A Fast Display Method of Sky Colour Using Basis Functions

Computer graphics are being used for visual environmental assessment or architectural designs. Displaying the sky as a background is indispensable in generating photorealistic images for such applications. In this paper, we propose a fast display method of the sky colour by expressing the intensity distribution of the sky using basis functions, even if the sun position and/or the camera position are altered. In the proposed method, cosine functions are used as basis functions. The sun altitude is altered at certain intervals and the distributions of the sky colour for each sun altitude are precalculated and stored efficiently using basis functions. The colour of the sky in the view direction of an arbitrary sun position can be obtained from the stored distributions and displayed quickly. © 1997 by John Wiley & Sons, Ltd.     

Polyhedral Finite Elements Using Harmonic Basis Functions

Finite element simulations in computer graphics are typically based on tetrahedral or hexahedral elements, which enables simple and efficient implementations, but in turn requires complicated remeshing in case of topological changes or adaptive refinement. We propose a flexible finite element method for arbitrary polyhedral elements, thereby effectively avoiding the need for remeshing. Our polyhedral finite elements are based on harmonic basis functions, which satisfy all necessary conditions for FEM simulations and seamlessly generalize both linear tetrahedral and trilinear hexahedral elements. We discretize harmonic basis functions using the method of fundamental solutions, which enables their flexible computation and efficient evaluation. The versatility of our approach is demonstrated on cutting and adaptive refinement within a simulation framework for corotated linear elasticity.     

A Quick Rendering Method Using Basis Functions for Interactive Lighting Design

When designing interior lighting effects, it is desirable to compare a variety of lighting designs involving different lighting devices and directions of light. It is, however, time-consuming to generate images with many different lighting parameters, taking interreflection into account, because all luminances must be calculated and recalculated. This makes it difficult to design lighting effects interactively. To address this problem, this paper proposes a method of quickly generating images of a given scene illustrating an interreflective environment illuminated by sources with arbitrary luminous intensity distributions. In the proposed method, the luminous intensity ditribution is expressed with basis functions. The proposed method uses a series of spherical harmonic functions as basis functions, and calculates in advance each intensity on surfaces lit by the light sources whose luminous intensity distribution are the same as the spherical harmonic functions. The proposed method makes it possible to generate images so quickly that we can change the luminous intensity distribution interactively. Combining the proposed method with an interactive walk-through that employs intensity mapping, an interactive system for lighting design is implemented. The usefulness of the proposed method is demonstrated by its application to interactive lighting design, where many images are generated by altering lighting devices and/or direction of light.     

Semi-Procedural Textures Using Point Process Texture Basis Functions

We introduce a novel semi-procedural approach that avoids drawbacks of procedural textures and leverages advantages of data-driven texture synthesis. We split synthesis in two parts: 1) structure synthesis, based on a procedural parametric model and 2) color details synthesis, being data-driven. The procedural model consists of a generic Point Process Texture Basis Function (PPTBF), which extends sparse convolution noises by defining rich convolution kernels. They consist of a window function multiplied with a correlated statistical mixture of Gabor functions, both designed to encapsulate a large span of common spatial stochastic structures, including cells, cracks, grains, scratches, spots, stains, and waves. Parameters can be prescribed automatically by supplying binary structure exemplars. As for noise-based Gaussian textures, the PPTBF is used as stand-alone function, avoiding classification tasks that occur when handling multiple procedural assets. Because the PPTBF is based on a single set of parameters it allows for continuous transitions between different visual structures and an easy control over its visual characteristics. Color is consistently synthesized from the exemplar using a multiscale parallel texture synthesis by numbers, constrained by the PPTBF. The generated textures are parametric, infinite and avoid repetition. The data-driven part is automatic and guarantees strong visual resemblance with inputs.     

