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interpolation of rotation and motion

MULTIBODY SYSTEM DYNAMICS 2014年第3期31卷 339-370页

作者： Bauchau, Olivier A. Han, Shilei Univ Michigan Shanghai Jiao Tong Univ Joint Inst Shanghai Peoples R China

In Cosserat solids such as shear deformable beams and shells, the displacement and rotation fields are independent. The finite element implementation of these structural components within the framework of flexible multibody dynamics requires the interpolation of rotation and motion fields. In general, the interpolation process does not preserve fundamental properties of the interpolated field. For instance, interpolation of an orthogonal rotation tensor does not yield an orthogonal tensor, and furthermore, does not preserve the tensorial nature of the rotation field. Consequently, many researchers have been reluctant to apply the classical interpolation tools used in finite element procedures to interpolate these fields. This paper presents a systematic study of interpolation algorithms for rotation and motion. All the algorithms presented here preserve the fundamental properties of the interpolated rotation and motion fields, and furthermore, preserve their tensorial nature. It is also shown that the interpolation of rotation and motion is as accurate as the interpolation of displacement, a widely accepted tool in the finite element method. The algorithms presented in this paper provide interpolation tools for rotation and motion that are accurate, easy to implement, and physically meaningful.

关键词： Finite rotation Finite motion interpolation algorithms Finite element procedures Flexible multibody systems

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Local and Nonlocal Regularization to Image interpolation

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MATHEMATICAL PROBLEMS IN ENGINEERING 2014年第1期2014卷 1-8页

作者： Zhan, Yi Li, Sheng Jie Li, Meng Chongqing Univ Coll Comp Sci Chongqing 400030 Peoples R China Chongqing Technol & Business Univ Coll Math & Stat Chongqing 400067 Peoples R China Chongqing Univ Coll Math & Sci Chongqing 400044 Peoples R China Chongqing Univ Arts & Sci Dept Math Chongqing 402160 Peoples R China Chongqing Univ Arts & Sci KLDAIP Chongqing 402160 Peoples R China

This paper presents an image interpolation model with local and nonlocal regularization. A nonlocal bounded variation (BV) regularizer is formulated by an exponential function including gradient. It acts as the Perona-Malik equation. Thus our nonlocal BV regularizer possesses the properties of the anisotropic diffusion equation and nonlocal functional. The local total variation (TV) regularizer dissipates image energy along the orthogonal direction to the gradient to avoid blurring image edges. The derived model efficiently reconstructs the real image, leading to a natural interpolation which reduces blurring and staircase artifacts. We present experimental results that prove the potential and efficacy of the method.

关键词： REGULARIZATION (Mathematics) interpolation algorithms ENERGY dissipation ANISOTROPY MATHEMATICAL proofs

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Accuracy of Sine-wave Frequency Estimation by an Iterative Interpolated DFT Algorithm

Accuracy of Sine-wave Frequency Estimation by an Iterative I...

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IEEE International Instrumentation and Measurement Technology Conference

作者： Daniel Belega Dario Petri Dominique Dallet Department of Measurements and Optical Electronics "Politehnica" University of Timisoara Timisoara Romania Department of Industrial Engineering University of Trento Trento Italy IMS Laboratory University of Bordeaux-IPB ENSEIRB MATMECA Talence France

ISBN: (纸本)9781479961153

In this paper the accuracy of the sine-wave frequency estimator returned by an iterative Interpolated Discrete Fourier Transform (IpDFT) algorithm based on a Maximum Sidelobe Decay (MSD) window is analyzed. The expressions for the contribution to the frequency estimation error of either the spectral interference from the sine-wave image component and wideband noise are derived. It is shown that two algorithm iterations ensure the minimum noise sensitivity achievable with the adopted window. The accuracy of the derived expressions is verified by means of computer simulations and validated by experimental results.

关键词： Uncertainty analysis frequency estimation interpolation algorithms sine-wave windowing

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Ultra-low-cost colour demosaicking VLSI design for real-time video applications

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ELECTRONICS LETTERS 2014年第22期50卷 1585-1586页

作者： Chen, Shih-Lun Chang, Huan-Rui Lin, Ting-Lan Chung Yuan Christian Univ Dept Elect Engn Chung Li City Taiwan

A novel low-complexity and high-quality colour demosaicking algorithm is proposed for very large-scale integration (VLSI) implementation for real-time video applications. It consists of a boundary detector, a boundary mirror model and five green and red-blue colour interpolation models. Two of the five interpolation models can be selected adaptively according to boundary and position information. In addition, a boundary mirror machine and identical direction technique were used to improve the qualities of the reconstructed images. To reduce the hardware cost, memory requirement and power consumption, a hardware-sharing technique and register bank design were used to realise the proposed algorithm. The VLSI architecture of this work contains only 2.9 K gate counts and its core area is 35 966 mu m(2) synthesised by a 0.18 mu m CMOS process. The synthesised results show that this design performs an operating frequency of 100 MHz processing rate by consuming only 1.83 mW. Compared with the previous low-complexity designs, this work not only reduces at least 48.2% of gate counts and 96.7% of power consumption but also improves the average CPSNR quality by more than 0.78 dB.

