Joint reversible watermarking and progressive compression of 3D meshes

A new reversible 3D mesh watermarking scheme is proposed in conjunction with progressive compression. Progressive 3D mesh compression permits a progressive refinement of the model from a coarse to a fine representation by using different levels of detail (LoDs). A reversible watermark is embedded into all refinement levels such that (1) the refinement levels are copyright protected, and (2) an authorized user is able to reconstruct the original 3D model after watermark extraction, hence reversible. The progressive compression considers a connectivity-driven algorithm to choose the vertices that are to be refined for each LoD. The proposed watermarking algorithm modifies the geometry information of these vertices based on histogram bin shifting technique. An authorized user can extract the watermark in each LoD and recover the original 3D mesh, while an unauthorized user which has access to the decompression algorithm can only reconstruct a distorted version of the 3D model. Experimental results show that the proposed method is robust to several attack scenarios while maintaining a good compression ratio.     

A framework for automated and certified refinement steps

The refinement calculus provides a methodology for transforming an abstract specification into a concrete implementation, by following a succession of refinement rules. These rules have been mechanized in theorem provers, thus providing a formal and rigorous way to prove that a given program refines another one. In a previous work, we have extended this mechanization for object-oriented programs, where the memory is represented as a graph, and we have integrated our approach within the rCOS tool, a model-driven software development tool providing a refinement language. Hence, for any refinement step, the tool automatically generates the corresponding proof obligations and the user can manually discharge them, using a provided library of refinement lemmas. In this work, we propose an approach to automate the search of possible refinement rules from a program to another, using the rewriting tool Maude. Each refinement rule in Maude is associated with the corresponding lemma in Isabelle, thus allowing the tool to automatically generate the Isabelle proof when a refinement rule can be automatically found. The user can add a new refinement rule by providing the corresponding Maude rule and Isabelle lemma.     

三维实体仿真建模的网格自动生成方法

有限元网格模型的生成与几何拓扑特征和力学特性有直接关系。建立网格模型时，为了更真实地反映原几何形体的特征，在小特征尺寸或曲率较大等局部区域网格应加密剖分；为提高有限元分析精度和效率，在待分析的开口、裂纹、几何突变、外载、约束等具有应力集中力学特性的局部区域，网格应加密剖分。为此，该文提出了基于几何特征和物理特性相结合的网格自动生成方法。该方法既能有效地描述几何形体，又能实现应力集中区域的网格局部加密及粗细网格的均匀过渡。实例表明本方法实用性强、效果良好。     

卫星导航多干扰源直接定位方法

卫星导航信号到达地面时非常微弱,容易受到各种干扰,给用户带来一定的影响;针对此种情况,面向卫星导航系统多干扰源定位场景,传统两步定位算法受参数估计精度影响较大, DPD_MVDR算法虽然改进了MUSIC算法需要估计目标数这一缺点,但由于使用固定网格分辨率,定位精度与计算复杂度二者无法兼得;针对上述问题,提出一种改进DPD_MVDR的直接定位方法,在直接定位这一关键技术上运用自适应网格细化,其最大优势在于只对干扰源位置附近的网格实现多级细化,能很好地兼顾定位精度与计算复杂度,避免了传统穷举搜索带来的巨大计算复杂度。首先使用DPD_MVDR算法在粗网格下进行位置初始估计,然后在估计位置处进行迭代自适应网格细化,在降低计算复杂度的同时,提高定位精度。仿真表明,改进算法在100 m网格分辨率下计算复杂度明显降低且较DPD_MVDR算法定位精度得到明显提高;适用于对定位精度和定位实时性均有一定要求的场景。     

Adaptive finite-volume solution of complex turbulent flows

This paper describes an automatic local grid adaptation procedure driven by an evaluation of the differential residuals of the RANS equations computed using a higher-order reconstruction operator. A suitable data structure is developed for the local mesh adaptation process to be flexible and low CPU time consuming. The whole procedure is designed in the framework of finite-volume methods on unstructured grids. To avoid the appearance of ill-conditioned near-wall cells in the vicinity of curved surfaces of bodies a global mesh deformation technique is used. The whole procedure is applied to a complex turbulent flow around a high-lift multiple element airfoil in take-off configuration using the Spalart-Allmaras turbulence model. The adaptation is controlled by as many indicators as there are equations involved in the problem. It is demonstrated that the proposed methodology performs rigorous local adaptive mesh refinement and automatically achieves grid independent results. Thus, interesting gains are obtained in terms of CPU time, memory requirement and user effort compared to single mesh computations.     