Reduced Collocation Methods: Reduced Basis Methods in the Collocation Framework

In this paper, we present the first reduced basis method well-suited for the collocation framework. Two fundamentally different algorithms are presented: the so-called Least Squares Reduced Collocation Method (LSRCM) and Empirical Reduced Collocation Method (ERCM). This work provides a reduced basis strategy to practitioners who prefer a collocation, rather than Galerkin, approach. Furthermore, the empirical reduced collocation method eliminates a potentially costly online procedure that is needed for non-affine problems with Galerkin approach. Numerical results demonstrate the high efficiency and accuracy of the reduced collocation methods, which match or exceed that of the traditional reduced basis method in the Galerkin framework.     

Implicit Fitting Using Radial Basis Functions with Ellipsoid Constraint

Implicit planar curve and surface fitting to a set of scattered points plays an important role in solving a wide variety of problems occurring in computer graphics modelling, computer graphics animation, and computer assisted surgery. The fitted implicit surfaces can be either algebraic or non‐algebraic. The main problem with most algebraic surface fitting algorithms is that the surface fitted to a given data set is often unbounded, multiple sheeted, and disconnected when a high degree polynomial is used, whereas a low degree polynomial is too simple to represent general shapes. Recently, there has been increasing interest in non‐algebraic implicit surface fitting. In these techniques, one popular way of representing an implicit surface has been the use of radial basis functions. This type of implicit surface can represent various shapes to a high level of accuracy. In this paper, we present an implicit surface fitting algorithm using radial basis functions with an ellipsoid constraint. This method does not need to build interior and exterior layers for the given data set or to use information on surface normal but still can fit the data accurately. Furthermore, the fitted shape can still capture the main features of the object when the data sets are extremely sparse. The algorithm involves solving a simple general eigen‐system and a computation of the inverse or psedo‐inverse of a matrix, which is straightforward to implement.     

一个新的图像单幅可视隐藏方案

作为一种数字水印的技术方法,提出了一种新的单幅图像可视隐藏方案.在该方案中,仅使用一幅加密图便能可视恢复密图,加密图本身既是编码又是解码.与已有的基于移位的方案不同,该方案通过加密图逆时针旋转90°后和自身的叠加来恢复原图.给出了实现单幅图像可视隐藏的新方案的设计方法,对方案的性能进行了分析,并且指出新方案具有较好的抗压缩性、抗破损性、抗放缩性,且能充分利用密图的容量.     

一种新的基于智能卡的双向身份认证方案设计

身份认证问题是网络安全中的重要研究课题。最近,Chien 等人提出了一种有效的基于智能卡的身份认证方案,但从文献［8］及本文的分析看,该方案容易遭受Reflection Attack,Parallel Attack、重传攻击等。在分析其方案漏洞的基础上,提出了一种新的双向身份认证方案。     

Prediction of Critical Desalination Parameters Using Radial Basis Functions Networks

Prediction of critical desalination parameters (recovery and salt rejection) of two distinct processes based on real operational data is presented. The proposed method utilizes the radial basis function network using data clustering and histogram equalization. The scheme involves center selection and shape adjustment of the localized receptive fields. This algorithm causes each group of radial basis functions to adapt to regions of the clustered input space. Networks produced by the proposed algorithm have good generalization performance on prediction of non-linear input–output mappings and require a small number of connecting weights. The proposed method was used for the prediction of two different critical parameters for two distinct Reverse Osmosis (RO) plants. The simulation results indeed confirm the effectiveness of the proposed prediction method.     

一种新型的使用Raw IP的IP追踪方法

提出了一种新型的使用Raw IP的IP追踪方法,该方法引入了抑制期的概念,其最大的优点就是可以直接定位攻击者,而无需像其他方法那样重组整个路径。通过模拟和分析得出,该方法是一个对路由器、网络带宽、受害主机的额外负担很小,同时还具有DDoS追踪能力的有效方法。     

Variational Modeling of Free-form Curve and Surface Using Wavelet Basis Functions

Variational modeling approach is often used to interactively design free-form curves and surfaces. Traditionally, a variational problem can be transformed to the optimization of control points. Unfortunately, as the number of basis functions grows, the local support property of B-spline often makes the computation of an optimization system time-consuming. To solve this problem, wavelet basis instead of B-spline basis is used to represent the curves or surfaces. Because the wavelet basis is a hierarchical basis with multiresolution property, the coarse wavelet basis can be used to describe the overall shape of the curves/surfaces, while the finer wavelet basis used to describe the details of the curves/surfaces. Thus, the computing speed of the optimization system can be raised greatly.     

