实验表明,该方法与现有算法相比具有更高的定位精度和定位稳定性。     

An optimization-driven approach for computing geodesic paths on triangle meshes

There are many application scenarios where we need to refine an initial path lying on a surface to be as short as possible. A typical way to solve this problem is to iteratively shorten one segment of the path at a time. As local approaches, they are conceptually simple and easy to implement, but they converge slowly and have poor performance on large scale models. In this paper, we develop an optimization driven approach to improve the performance of computing geodesic paths. We formulate the objective function as the total length and adopt the L-BFGS solver to minimize it. Computational results show that our method converges with super-linear rate, which significantly outperforms the existing methods. Moreover, our method is flexible to handle anisotropic metric, non-uniform density function, as well as additional user-specified constraints, such as coplanar geodesics and equally-spaced geodesic helical curves, which are challenging to the existing local methods.     

Extracting Microfacet‐based BRDF Parameters from Arbitrary Materials with Power Iterations

We introduce a novel fitting procedure that takes as input an arbitrary material, possibly anisotropic, and automatically converts it to a microfacet BRDF. Our algorithm is based on the property that the distribution of microfacets may be retrieved by solving an eigenvector problem that is built solely from backscattering samples. We show that the eigenvector associated to the largest eigenvalue is always the only solution to this problem, and compute it using the power iteration method. This approach is straightforward to implement, much faster to compute, and considerably more robust than solutions based on nonlinear optimizations. In addition, we provide simple conversion procedures of our fits into both Beckmann and GGX roughness parameters, and discuss the advantages of microfacet slope space to make our fits editable. We apply our method to measured materials from two large databases that include anisotropic materials, and demonstrate the benefits of spatially varying roughness on texture mapped geometric models.     

A Theoretical Framework for Convex Regularizers in PDE-Based Computation of Image Motion

Many differential methods for the recovery of the optic flow field from an image sequence can be expressed in terms of a variational problem where the optic flow minimizes some energy. Typically, these energy functionals consist of two terms: a data term, which requires e.g. that a brightness constancy assumption holds, and a regularizer that encourages global or piecewise smoothness of the flow field. In this paper we present a systematic classification of rotation invariant convex regularizers by exploring their connection to diffusion filters for multichannel images. This taxonomy provides a unifying framework for data-driven and flow-driven, isotropic and anisotropic, as well as spatial and spatio-temporal regularizers. While some of these techniques are classic methods from the literature, others are derived here for the first time. We prove that all these methods are well-posed: they posses a unique solution that depends in a continuous way on the initial data. An interesting structural relation between isotropic and anisotropic flow-driven regularizers is identified, and a design criterion is proposed for constructing anisotropic flow-driven regularizers in a simple and direct way from isotropic ones. Its use is illustrated by several examples.     

Gaussian MRF rotation-invariant features for image classification

Features based on Markov random field (MRF) models are sensitive to texture rotation. This paper develops an anisotropic circular Gaussian MRF (ACGMRF) model for retrieving rotation-invariant texture features. To overcome the singularity problem of the least squares estimate method, an approximate least squares estimate method is designed and implemented. Rotation-invariant features are obtained from the ACGMRF model parameters using the discrete Fourier transform. The ACGMRF model is demonstrated to be a statistical improvement over three published methods. The three methods include a Laplacian pyramid, an isotropic circular GMRF (ICGMRF), and gray level cooccurrence probability features.     

基于结构张量的自适应CTV彩色图像恢复模型

讨论一种基于非线性扩散方程的彩色图像去噪方法。在图像去噪的3个基本要求的基础上,总结出调和项模型和彩色总变差去噪模型中的不足,利用图像的局部信息构造函数使得模型在接近图像边缘处各向异性平滑并保持边界。在平坦区域各向同性平滑,防止阶梯效应的产生,并利用角点信息保持了角点形状。实验结果表明,所建模型能够较好地保持图像中目标的几何结构,同时具有良好的去噪能力。     

Elasto-plastic analysis of a plane stress problem using linearized yield surface and mixed hardening rule

The objective of this paper is to present the mathematical formulations in the incremental theory of plasticity, which is based on the mixed hardening rule and a linear yield surface. A three-parameter, uniaxial symmetric, linear yield surface suitable for tension-weak as well as equal tension and compression yield stress material is presented. This yield condition, along with the mixed hardening and associated flow rules is used to formulate the constitutive laws for sides and corners of the yield surface. The formulation is based on incremental plasticity with the assumption of small displacements and is suitable for plane stress problems under monotonie and cyclic loading.