Theminimal user interface of a simple refinement tool

RefStep is a simple tool for program refinement intended to provide a minimal user interface that supports basicmathematicalmanipulations of terms used for transforming algebraic specifications into imperative programs under the control of refinement rules. Even though the tool has been designed primarily for program refinement, its interface is well suited for general calculational proofs.     

Can local NURBS refinement be achieved by modifying only the user interface?

NURBS patches have a serious restriction: they are constrained to a strict rectangular topology. This means that a request to insert a single new control point will cause a row of control points to appear across the NURBS patch, a global refinement of control. We investigate a method that can hide unwanted control points from the user so that the user’s interaction is with local, rather than global, refinement. Our method requires only straightforward modification of the user interface and the data structures that represent the control mesh, making it simpler than alternatives that use hierarchical or T-constructions. Our results show that our method is effective in many cases but has limitations where inserting a single new control point in certain cases will still cause a cascade of new control points to appear across the NURBS patch.     

基于模式匹配度的用户移动规则挖掘及位置预测方法研究

传统的移动用户位置预测方法由于模式支持度计算方式不合理,存在预测精度偏低的问题。为此,提出了一种基于模式匹配度的用户移动规则挖掘及位置预测方法,并将其用于移动通信系统中,以基台覆盖范围网格为单元的用户位置预测。具体包括三个步骤：通过图的遍历挖掘用户移动模式、基于用户移动模式生成用户移动规则和依据用户移动规则进行位置预测。实验分析使用10个批次轨迹数据进行用户移动规则挖掘,结果表明,该方法挖掘出的用户移动规则数少、支持度高和置信度高,具有高精度的优点。     

Development of adaptive mesh refinement scheme for engine spray simulations

Spray modeling is a critical component to engine combustion and emissions simulations. Accurate spray modeling often requires a fine computational mesh for better numerical resolutions. However, computations with a fine mesh will require extensive computer time. This study developed a methodology that uses a locally refined mesh in the spray region. The fine mesh virtually moves with the liquid spray. Such adaptive mesh refinement can enable greater resolution of the liquid-gas interaction while incurring only a small increase in the total number of computational cells. The present study uses an h-refinement adaptive method. A face-based approach is used for the inter-level boundary condition. The prolongation and restriction procedure preserves conservation of properties in performing grid refinement/coarsening. The refinement criterion is based on the total mass of liquid drops and fuel vapor in each cell. The efficiency and accuracy of the present adaptive mesh refinement scheme is described in the paper. Results show that the present scheme can achieve the same level of accuracy in modeling sprays with significantly lower computational cost as compared to a uniformly fine mesh.     

栅格法三维六面体网格局部加密算法

有限元数值分析的精度和效率与网格单元的划分质量以及疏密程度密切相关,针对三维六面体网格单元之间疏密过渡必须平缓和协调的要求,提出了一套基于8分法的六面体网格加密模板,并给出了相应的数据结构和模板应用方式.为使所有加密单元都有相对应的加密模板,建立了加密信息场调整规则;对需要进行加密的区域首先补充加密单元,按照节点加密属性调整加密信息场,然后根据单元加密属性对加密单元进行分类,按照全加密单元、面加密单元、边加密单元以及过渡加密单元的顺序依次采用相应的模板进行加密,从而实现三维六面体网格的局部协调加密.实例结果表明,采用该套加密模板的六面体网格局部加密算法能够保障密集网格向稀疏网格的平缓和协调过渡,所生成的网格可满足有限元数值计算的要求.     

