Texture mapping on surfaces of arbitrary topology using norm preserving-based optimization

A simple and yet highly efficient, high-quality texture mapping method for surfaces of arbitrary topology is presented. The new method projects the given surface from the 3D object space into the 2D texture space to identify the 2D texture structure that will be used to texture the surface. The object space to texture space projection is optimized to ensure minimum distortion of the texture mapping process. The optimization is achieved through a commonly used norm preserving minimization process on edges of the surface. The main difference here is, by using an initial value approach, the optimization problem can be set up as a quadratic programming problem and, consequently, solved by a linear least squares method. Three methods to choose a good initial value are presented. Test cases show that the new method works well on surfaces of arbitrary topology, with the exception of surfaces with exceptionally abnormal curvature distribution. Other advantages of the new method include uniformity and seamlessness of the texture mapping process. The new method is suitable for applications that do not require precise texture mapping results but demand highly efficient mapping process such as computer animation or video games.     

Multiresolution free-form deformation with subdivision surface of arbitrary topology

A new free-from deformation method is presented in this paper. Object deformation is controlled by a mesh of arbitrary topology, namely a control mesh. The subdivision surface determined by the control mesh spans an intermediate deformation space. The object is embedded into the space by the nearest point rule. When the shape of the control mesh is changed, the object embedded in the intermediate deformation space will be deformed accordingly. Since the subdivision surface has a multiresolution property, the proposed deformation method naturally has a multiresolution property. A technique for generating control meshes is also introduced in the paper. Compared with previous deformation methods with arbitrary topology control tools, the proposed method has the advantages of flexible control and computational efficiency.     

Globally optimal benchmark solutions to some small-scale discretized continuum topology optimization problems

In this note, globally optimal solutions to three sets of small-scale discretized continuum topology optimization problems are presented. All the problems were discretized by the use of nine-node isoparametric finite elements. The idea is that these solutions can be used as benchmark problems when testing new algorithms for finding pure 0–1 solutions to topology optimization problems defined on discretized ground structures.     

Curve interpolation in recursively generated B-spline surfaces over arbitrary topology

Recursive subdivision is receiving a great deal of attention in the definition of B-spline surfaces over arbitrary topology. The technique has recently been extended to generate interpolating surfaces with given normal vectors at the interpolated vertices. This paper describes an algorithm to generate recursive subdivision surfaces that interpolate B-spline curves. The control polygon of each curve is defined by a path of vertices of the polyhedral network describing the surface. The method consists of applying a one-step subdivision of the initial network and modifying the topology in the neighborhood of the vertices generated from the control polygons. Subsequent subdivisions of the modified network generate sequences of polygons each of which converges to a curve interpolated by the limit surface. In the case of regular networks, the method can be reduced to a knot insertion process.     

拓扑最优的可展网格曲面放样建模

在服装、制鞋、钣金等行业的产品外形设计中,经常需要插值多条特征空间曲线,构建可展曲面 (可无伸缩地展开成平面)。针对这一问题,基于Dijkstra算法提出了一种新的放样建模算法：给定多条参数曲线,经过自适应离散后,寻找一个全局拓扑最优的可展网格放样曲面（针对不同的目标曲面能量,同样可以产生目标能量定义的拓扑最优的放样网格曲面）。该问题最终可转化为有向无环图(DAG)的单源最短路径的求解,算法的时间复杂度为O(N log N),其中N为搜寻空间。测试结果表明该算法在相关行业的放样外形设计方面具有实际工程应用价值。     

Multiform frequency selective surfaces optimal design based on topology optimization

This article proposes an optimization design method for various frequency selective surfaces (FSSs) based on topology optimization algorithm incorporated with the genetic algorithm. The present method takes the connectivity condition both in simulation and fabrication of the elements into consideration. For the filling elements structural design methodology, the novel hexagonal‐pixel filling element structural design is employed for improving the patch connection. As examples, various FSSs, such as a large‐angle‐stability band‐pass FSS, wideband band‐pass FSS, and multiple band‐pass FSS, are designed. Furthermore, the validity of the present method is proved by the agreement between the simulation and the measurement.     

