Direct interpolation algorithm for pen-cutting of sculptured surfaces

A direct interpolation algorithm for spatial curves on a surface is proposed for pen-cutting of sculptured surfaces. The algorithm can carry out the direct interpolation for projective curves lying on the sculptured surface. It is based on the geometric and kinetic relationships between drive curves and cutter-contact （C-C） curves. It evaluates the parameter of drive curves corresponding to interpolation points by the Taylor formula. Then it gains coordinates of interpolation points indirectly by inverse calculation. Finally, it generates the motion commands for machine tool controller. This method extends the locus-controlled function in the computer numerical control （CNC） system effectively and improves the efficiency for the numerical control （NC） machining of sculptured surfaces. The simulation shows that the proposed algorithm is feasible and practical. This algorithm can also be applied to the machining of the whole surface.

ALGORITHMS OF GENERATION MOTION AND DIRECT INTERPOLATION FOR SPIRAL BEVEL GEAR NC MACHINING

The generating motion of the generating gear and the work gear on spiral bevel gear NC machining is analyzed. The mathematical model of the tooth surface of spiral bevel gear is presented. A direct interpolation algorithm of spiral bevel gear NC machining is proposed, thus establishing the relationship between the motion of the cutter-head center and the rotation of the work gear. The interpolation algorithm is implemented to control the gear cutting on self-developed spiral bevel gear NC cutting machine. An example is given to verify the mathematical model and the interpolation algorithm.

Radial Basis Function Interpolation and Galerkin Projection for Direct Trajectory Optimization and Costate Estimation

This work presents a novel approach combining radial basis function(RBF)interpolation with Galerkin projection to efficiently solve general optimal control problems.The goal is to develop a highly flexible solution to optimal control problems,especially nonsmooth problems involving discontinuities,while accounting for trajectory accuracy and computational efficiency simultaneously.The proposed solution,called the RBF-Galerkin method,offers a highly flexible framework for direct transcription by using any interpolant functions from the broad class of global RBFs and any arbitrary discretization points that do not necessarily need to be on a mesh of points.The RBF-Galerkin costate mapping theorem is developed that describes an exact equivalency between the Karush-Kuhn-Tucker(KKT)conditions of the nonlinear programming problem resulted from the RBF-Galerkin method and the discretized form of the first-order necessary conditions of the optimal control problem,if a set of discrete conditions holds.The efficacy of the proposed method along with the accuracy of the RBF-Galerkin costate mapping theorem is confirmed against an analytical solution for a bang-bang optimal control problem.In addition,the proposed approach is compared against both local and global polynomial methods for a robot motion planning problem to verify its accuracy and computational efficiency.

New Edge-Directed Interpolation Based-Lifting DWT and MSPIHT Algorithm for Image Compression

The amount of image data generated in multimedia applications is ever increasing. The image compression plays vital role in multimedia applications. The ultimate aim of image compression is to reduce storage space without degrading image quality. Compression is required whenever the data handled is huge they may be required to sent or transmitted and also stored. The New Edge Directed Interpolation (NEDI)-based lifting Discrete Wavelet Transfrom (DWT) scheme with modified Set Partitioning In Hierarchical Trees (MSPIHT) algorithm is proposed in this paper. The NEDI algorithm gives good visual quality image particularly at edges. The main objective of this paper is to be preserving the edges while performing image compression which is a challenging task. The NEDI with lifting DWT has achieved 99.18% energy level in the low frequency ranges which has 1.07% higher than 5/3 Wavelet decomposition and 0.94% higher than traditional DWT. To implement this NEDI with Lifting DWT along with MSPIHT algorithm which gives higher Peak Signal to Noise Ratio (PSNR) value and minimum Mean Square Error (MSE) and hence better image quality. The experimental results proved that the proposed method gives better PSNR value (39.40 dB for rate 0.9 bpp without arithmetic coding) and minimum MSE value is 7.4.

FEATURE PRESERVING IMAGE INTERPOLATION BY ADAPTIVE BIDIRECTIONAL FLOW

Most image interpolation algorithms currently used suffer visually to some extent the effects of blurred edges and jagged artifacts in the image. This letter presents an adaptive feature preserving bidirectional flow process, where an inverse diffusion is performed to enhance edges along the normal directions to the iso-phote lines (edges), while a normal diffusion is done to remove artifacts ('jaggies') along the tangent directions. In order to preserve image features such as edges, angles and textures, the nonlinear diffusion coefficients are locally adjusted according to the first order and the second order directional derivatives of the image. Experimental results on the Lena image demonstrate that our interpolation algorithm substantially improves the subjective quality of the interpolated images over conventional interpolations.