Context‐Based Coding of Adaptive Multiresolution Meshes

Multiresolution meshes provide an efficient and structured representation of geometric objects. To increase the mesh resolution only at vital parts of the object, adaptive refinement is widely used. We propose a lossless compression scheme for these adaptive structures that exploits the parent–child relationships inherent to the mesh hierarchy. We use the rules that correspond to the adaptive refinement scheme and store bits only where some freedom of choice is left, leading to compact codes that are free of redundancy. Moreover, we extend the coder to sequences of meshes with varying refinement. The connectivity compression ratio of our method exceeds that of state‐of‐the‐art coders by a factor of 2–7. For efficient compression of vertex positions we adapt popular wavelet‐based coding schemes to the adaptive triangular and quadrangular cases to demonstrate the compatibility with our method. Akin to state‐of‐the‐art coders, we use a zerotree to encode the resulting coefficients. Using improved context modelling we enhanced the zerotree compression, cutting the overall geometry data rate by 7% below those of the successful Progressive Geometry Compression. More importantly, by exploiting the existing refinement structure we achieve compression factors that are four times greater than those of coders which can handle irregular meshes.     

Mesh generation and mesh refinement procedures for the analysis of concrete shells

In this paper, a mesh generation and mesh refinement procedure for adaptive finite element (FE) analyses of real-life surface structures are proposed. For mesh generation, the advancing front method is employed. FE meshes of curved structures are generated in the respective 2D parametric space of the structure. Thereafter, the 2D mesh is mapped onto the middle surface of the structure. For mesh refinement, two different modes, namely uniform and adaptive mesh refinement, are considered. Remeshing in the context of adaptive mesh refinement is controlled by the spatial distribution of the estimated error of the FE results. Depending on this distribution, remeshing may result in a partial increase and decrease, respectively, of the element size. In contrast to adaptive mesh refinement, uniform mesh refinement is characterized by a reduction of the element size in the entire domain. The different refinement strategies are applied to ultimate load analysis of a retrofitted cooling tower. The influence of the underlying FE discretization on the numerical results is investigated.     

Elastic mesh technique for 3D BIM simulation with an application to underwater explosion bubble dynamics

The proposed elastic mesh technique (EMT) is a mesh regulation technique, which is based on the assumption that the segments of a mesh are elastic. EMT can be employed in conjunction with the boundary integral method (BIM) for the simulation of three-dimension bubble dynamics in which problems relating to severe mesh distortion as the bubble evolves are a common occurrence. With EMT, the mesh is advanced not by the material velocity, but the optimum shift velocity obtained by minimizing the total elastic energy stored in every segment of the mesh at each time step. In doing so, the prohibitively small time stepping associated with small meshes without EMT in order to maintain numerical stability is mitigated to a large extent. An important feature is that the EMT scheme accords the user the flexibility to implement a non-uniform optimum constitutive relation governing the elastic behavior of mesh segment and which can be further varied with time. Tests were performed for an underwater explosion bubble exhibiting the dynamics of strong jet development with and without EMT for comparison, and the consideration of incorporating EMT as a hybrid system serving as an alternative to the required mesh refinement which is computationally intensive. A full three-dimension simulation of explosion bubble(s) and in the presence of the free surface were further carried out to elucidate the associated flow physics.     

An adaptive learning approach for 3-D surface reconstruction from point clouds.

In this paper, we propose a multiresolution approach for surface reconstruction from clouds of unorganized points representing an object surface in 3-D space. The proposed method uses a set of mesh operators and simple rules for selective mesh refinement, with a strategy based on Kohonen's self-organizing map (SOM). Basically, a self-adaptive scheme is used for iteratively moving vertices of an initial simple mesh in the direction of the set of points, ideally the object boundary. Successive refinement and motion of vertices are applied leading to a more detailed surface, in a multiresolution, iterative scheme. Reconstruction was experimented on with several point sets, including different shapes and sizes. Results show generated meshes very close to object final shapes. We include measures of performance and discuss robustness.     

