A local tangential lifting differential method for triangular meshes

In this note we present a local tangential lifting (LTL) algorithm to compute differential quantities for triangular meshes obtained from regular surfaces. First, we introduce a new notation of the local tangential polygon and lift functions and vector fields on a triangular mesh to the local tangential polygon. Then we use the centroid weights proposed by Chen and Wu [4] to define the discrete gradient of a function on a triangular mesh. We also use our new method to define the discrete Laplacian operator acting on functions on triangular meshes. Higher order differential operators can also be computed successively. Our approach is conceptually simple and easy to compute. Indeed, our LTL method also provides a unified algorithm to estimate the shape operator and curvatures of a triangular mesh and derivatives of functions and vector fields. We also compare three different methods : our method, the least square method and Akima’s method to compute the gradients of functions.     

Single-factor lifting and factorization of polynomials over local fields

Let f(x)$f\left(x\right)$ be a separable polynomial over a local field. The Montes algorithm computes certain approximations to the different irreducible factors of f(x)$f\left(x\right)$, with strong arithmetic properties. In this paper, we develop an algorithm to improve any one of these approximations, till a prescribed precision is attained. The most natural application of this “single-factor lifting” routine is to combine it with the Montes algorithm to provide a fast polynomial factorization algorithm. Moreover, the single-factor lifting algorithm may be applied as well to accelerate the computational resolution of several global arithmetic problems in which the improvement of an approximation to a single local irreducible factor of a polynomial is required.     

面向本地差分隐私的K-Prototypes聚类方法

为了在聚类分析中保护数据隐私的同时确保数据的可用性,提出一种基于本地化差分隐私（LDP）技术的隐私保护聚类方案——LDPK-Prototypes。首先,用户对混合型数据集进行编码;其次,采用随机响应机制对敏感数据进行扰动,而第三方在收集到用户的扰动数据后以最大限度恢复原始数据集;然后,执行K-Prototypes聚类算法,在聚类过程中,使用相异性度量方法确定初始聚类中心,并利用熵权法重新定义新的距离计算公式。理论分析和实验结果表明,所提方案与基于中心化差分隐私（CDP）技术的ODPC算法相比,在Adult和Heart数据集上的平均准确率分别提高了2.95%和12.41%,有效提高了聚类的可用性。同时,LDPK-Prototypes扩大了数据之间的差异性,有效避免了局部最优,提高了聚类算法的稳定性。     

任意三角网格模型体积的快速精确计算方法

三角网格是使用最为广泛的网格模型。提出了一种仅根据三角网格模型的三角面片集合计算模型体积的方法。该方法通过指定投影平面,计算每个三角面片及其在投影平面上的投影所围成的凸五面体的带符号体积（必要时对三角面片进行细分）,整个模型的体积为所有凸五面体带符号体积的代数和。所提出的三角网格模型体积计算方法能实现模型体积的快速准确计算。在大型水电工程施工模拟中施工单元的方量计算测试和不同规模的三角网格模型体积计算测试都证实了该方法的有效性。     

A comparison of local parametric C Bézier interpolants for triangular meshes

Parametric curved shape surface schemes interpolating vertices and normals of a given triangular mesh with arbitrary topology are widely used in computer graphics for gaming and real-time rendering due to their ability to effectively represent any surface of arbitrary genus. In this context, continuous curved shape surface schemes using only the information related to the triangle corresponding to the patch under construction, emerged as attractive solutions responding to the requirements of resource-limited hardware environments. In this paper we provide a unifying comparison of the local parametric C⁰ curved shape schemes we are aware of, based on a reformulation of their original constructions in terms of polynomial Bézier triangles. With this reformulation we find a geometric interpretation of all the schemes that allows us to analyse their strengths and shortcomings from a geometrical point of view. Further, we compare the four schemes with respect to their computational costs, their reproduction capabilities of analytic surfaces and their response to different surface interrogation methods on arbitrary triangle meshes with a low triangle count that actually occur in their real-world use.     

Removing local irregularities of triangular meshes with highlight line models

The highlight line model is a powerful tool in assessing the quality of a surface. It increases the flexibility of an interactive design environment. In this paper, a method to generate a highlight line model on an arbitrary triangular mesh is presented. Based on the highlight line model, a technique to remove local shape irregularities of a triangular mesh is then presented. The shape modification is done by solving a minimization problem and performing an iterative procedure. The new technique improves not only the shape quality of the mesh surface, but also the shape of the highlight line model. It provides an intuitive and yet suitable method for locally optimizing the shape of a triangular mesh. Supported by National Science Foundation of China (Grant Nos. 60533070, 60625202), National Basic Research Program of China (Grant No. 2004CB719400), National High-Tech Research & Development Program of China (Grant No. 2007AA040401), Fok Ying Tung Education Foundation (Grant No. 111070), National Science Foundation of USA (Grant Nos. DMI-0422126, DMS-0310645), and Kentucky Science & Technology Corporation (Grant No. COMM-Fund-712)     