The mixed hardening rule, which is mathematically modeled, could be changed to either kinematic or isotropic hardening by a simple change in the model. This hardening rule could handle different degrees of Bauschinger effect, as opposed to kinematic hardening, which assumes only an ideal Bauschinger effect, or isotropic hardening, which does not account for the effect at all. The theory is applied to a ductile material using the finite element method and cyclic loading.     

高精度自适应hp-FEM在电法测井数值模拟中的应用*

介绍了电法测井数值模拟的建模方法并提出一种新型的自适应高阶有限元方法(hp-FEM)用于求解各向异性地层中的电场问题。电场数值模型在相同的误差精度下,从计算时间和计算自由度的角度对h-FEM、p-FEM和hp-FEM进行了计算比较。数值结果表明,在各向同性和各向异性模式下,该自适应hp-FEM的性能(指数速率收敛)明显优于h-FEM和p-FEM。探讨了算法的收敛性,提出的hp-FEM可以改进现有的正演模拟方法,提高分析的正确性和工作效率,对于减小研究周期有重要的应用价值。     

Linear approximation of Bidirectional Reflectance Distribution Functions

Various empirical and theoretical models of the surface reflectance have been introduced so far. Most of these models are based on functions with non-linear parameters and therefore faces some computational difficulties involved in non-linear optimization processes. In this paper, we introduce a new approach for approximating Bidirectional Reflectance Distribution Functions (BRDF) by employing response surface methodology. The proposed model employs principal component transformations of the explanatory variables which are essentially functions of incoming and outgoing light directions. The resulting model is linear and can be used to represent both isotropic and anisotropic reflectance for diffuse and glossy materials. Considering some widely used reflection models including the Ward model, the Ashikhmin–Shirley model and the Lafortune model, we demonstrate empirically that satisfactory approximations can be made by means of the proposed general, simple and computationally efficient linear model.     

Horizontal Large Eddy Simulation of Stratified Mixing in a Lock-Exchange System

This paper presents analytical and numerical results for two new anisotropic modifications of the Rational and Clark-α LES models. The main difference from their standard form is that in this study horizontal (as opposed to isotropic) spatial filtering is used, which is appropriate for turbulent mixing in stratified flows. We present several mathematical results regarding the horizontal Rational and Clark-α LES models. We also present numerical experiments that support the analytical developments and show that both horizontal LES models perform better than their standard, isotropic counterparts in approximating mixing in a 3D lock-exchange problem at Reynolds number Re=10,000.     

Adaptive fingerprint pore modeling and extraction

Sweat pores on fingerprints have proven to be discriminative features and have recently been successfully employed in automatic fingerprint recognition systems (AFRS), where the extraction of fingerprint pores is a critical step. Most of the existing pore extraction methods detect pores by using a static isotropic pore model; however, their detection accuracy is not satisfactory due to the limited approximation capability of static isotropic models to various types of pores. This paper presents a dynamic anisotropic pore model to describe pores more accurately by using orientation and scale parameters. An adaptive pore extraction method is then developed based on the proposed dynamic anisotropic pore model. The fingerprint image is first partitioned into well-defined, ill-posed, and background blocks. According to the dominant ridge orientation and frequency on each foreground block, a local instantiation of appropriate pore model is obtained. Finally, the pores are extracted by filtering the block with the adaptively generated pore model. Extensive experiments are performed on the high resolution fingerprint databases we established. The results demonstrate that the proposed method can detect pores more accurately and robustly, and consequently improve the fingerprint recognition accuracy of pore-based AFRS.