Globally optimal robust process control

A computational approach is developed for designing a globally optimal controller which is robust to time-varying nonlinear perturbations in the plant. This controller design problem is formulated as an optimization with bilinear matrix inequality (BMI) constraints, and is solved to optimality by a branch and bound algorithm. The algorithm is applied to a reactive ion etcher, and provides superior performance while providing robustness to nonlinear plant/model mismatch. The algorithm is also applied to a well known benchmark problem.     

A practical construction of G smooth biquintic B-spline surfaces over arbitrary topology

The motivation of this paper is to develop a local scheme of constructing G¹ smooth B-spline surfaces with single interior knots over arbitrary topology. In this paper, we obtain the conditions of G¹ continuity between two adjacent biquintic B-spline surfaces with interior single knots. These conditions are directly represented by the relevant control points of the two B-spline surfaces. By utilizing these G¹ conditions, we develop the first local scheme of constructing G¹ smooth biquintic B-spline surfaces with interior single knots for arbitrary topological type. The high complexity of deriving the local G¹ scheme is well overwhelmed. The biquintic is the lowest degree for which there exists a local scheme of constructing G¹ smooth B-spline surfaces with interior single knots over arbitrary topology.     

Globally optimal fuzzy decision trees for classification andregression

A fuzzy decision tree is constructed by allowing the possibility of partial membership of a point in the nodes that make up the tree structure. This extension of its expressive capabilities transforms the decision tree into a powerful functional approximant that incorporates features of connectionist methods, while remaining easily interpretable. Fuzzification is achieved by superimposing a fuzzy structure over the skeleton of a CART decision tree. A training rule for fuzzy trees, similar to backpropagation in neural networks, is designed. This rule corresponds to a global optimization algorithm that fixes the parameters of the fuzzy splits. The method developed for the automatic generation of fuzzy decision trees is applied to both classification and regression problems. In regression problems, it is seen that the continuity constraint imposed by the function representation of the fuzzy tree leads to substantial improvements in the quality of the regression and limits the tendency to overfitting. In classification, fuzzification provides a means of uncovering the structure of the probability distribution for the classification errors in attribute space. This allows the identification of regions for which the error rate of the tree is significantly lower than the average error rate, sometimes even below the Bayes misclassification rate     

Mesh composition on models with arbitrary boundary topology

This paper presents a new approach for the mesh composition on models with arbitrary boundary topology. After cutting the needed parts from existing mesh models and putting them into the right pose, an implicit surface is adopted to smoothly interpolate the boundaries of models under composition. An interface is developed to control the shape of the implicit transient surface by using sketches to specify the expected silhouettes. After that, a localized Marching Cubes algorithm is investigated to tessellate the implicit transient surface so that the mesh surface of composed model is generated. Different from existing approaches in which the models under composition are required to have pairwise merging boundaries, the framework developed based on our techniques have the new function to fuse models with arbitrary boundary topology.     

Isogeometric analysis with trimming technique for problems of arbitrary complex topology

Trimming technique is a powerful and efficacious way of endowing an arbitrary complex topology to CAD files created by using NURBS. In the present work, it is shown that any complex multiply-connected NURBS domain can be described by using trimming curves only. Isogeometric analysis for linear elasticity problems of complex topology described in this way is presented. For fully communicative interaction between CAD and CAE, a specific searching algorithm and an integration scheme of trimmed elements are introduced to utilize the IGES files exported from CAD system for Isogeometric analysis. Schemes for imposing essential and traction boundary conditions on trimming curves are presented. It has been demonstrated that with the presented schemes trimmed cases in any complicated situations can be successfully treated. With the examples of complex topology that could be described by employing trimming curves only, effectiveness and robustness of present method are demonstrated.     