一种3维模型的网格盲水印算法

3维模型的数字水印是数字水印研究的热点之一,鲁棒性、嵌入可读性水印和盲检测是3维模型数字水印的难点所在。从增强3维模型数字水印的鲁棒性出发,提出一种基于局部几何空间的3维模型数字水印算法,它以模型三角网格顶点在其一环邻居顶点为所确定的局部几何空间;通过改变顶点在局部几何空间中的位置来嵌入水印,并以调整其间的夹角来嵌入水印序列的索引,而调整顶点与圆心的距离来嵌入较高比特的二进制数值。本文算法在水印检测时,无需原始模型,且可抵抗平移、旋转、均匀缩放、顶点乱序、剪切及网格简化等攻击。实验结果表明, 该水印算法具有很好的鲁棒性、可读水印的不可感知性和盲水印检测的优势。     

Etree: a database-oriented method for generating large octree meshes

This paper presents the design, implementation, and evaluation of the etree, a database-oriented method for large out-of-core octree mesh generation. The main idea is to map an octree to a database structure and perform all octree operations by querying and updating the database. We apply two standard database techniques, the linear octree and the B-tree, to index and store the octants on disk. Then we introduce two new techniques, auto-navigation and local balancing, to address the special needs of mesh generation. Preliminary evaluation suggests that the etree method is an effective way of generating very large octree meshes on desktop machines.     

A local search method for periodic inventory routing problem

Inventory routing problem considers inventory allocation and routing problems simultaneously, in which the replenishment policies and routing arrangement are determined by the supplier under the vendor managed inventory mode. What we consider here is a periodic inventory routing problem that once the delivery time, quantity and routing are determined, they will remain the same in the following periods. The problem is modeled concisely, and then it is decomposed into two subproblems, inventory problem and vehicle routing problem. The inventory problem is solved by proposing a local search method, which is achieved by four operators on delivery quantity and retailer’s demand. Insertion operator aims to insert a new replenishment point of a retailer while removal operator is to remove a replenishment point. Besides, addition operator is adopted as an assistant tool, and crossover operator is proposed for some special cases. We also propose a tabu search method to solve the routing problem. Finally, the computational results show that the method is efficient and stable.     

Topological refinement procedures for triangular finite element meshes

This paper presents a topological approach to improve the quality of unstructured triangular finite element meshes. Topological improvement procedures are presented both for elements that are interior to the mesh and for elements connected to the boundary. Optimal ordering of the topology improvement operations and their efficient implementation is also discussed. Several example meshes are included to demonstrate the effectiveness of the approach in improving element quality in a finite element mesh.     

Feature sensitive deformation for triangular mesh models

Shape deformation is a useful tool for shape modeling and animation in computer graphics. In this paper, we propose a novel surface deformation method based on a feature sensitive (FS) metric. Firstly, taking unit normal vectors into account, we derive a FS Laplacian operator, which is more sensitive to featured regions of mesh models than existing operators. Secondly, we use the 1‐ring tetrahedron in the dual mesh, a volumetric structure, to encode geometric details. To preserve the shape of the tetrahedron, we introduce linear tetrahedron constraints minimizing both the distortion of the base triangle and the change of the corresponding height. These ensure that geometric details are accurately preserved during deformation. The time complexity of our new method is similar to that of existing linear Laplacian methods. Examples are included to show that our FS deformation method better preserves mesh details, especially features, than existing Laplacian methods. Copyright © 2010 John Wiley & Sons, Ltd.     

三角网格曲面上离散曲率改进算法

计算三角网格离散曲面曲率的Meyer方法几何意义简明,计算量较小,但其计算效果仍有进一步提高的潜力。通过对Meyer方法的深入分析,提出了平均曲率构造向量和Gauss曲率构造角的概念,并指出了它们的几何意义,在此基础上构造了对Meyer方法的改进算法。经分析,提出的改进算法精简了各个主要计算步骤,避免了不必要的计算误差。仿真计算结果表明,改进算法是有效的,提高了三角网格离散曲率的计算精度和计算效率。     

Generalised tangential interpolation for model reduction of discrete-time MIMO bilinear systems

In this article, we discuss a model order reduction method for multiple-input and multiple-output discrete-time bilinear control systems. Similar to the continuous-time case, we will show that a system can be characterised by a series of generalised transfer functions. This will be achieved by a multivariate Z-transform of kernels corresponding to an explicit solution formula for discrete-time systems. We will further address the problem of generalised tangential interpolation which naturally comes along with this approach. We will introduce a reasonable generalisation of the linear ?₂-norm. Based on this concept, we discuss the choice of interpolation points. Furthermore, an efficient discretisation of continuous-time systems is provided. The performance of the proposed method is evaluated in some numerical examples and compared with the method of balanced truncation for bilinear systems.     