非矩形定义域上的散乱数据曲面重建的Multiquadric基函数拟合法

传统的Multiquadric基函数拟合散乱数据方法,只能用于定义域呈矩形拓扑的散乱数据集上,而逆向工程中通常遇到的是非矩形定义域上的散乱数据集,因此不能用传统方法。文章提出一种新的Multiquadric基函数拟合非矩形定义域上的散乱数据集。该方法首先找到一个与该散乱数据集所在曲面拓扑等价的参数曲面,通过将散乱数据点(xi,yi,zi)一一映射到此参数曲面,反求出其对应参数(ui,vi),由于(ui,vi)∈犤0,1犦×犤0,1犦,从而将非矩形定义域上的Multiquadric基函数拟合方法转化为传统的方法。将Multiquadric曲面与B-样条曲面进行了比较,指出了Multiquadric曲面优于B-样条曲面之处。     

A Parallel Multivariate Interpolation Algorithm With Radial Basis Functions

This paper presents an efficient and highly scalable parallel version of the Modified RBF Shepard's method presented in [5]. This method maintains the "metric" nature and the advantages of Shepard's method and, at the same time, improves its accuracy by exploiting the characteristics of flexibility and accuracy which have made the radial basis functions a well-established tool for multivariate interpolation. Due to its locality, this method can be easily and efficiently parallelized on a distributed memory parallel architecture. The performance of the parallel algorithm has been studied theoretically and the experimental results obtained by running its implementation on a Cray T3E parallel machine, using the MPI interface, confirm the theoretical efficiency.     

Hermite Radial Basis Functions Implicits

The Hermite radial basis functions (HRBF) implicits reconstruct an implicit function which interpolates or approximates scattered multivariate Hermite data (i.e. unstructured points and their corresponding normals). Experiments suggest that HRBF implicits allow the reconstruction of surfaces rich in details and behave better than previous related methods under coarse and/or non‐uniform samplings, even in the presence of close sheets. HRBF implicits theory unifies a recently introduced class of surface reconstruction methods based on radial basis functions (RBF), which incorporate normals directly in their problem formulation. Such class has the advantage of not depending on manufactured offset‐points to ensure existence of a non‐trivial implicit surface RBF interpolant. In fact, we show that HRBF implicits constitute a particular case of Hermite–Birkhoff interpolation with radial basis functions, whose main results we present here. This framework not only allows us to show connections between the present method and others but also enable us to enhance the flexibility of our method by ensuring well‐posedness of an interesting combined interpolation/regularization approach.     

Wang-Ball基函数的对偶基及其应用

对于n次Wang-Ball曲线给出其对偶基,进而得到从Bernstein基到Wang-Ball基函数的显式转换公式．     

A Collocation Solution For Burgers Equation Using Quadratic B-Spline Finite Elements

This paper discusses solving one of the important equations in Fluid Dynamics; which is the one-dimensional Burgers equation. For that purpose, we use quadratic B-spline finite elements within a Collocation method. It is shown that this method is capable of solving Burgers equation accurately for values of viscosity from small to large. Numerical results are obtained for test problems to show the behavior of the solutions of time dependent problems. Computed results are compared with other numerical results.     