Hybrid Discretization Methods with Adaptive Yield Surface Detection for Bingham Pipe Flows

We devise a hybrid low-order method for Bingham pipe flows, where the velocity is discretized by means of one unknown per mesh face and one unknown per mesh cell which can be eliminated locally by static condensation. The main advantages are local conservativity and the possibility to use polygonal/polyhedral meshes. We exploit this feature in the context of adaptive mesh refinement to capture the yield surface by means of local mesh refinement and possible coarsening. We consider the augmented Lagrangian method to solve iteratively the variational inequalities resulting from the discrete Bingham problem, using piecewise constant fields for the auxiliary variable and the associated Lagrange multiplier. Numerical results are presented in pipes with circular and eccentric annulus cross-section for different Bingham numbers.     

Refinement and coarsening of surface meshes

This paper presents an adaptation scheme for surface meshes. Both refinement and coarsening tools are based upon local retriangulation. They can maintain the geometric features of the given surface mesh and its quality as well. A mesh gradation tool to smooth out large size differences between neighboring (in space) mesh faces and a procedure to detect and resolve self-intersections in the mesh are also presented. Both are driven by an octree structure and make use of the presented refinement tool.     

Interactive texture design and synthesis from mesh sketches

Geometry mesh introduces user control into texture synthesis and editing, and brings more variations in the synthesized results. But still two problems related remain in need of better solutions. One problem is generating the meshes with desired size and pattern efficiently from easier user inputs. The other problem is improving the quality of synthesized results with mesh information. We present a new two-step texture design and synthesis method that addresses these two problems. Besides example texture, a small piece of mesh sketch drawn by hand or detected from example texture is input to our algorithm. And then a mesh synthesis method of geometry space is provided to avoid optimizations cell by cell. Distance and orientation features are introduced to improve the quality of mesh rasterization. Results show that with our method, users can design and synthesize textures from mesh sketches easily and interactively.     

Generation of 3D mixed element meshes using a flexible refinement approach

This paper describes and discusses the main characteristics and implementation issues of a 3D mixed element mesh generator based on a generalization of the modified octree approach. This mesh generator uses primitive elements of different type as internal nodes, a flexible refinement approach as refinement strategy (primitive elements are not always bisected), and bricks, pyramids, prisms and tetrahedra as final elements. The mesh generation process is divided in several steps: the generation of the initial mesh composed of primitive elements, the refinement of primitive elements until the point density requirements are fulfilled, the generation of a graded mesh between dense and coarse regions, and finally, the recognition of the final elements. The main algorithms and data structures are described in detail for each step of the mesh generation process. As result, examples of meshes that satisfy the Delaunay condition and that can be used with the control volume method are shown.     

A unified subdivision approach for multi-dimensional non-manifold modeling

This paper presents a new unified subdivision scheme that is defined over a k-simplicial complex in n-D space with k≤3. We first present a series of definitions to facilitate topological inquiries during the subdivision process. The scheme is derived from the double (k+1)-directional box splines over k-simplicial domains. Thus, it guarantees a certain level of smoothness in the limit on a regular mesh. The subdivision rules are modified by spatial averaging to guarantee C¹ smoothness near extraordinary cases. Within a single framework, we combine the subdivision rules that can produce 1-, 2-, and 3-manifolds in arbitrary n-D space. Possible solutions for non-manifold regions between the manifolds with different dimensions are suggested as a form of selective subdivision rules according to user preference. We briefly describe the subdivision matrix analysis to ensure a reasonable smoothness across extraordinary topologies, and empirical results support our assumption. In addition, through modifications, we show that the scheme can easily represent objects with singularities, such as cusps, creases, or corners. We further develop local adaptive refinement rules that can achieve level-of-detail control for hierarchical modeling. Our implementation is based on the topological properties of a simplicial domain. Therefore, it is flexible and extendable. We also develop a solid modeling system founded on our subdivision schemes to show potential benefits of our work in industrial design, geometric processing, and other applications.