An efficient algorithm for characteristic tracking on two-dimensional triangular meshes

Tracking characteristics on unstructured meshes is an important part of many numerical methods in computational fluid mechanics. In this paper, we propose an efficient algorithm for characteristic tracking on two-dimensional unstructured triangular meshes. Numerical experiments, including an example for applying this algorithm with the Eulerian-Lagrangian localized adjoint method (ELLAM) to solve a convection-dominated convection-diffusion problem, are presented to demonstrate the efficiency of this algorithm.     

Stable local dimensionality reduction approaches

Dimensionality reduction is a big challenge in many areas. A large number of local approaches, stemming from statistics or geometry, have been developed. However, in practice these local approaches are often in lack of robustness, since in contrast to maximum variance unfolding (MVU), which explicitly unfolds the manifold, they merely characterize local geometry structure. Moreover, the eigenproblems that they encounter, are hard to solve. We propose a unified framework that explicitly unfolds the manifold and reformulate local approaches as the semi-definite programs instead of the above-mentioned eigenproblems. Three well-known algorithms, locally linear embedding (LLE), laplacian eigenmaps (LE) and local tangent space alignment (LTSA) are reinterpreted and improved within this framework. Several experiments are presented to demonstrate the potential of our framework and the improvements of these local algorithms.     

An improved experimental method for local clothing ventilation measurement

A clothing local ventilation measuring device based on the Lotens–Havenith steady state tracer gas method was developed and an improved experimental method for understanding local ventilation mechanisms was proposed. The local ventilation system can measure the arm, chest and back ventilation rates at the same time. Local ventilation mechanisms of an impermeable garment at two activities (static, walking) and two wind speeds (no wind, 1.2 m/s) were studied, with a focus on determining the pathways of ventilation through the different garment openings. The results showed that local ventilation rates of chest, back and arm varied considerably over locations and conditions. As expected, ventilation rates were highest for all locations at walking with wind conditions. Ventilation mechanism changed at different walking and wind conditions. The main air exchange pathway for all locations was through the garment bottom. Wind had a greater impact on clothing local ventilation than walking.     

A general finite difference method for arbitrary meshes

A two-dimensional finite-difference technique for irregular meshes is formulated for derivatives up to the second order. The domain in the vicinity of a given central point is broken into eight 45 degree pie shaped segments and the closest finite-difference point in each segment to the center point is noted. By utilizing Taylor series expansions about a central point with a unique averaging process for the points in the four diagonal segments, good approximations to all derivatives up to the second order and including the mixed derivatives are obtained. For square meshes the general derivative expressions for arbitrary meshes which were determined reduce to the usual finite difference formulae. In one example problem the Poisson equation is solved for an irregular mesh. In a second example for the first time a problem with a geometric nonlinearity, namely large deflection response of a flat membrane, is solved with an irregular mesh. The solutions compare very favorably with results obtained previously. Some discussion is given on possible approaches for determination of finite difference derivatives higher than the second.     

A method for conservative remapping on hexahedral meshes

A method for conservative interpolation (remapping) of physical parameters from one structured hexahedral mesh to another is described. The conservative remapping is reduced to determining the volume of the overlapping between the old and new mesh cells. A hexahedral cell with ruled faces is replaced by two dodecahedra with planar triangular faces. As a result, the remapping is reduced to construction of the overlapping between two dodecahedra. An optimal algorithm is suggested for examining the old mesh cells that have a nonempty overlapping with the current cell of the new mesh. The interpolation error is estimated. Examples of remapping are presented.     

A perception correlated comparison method for dynamic meshes

There are multiple areas of computer graphics where triangular meshes are being altered in order to reduce their size or complexity, while attempting to preserve the original shape of the mesh as closely as possible. Recently, this area of research has been extended to cover even a dynamic case, i.e., surface animations which are compressed and simplified. However, to date very little effort has been made to develop methods for evaluating the results, namely the amount of distortion introduced by the processing. Even the most sophisticated compression methods use distortion evaluation by some kind of mean squared error while the actual relevance of such measure has not been verified so far. In this paper, we point out some serious drawbacks of the existing error measures. We present results of the subjective testing that we have performed, and we derive a new measure called Spatiotemporal edge difference (STED) which is shown to provide much better correlation with subjective opinions on mesh distortion.