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In spline toolpath interpolation, a crucial point is solving the mapping between the spline parameter (u) and actual arc length (s) accurately, so that the toolpath is traveled without undesirable fluctuations or discontinuities in the feedrate profile. To achieve this, various techniques have been proposed in literature, including Taylor series interpolation, iterative numerical methods, and approximating the mapping between u and s with a feed correction polynomial. This paper presents a new way to parameterize the seventh order feed correction polynomial, which was introduced by Erkorkmaz and Altintas (2005, "Quintic Spline Interpolation With Minimal Feed Fluctuation," ASME J. Manuf. Sci. Eng., 127(2), pp. 339-349). The proposed technique has a closedform solution that can be efficiently implemented in real-time, rather than having to construct and solve a linear equation system with 14 unknowns for each spline segment. In this paper, the new solution is derived step by step, and simulation case studies are presented which demonstrate that the new method accurately parameterizes the feed correction polynomial in approximately 43% less computational time, compared to applying the former solution of Erkorkmaz and Altintas (2005, "Quintic Spline Interpolation With Minimal Feed Fluctuation," ASME J. Manuf. Sci. Eng., 127(2), pp. 339-349). This is because matrix multiplication operations and a dedicated linear equation solver, which are cumbersome to implement inside a real-time computer numerical controller (CNC), are avoided in the new solution. [ABSTRACT FROM AUTHOR]

An end-to-end network traffic matrix is significantly helpful for network management and for Software Defined Networks (SDN). However, the end-to-end network traffic matrix's inferences and estimations are a challenging problem. Moreover, attaining the traffic matrix in high-speed networks for SDN is a prohibitive challenge. This paper investigates how to estimate and recover the end-to-end network traffic matrix in fine time granularity from the sampled traffic traces, which is a hard inverse problem. Different from previous methods, the fractal interpolation is used to reconstruct the finer-granularity network traffic. Then, the cubic spline interpolation method is used to obtain the smooth reconstruction values. To attain an accurate the end-to-end network traffic in fine time granularity, we perform a weighted-geometric-average process for two interpolation results that are obtained. The simulation results show that our approaches are feasible and effective. [ABSTRACT FROM AUTHOR]

Anonymity, which is more and more important to multi-receiver schemes, has been taken into consideration by many researchers recently. To protect the receiver anonymity, in 2010, the first multi-receiver scheme based on the Lagrange interpolating polynomial was proposed. To ensure the sender’s anonymity, the concept of the ring signature was proposed in 2005, but afterwards, this scheme was proven to has some weakness and at the same time, a completely anonymous multi-receiver signcryption scheme is proposed. In this completely anonymous scheme, the sender anonymity is achieved by improving the ring signature, and the receiver anonymity is achieved by also using the Lagrange interpolating polynomial. Unfortunately, the Lagrange interpolation method was proven a failure to protect the anonymity of receivers, because each authorized receiver could judge whether anyone else is authorized or not. Therefore, the completely anonymous multi-receiver signcryption mentioned above can only protect the sender anonymity. In this paper, we propose a new completely anonymous multi-receiver signcryption scheme with a new polynomial technology used to replace the Lagrange interpolating polynomial, which can mix the identity information of receivers to save it as a ciphertext element and prevent the authorized receivers from verifying others. With the receiver anonymity, the proposed scheme also owns the anonymity of the sender at the same time. Meanwhile, the decryption fairness and public verification are also provided. [ABSTRACT FROM AUTHOR]

This paper concerns kernel-based interpolation methods for vector data with correlated components. It gives conditions for a matrix kernel to be conditionally positive definite in an appropriate sense. The conditions allow construction of matrix kernels from nonsymmetric mixtures and scalings of scalar kernels. In particular the kernel used to model the influence of component i on component j can be different from that used to model the influence of component j on component i. The vector modeling techniques considered are particularly appropriate when there are relatively few measurements of one quantity and relatively many of another "correlated" quantity. The paper concludes with some numerical tests on model problems. [ABSTRACT FROM AUTHOR]

Contemporary land information systems allow the generation of models of numerical surfaces by applying a number of interpolation algorithms. The appropriate selection of measurement points included in the calculations is one of the key factors influencing the quality and accuracy of interpolation. Properly selected points contribute to improving the accuracy of the generated surface models and to shortening the computation process. This paper analyzes the effect of the location and density of measurement points on the accuracy of interpolation surfaces in view of the morphological differentiation of the generated models. [ABSTRACT FROM AUTHOR]