关键词： DESIGN & construction of very large scale integration of circuits ALGORITHM research MATHEMATICAL models RESEARCH COMPLEMENTARY metal oxide semiconductors interpolation algorithms

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On Fast and Stable Implementation of Clenshaw-Curtis and Fejer-Type Quadrature Rules

ABSTRACT AND APPLIED ANALYSIS

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ABSTRACT AND APPLIED ANALYSIS 2014年第Spe9期000卷 1-10页

作者： Xiang, Shuhuang He, Guo Wang, Haiyong Cent South Univ Sch Math & Stat Changsha 410083 Hunan Peoples R China Huazhong Univ Sci & Technol Sch Math & Stat Wuhan 430074 Hubei Peoples R China

Based upon the fast computation of the coefficients of the interpolation polynomials at Chebyshev-type points by FFT, together with the efficient evaluation of the modified moments by forward recursions or by Oliver's algorithms, this paper presents fast and stable interpolating integration algorithms, by using the coefficients and modified moments, for Clenshaw-Curtis, Fejer's first- and second-type rules for Jacobi weights or Jacobi weights multiplied by a logarithmic function. Numerical examples illustrate the stability, efficiency, and accuracy of these quadratures.

关键词： interpolation algorithms QUADRATURE domains POLYNOMIALS NUMERICAL analysis DIFFERENTIAL equations

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An analysis of processing bulk data with regard to the efficiency of the creation of the GRID structure used in the generation of the digital terrain mode 9

An analysis of processing bulk data with regard to the effic...

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9th International Conference on Environmental Engineering (ICEE)

作者： Gosciewski, Dariusz Univ Warmia & Mazury Fac Geodesy & Land Management Inst Geodesy PL-10957 Olsztyn Poland

ISBN: (纸本)9786094576409

Current survey systems (LiDAR, multibeam echo sounders) allow the automated obtaining of a large amount of surface object measurements in a relatively short time. The large amount of information, survey specificity and the character of the created data sets, as a rule, do not allow them to be used directly for the generation of the digital terrain model (DTM) in spatial information systems (SIS, GIS). The handling of measurement results of this type consists in optimization of set sizes and adaptation of their structure to both the user's requirements and technical processing capabilities. The specificity and universal character of the DTM information layer are an inducement to place particular emphasis on data recording organization and keeping their amount to a minimum. At the same time, it is intended to maintain maximum space description fidelity and its dynamic transformation. Efficient generation of information stored in digital map databases often requires data structure analysis and rationalization of the whole process with regard to processing speed. This paper shows an example of optimizing the efficiency of handling bulk measurement results for DTM creation using the GRID structure. Measurement sets and their processing sequence are also analysed. Methods for selecting the location of measurement points and efficient interpolation algorithms allowing an accurate GRID structure to be generated in a relatively short time are then presented.

关键词： GIS digital terrain model regular GRID structure interpolation algorithms large observation sets

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Newton's interpolation Polynomial for the Sums of Powers of Integers

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American Mathematical Monthly 2015年第10期122卷 1007-1007页

作者： Cereceda, José Luis jl.cereceda@movistar.es

The article presents a mathematical equation explaining Newton interpolation polynomial for the sums of powers of integers in response to the Lgrange interpolation polynomial formula for the powers of integers.

关键词： interpolation algorithms INTEGERS POLYNOMIALS

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A New Approach to General interpolation Formulae for Bivariate interpolation

ABSTRACT AND APPLIED ANALYSIS

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ABSTRACT AND APPLIED ANALYSIS 2014年第SI10期000卷 1-11页

作者： Zou, Le Tang, Shuo Hefei Univ Key Lab Network & Intelligent Informat Proc Hefei 230601 Peoples R China Hefei Univ Technol Dept Math Hefei 230039 Peoples R China

General interpolation formulae for bivariate interpolation are established by introducing multiple parameters, which are extensions and improvements of those studied by Tan and Fang. The general interpolation formulae include general interpolation formulae of symmetric branched continued fraction, general interpolation formulae of univariate and bivariate interpolation, univariate block based blending rational interpolation, bivariate block based blending rational interpolation and their dual schemes, and some interpolation form studied by many scholars in recent years. We discuss the interpolation theorem, algorithms, dual interpolation, and special cases and give many kinds of interpolation scheme. Numerical examples are given to show the effectiveness of the method.

关键词： interpolation algorithms BIVARIATE analysis THEOREMS (Mathematics) SYMMETRIC functions POLYNOMIALS

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Grid adaptive interpolation filters

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ELECTRONICS LETTERS 2013年第3期49卷 181-182页

作者： Won, Chee Sun Dongguk Univ Seoul Dept Elect & Elect Engn Seoul 100715 South Korea

A general framework for image interpolation in a uniformly spaced image grid is presented. The proposed formulation is suitable for representing fractional (or sub-pixel) pixels as well as integer pixel interpolations. Also, by fitting an interpolation kernel to the grid formulation, finite impulse response filter coefficients can be readily determined for a given sampling interval and filter length. As an example, a four-tap lowpass filter is derived by fitting the Lagrange interpolation kernel to a row (or column) expansion by 2 on integer pixel locations.

关键词： IMPULSE response interpolation algorithms PIXELS INTEGERS FINITE impulse response filters (Signal processing)

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Boundedness of One-Sided Oscillatory Integral Operators on Weighted Lebesgue Spaces

ABSTRACT AND APPLIED ANALYSIS

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ABSTRACT AND APPLIED ANALYSIS 2014年第SI26期2014卷 1-7页

作者： Fu, Zunwei Lu, Shanzhen Pan, Yibiao Shi, Shaoguang Linyi Univ Dept Math Linyi 276005 Peoples R China Beijing Normal Univ Sch Math Sci Beijing 100875 Peoples R China Univ Pittsburgh Dept Math Pittsburgh PA 15260 USA

We consider one-sided weight classes of Muckenhoupt type, but larger than the classical Muckenhoupt classes, and study the boundedness of one-sided oscillatory integral operators on weighted Lebesgue spaces using inte... 详细信息

关键词： INTEGRAL operators interpolation algorithms LEBESGUE measure OSCILLATING chemical reactions LEBESGUE-Radon-Nikodym theorems

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