Performance Evaluation of GPU-Accelerated Spatial Interpolation Using Radial Basis Functions for Building Explicit Surfaces

This paper focuses on evaluating the computational performance of parallel spatial interpolation with Radial Basis Functions (RBFs) that is developed by utilizing modern GPUs. The RBFs can be used in spatial interpolation to build explicit surfaces such as Discrete Elevation Models. When interpolating with large-size of data points and interpolated points for building explicit surfaces, the computational cost would be quite expensive. To improve the computational efficiency, we specifically develop a parallel RBF spatial interpolation algorithm on many-core GPUs, and compare it with the parallel version implemented on multi-core CPUs. Five groups of experimental tests are conducted on two machines to evaluate the computational efficiency of the presented GPU-accelerated RBF spatial interpolation algorithm. Experimental results indicate that: in most cases, the parallel RBF interpolation algorithm on many-core GPUs does not have any significant advantages over the parallel version on multi-core CPUs in terms of computational efficiency. This unsatisfied performance of the GPU-accelerated RBF interpolation algorithm is due to: (1) the limited size of global memory residing on the GPU, and (2) the need to solve a system of linear equations in each GPU thread to calculate the weights and prediction value of each interpolated point.     

A New Optimal Force Distribution Scheme of Multiple Cooperating Robots Using Dual Method

A new optimal force distribution scheme of multiple cooperating robots is proposed, in which the duality theory of nonlinear programming (NLP) is combined with the quadratic programming (QP) approach. The optimal force distribution problem is formulated as a QP problem with both linear and quadratic constraints, and its solution is obtained by an efficient algorithm. The use of the quadratic constraints is important in that it considerably reduces the number of constraints, thus enabling the Dual method of NLP to be used in the solution algorithm. Moreover, it can treat norm constraints without approximation, such as bound of the norm of the force exerted by each robot. The proposed scheme is more efficient in terms of speed than any other method. Numerical examples of two PUMA robot task using the proposed method and a well-known fast method are compared, and the results indicate the capability of real time application of our method.     

Comparison Between Reduced Basis and Stochastic Collocation Methods for Elliptic Problems

The stochastic collocation method (Babu?ka et al. in SIAM J Numer Anal 45(3):1005–1034, 2007; Nobile et al. in SIAM J Numer Anal 46(5):2411–2442, 2008a; SIAM J Numer Anal 46(5):2309–2345, 2008b; Xiu and Hesthaven in SIAM J Sci Comput 27(3):1118–1139, 2005) has recently been applied to stochastic problems that can be transformed into parametric systems. Meanwhile, the reduced basis method (Maday et al. in Comptes Rendus Mathematique 335(3):289–294, 2002; Patera and Rozza in Reduced basis approximation and a posteriori error estimation for parametrized partial differential equations Version 1.0. Copyright MIT, http://augustine.mit.edu, 2007; Rozza et al. in Arch Comput Methods Eng 15(3):229–275, 2008), primarily developed for solving parametric systems, has been recently used to deal with stochastic problems (Boyaval et al. in Comput Methods Appl Mech Eng 198(41–44):3187–3206, 2009; Arch Comput Methods Eng 17:435–454, 2010). In this work, we aim at comparing the performance of the two methods when applied to the solution of linear stochastic elliptic problems. Two important comparison criteria are considered: (1), convergence results of the approximation error; (2), computational costs for both offline construction and online evaluation. Numerical experiments are performed for problems from low dimensions $O(1)$ to moderate dimensions $O(10)$ and to high dimensions $O(100)$ . The main result stemming from our comparison is that the reduced basis method converges better in theory and faster in practice than the stochastic collocation method for smooth problems, and is more suitable for large scale and high dimensional stochastic problems when considering computational costs.     

新的基于身份的多签名体制

首次提出一个新的利用椭圆曲线上双线性对的基于身份的多签名体制。所提出的体制基于Hess的基于身份的签名体制,能实现并行和串行的签名结构,而且在此新多签名体制中,多签名的大小和验证与任意共同签名者产生的单个签名完全相同。同时也讨论了新体制抵抗外部攻击和内部攻击的安全性。