A surrogate modeling strategy, using effective interpolation and sampling methods, facilitates a reduction in the number of computational fluid dynamics simulations required to construct an aerodynamic model to a specified accuracy. In this paper, two adaptive sampling strategies are compared for generating surrogate models, based on Kriging and radial basis function interpolation, respectively. The relationships between the two model formulations are discussed, and three test cases are considered, including analytic functions and recovery of aerodynamic coefficients for two example applications: longitudinal flight mechanics analysis for the DLR-F12 aircraft and structural loads analysis of an RAE2822 airfoil. For the airfoil example, models of CL, CD, and CM were constructed with the two sampling strategies using Euler/boundary-layer-coupled computational fluid dynamics and a three-dimensional flight envelope of incidence, Mach, and Reynolds number. The two sampling approaches direct some samples toward exploration of the domain by minimizing model uncertainty and some toward refinement of local nonlinearities, by adapting to model curvature or extrema. The results provide some evidence that, for certain functions, in certain scenarios, each update scheme could be useful. Both methods were at least better than traditional space-filling sampling for all the test cases presented. [ABSTRACT FROM AUTHOR]

In this paper, four three-node triangular finite element models which can readily be incorporated into the standard finite element program framework are devised via a multi-field variational functional for the bounded plane Helmholtz problem. In the models, boundary and domain fields are independently assumed. The former is constructed by nodal interpolation and the latter comprises nonsingular solutions of the Helmholtz equation. The equality of the two fields are enforced along the element boundary. Among the four devised models, the most accurate one is 1/3 to 1/2 less erroneous than the conventional single-field model in most examples. [ABSTRACT FROM AUTHOR]

In this paper, we present a new approach of-spline curve fitting to a set of ordered points, which is motivated by an insight that properly selected points called dominant points can play an important role in producing better curve approximation. The proposed approach takes four main steps: parameterization, dominant point selection, knot placement, and least-squares minimization. The approach is substantially different from the conventional approaches in knot placement and dominant point selection. In the knot placement, the knots are determined by averaging the parameter values of the dominant points, which basically transforms-spline curve fitting into the problem of dominant point selection. We describe the properties of the knot placement including the property of local modification useful for adaptive curve refinement. We also present an algorithm for dominant point selection based on the adaptive refinement paradigm. The approach adaptively refines a-spline curve by selecting fewer dominant points at flat regions but more at complex regions. For the same number of control points, the proposed approach can generate a-spline curve with less deviation than the conventional approaches. When adopted in error-bounded curve approximation, it can generate a-spline curve with far fewer control points while satisfying the desired shape fidelity. Some experimental results demonstrate its usefulness and quality. [Copyright &y& Elsevier]

Reconstruction of freeform surfaces from scattered coordinate data is a difficult problem encountered in many surface fitting and geometric modeling applications. Conventional tessellation and parametric surface fitting techniques are limited because they require prior knowledge about the connectivity between the sampled points. The method of surface reconstruction described in this paper exploits the learning capability of a self-organizing feature map (SOFM) to adaptively fit a deformable sphere to the unorganized 3D coordinate data. The learning algorithm automatically establishes the connectivity between the measured points by iteratively changing the topological relationships within the map. By incorporating additional constraints during the learning process it is possible to have the deformable map follow the shape of objects with surface holes and cavities. Several examples of freeform surfaces with varying levels of complexity are discussed in order to demonstrate the performance of the algorithm. [ABSTRACT FROM AUTHOR]

This paper presents an error control method for application of the discrete cosine transform (DCT) to extraction of substrate parasitics in integrated circuits. In addition to the truncation error with approximating an infinite series with a finite number of terms, there are also errors in approximating the truncated series by the DCT. It is shown that this error is important for accurate parasitic extraction and isolation calculation and can be controlled by applying an interpolation method. The interpolation method also makes it possible to use a smaller DCT size without loss of accuracy. [ABSTRACT FROM AUTHOR]

The digital sinusoidal oscillator considered in this paper is one of the signal sources employed in the digital signal processing system. A construction of the oscillator is discussed where the memory capacity is reduced and the increasing rate of the noise is suppressed by interpolating the output of the oscillator of table look-up type or feedback type. A design method for the interpolation filter is presented first where no interpolation error is produced if the coefficient wordlength of the interpolation filter is infinite. Then, considering the case where the wordlength is kept finite, the hold-type sampling expander is proposed where the waveform distortion is kept low compared with the traditional zero-interpolation-type sampling rate expander. The distortion in the proposed method is analyzed where the wordlength of the interpolation filter coefficient is kept finite, and the waveform distortion is shown to be low. The increasing rate of the round-off error is examined by a computer simulation for the oscillator, which is obtained by applying the interpolation to the feedback-type oscillator. The effectiveness of the interpolation is demonstrated. Finally, a construction of the block-digital sinusoidal oscillator is shown with a smaller hardware complexity than in the traditional method, by constructing the block-structured oscillator by realizing the proposed interpolation filter as a polyphase filter. [ABSTRACT FROM AUTHOR]