Data/voice integration for fibre optic LANs with arbitrary topology

A high-performance protocol for arbitrary point-to-point fibre optic local area networks with combined voice and data traffic is described. Simulation on a 3 Mbit/s nine-node mesh network has shown that it is capable of supporting a substantial number of data users and more than 100 active voice calls (200 active telephone users, coding rate 64 kbit/s without silence detection) with a packet delay of less than 10 ms and without any loss of information. The network performance is superior to the previous reported voice protocol which used the modified anarchy flood routing (MAFR) technique. Performance limitation due to growing network size for flood-routed networks is also discussed. A method of extending the flood-routing protocols over subnetworks which are connected via bridges is also presented. This method enables a large network to be divided into smaller subnetworks which reduces the number of links required.     

n-Dimensional multiresolution representation of subdivision meshes with arbitrary topology

We present a new model for the representation of n-dimensional multiresolution meshes. It provides a robust topological representation of arbitrary meshes that are combined in closely interlinked levels of resolution. The proposed combinatorial model is formalized through the mathematical model of combinatorial maps allowing us to give a general formulation, in any dimensions, of the topological subdivision process that is a key issue to robustly and soundly define mesh hierarchies. It fully supports multiresolution edition what allows the implementation of most mesh processing algorithms – like filtering or compression – for n-dimensional meshes with arbitrary topologies.We illustrate this model, in dimension 3, with an new truly multiresolution representation of subdivision volumes. It allows us to extend classical subdivision schemes to arbitrary polyhedrons and to handle adaptive subdivision with an elegant solution to compliance issues. We propose an implementation of this model as an effective and relatively inexpensive data structure.     

Fine-grained cache deployment scheme for arbitrary topology in ICN

Neural Computing and Applications - Information-centric networking (ICN) is one of the promising candidates for the future network architecture. In-network caching deployed on the routers is the...     

Globally optimal quadratic Lyapunov functions for robust stability of systems with structured uncertainty

The robust stability problem for a nominally linear system with nonlinear, time-varying structured perturbations is considered. The system is of the form $$\dot x = A_N x + \sum\limits_{j = 1}^q { p_j A_j x} $$ The Lyapunov direct method has been often utilized to determine the bounds for nonlinear, time-dependent functions p_j which can be tolerated by a stable nominal system. In most cases quadratic forms are used either as components of vector Lyapunov function or as a function itself. The resulting estimates are usually conservative. Optimizing the Lyapunov function reduces the conservatism of the bounds. The main result of this article is a theorem formulating the necessary and sufficient conditions for a quadratic Lyapunov function to be globally optimal. The theorem is constructive and makes it possible to propose a recursive procedure of a design of optimal Lyapunov function. Examples demonstrate application of the proposed method.     

Globally minimal surfaces by continuous maximal flows

In this paper, we address the computation of globally minimal curves and surfaces for image segmentation and stereo reconstruction. We present a solution, simulating a continuous maximal flow by a novel system of partial differential equations. Existing methods are either grid-biased (graph-based methods) or suboptimal (active contours and surfaces). The solution simulates the flow of an ideal fluid with isotropic velocity constraints. Velocity constraints are defined by a metric derived from image data. An auxiliary potential function is introduced to create a system of partial differential equations. It is proven that the algorithm produces a globally maximal continuous flow at convergence, and that the globally minimal surface may be obtained trivially from the auxiliary potential. The bias of minimal surface methods toward small objects is also addressed. An efficient implementation is given for the flow simulation. The globally minimal surface algorithm is applied to segmentation in 2D and 3D as well as to stereo matching. Results in 2D agree with an existing minimal contour algorithm for planar images. Results in 3D segmentation and stereo matching demonstrate that the new algorithm is robust and free from grid bias.     

Globally optimal flight path update with adding or removing out-of-sequence measurements

In a multisensor target tracking system, observations produced by sensors can arrive at a central processor out of sequence. There have been some state estimate update algorithms for out-of-sequence measurements (OOSMs). In this paper, we propose a flight path update algorithm for a sequence with arbitrary delayed OOSMs. The new algorithm has three advantages: (1) it is a globally optimal recursive algorithm; (2) it is an algorithm for arbitrary delayed OOSMs including the case of interlaced OOSMs with less storage, compared with the optimal state update algorithm in Zhang, Li, and Zhu (2005); (3) it can update the current whole flight path in addition to the current single state with less computation, i.e., the dimension of the matrices which need to be inverted is not more than that of the state in the process of updating the past ? (lag steps) estimates and corresponding error covariances. Besides, this algorithm can be easily modified to derive a globally optimal flight path update with removing an earlier (incorrectly associated) measurement.