Graph-Directed Coalescence Hidden Variable Fractal Interpolation Functions

Fractal interpolation function (FIF) is a special type of continuous function which interpolates certain data set and the attractor of the Iterated Function System (IFS) corresponding to a data set is the graph of the FIF. Coalescence Hidden-variable Fractal Interpolation Function (CHFIF) is both self-affine and non self-affine in nature depending on the free variables and constrained free variables for a generalized IFS. In this article, graph directed iterated function system for a finite number of generalized data sets is considered and it is shown that the projection of the attractors on is the graph of the CHFIFs interpolating the corresponding data sets.

Two-level Bregmanized method for image interpolation with graph regularized sparse coding

A two-level Bregmanized method with graph regularized sparse coding （TBGSC） is presented for image interpolation. The outer-level Bregman iterative procedure enforces the observation data constraints, while the inner-level Bregmanized method devotes to dictionary updating and sparse represention of small overlapping image patches. The introduced constraint of graph regularized sparse coding can capture local image features effectively, and consequently enables accurate reconstruction from highly undersampled partial data. Furthermore, modified sparse coding and simple dictionary updating applied in the inner minimization make the proposed algorithm converge within a relatively small number of iterations. Experimental results demonstrate that the proposed algorithm can effectively reconstruct images and it outperforms the current state-of-the-art approaches in terms of visual comparisons and quantitative measures.

A Certified Cubic B-Spline Interpolation Method with Tangential Direction Constraints

Curve interpolation with B-spline is widely used in various areas. This problem is classic and recently raised in application scenario with new requirements such as path planning following the tangential vector field under certified error in CNC machining. This paper proposes an algorithm framework to solve Hausdorff distance certified cubic B-spline interpolation problem with or without tangential direction constraints. The algorithm has two stages: The first stage is to find the initial cubic B-spine fitting curve which satisfies the Hausdorff distance constraint;the second stage is to set up and solve the optimization models with certain constraints. Especially, the sufficient conditions of the global Hausdorff distance control for any error bound are discussed, which can be expressed as a series of linear and quadratic constraints. A simple numerical algorithm to compute the Hausdorff distance between a polyline and its B-spline interpolation curve is proposed to reduce our computation.Experimental results are presented to show the advantages of the proposed algorithms.

A novel DOA estimation algorithm using directional antennas in cylindrical conformal arrays

In this paper, a novel direction of arrival(DOA) estimation algorithm using directional antennas in cylindrical conformal arrays(CCAs) is proposed. To eliminate the shadow effect, we divide the CCAs into several subarrays to obtain the complete output vector. Considering the anisotropic radiation pattern of a CCA, which cannot be separated from the manifold matrix, an improved interpolation method is investigated to transform the directional subarray into omnidirectional virtual nested arrays without non-orthogonal perturbation on the noise vector. Then, the cross-correlation matrix(CCM) of the subarrays is used to generate the consecutive co-arrays without redundant elements and eliminate the noise vector. Finally, the full-rank equivalent covariance matrix is constructed using the output of co-arrays,and the unitary estimation of the signal parameters via rotational invariance techniques(ESPRIT) is performed on the equivalent covariance matrix to estimate the DOAs with low computational complexity. Numerical simulations verify the superior performance of the proposed algorithm, especially under a low signal-to-noise ratio(SNR) environment.

THE GLOBAL APPROXIMATION BY LEFT-BERNSTEIN-DURRMEYER QUASI-INTERPOLANTS IN Lp[0,1]

In this paper, we will use the 2r-th Ditzian-Totik modulus of smoothness wψ2r(f,t)p to discuss the direct and inverse theorem of approximation by Left-Bernstein-Durrmeyer quasi-interpolants Mn[2r-1]f for functions of the space Lp[0,1] (1≤ p≤ +∞).

DESIGN OF VIRTUAL UNIFORM LINEAR ARRAYS FOR EFFICIENT DIRECTION FINDING

The problem considered in this paper is to interpolate a virtual uniform array froma real two-dimensional array with arbitrary geometry via an interpolation matrix. The key to thisproblem is how to arrange these virtual sensors. It is shown that the virtual uniform linear arrayshould have the same main-lobe beam-pattern as the real array over an angular sector of interest.Simulation results are presented to illustrate the application of virtual array in direction finding.

A Discussion about Reducing the Amount of Calculation of Direct Method

The general interpolation mentioned in this a rticle provides an effective way for reducing the amount of calculation of direc t optimal exploration. It has been testified by real case calculations that the interpolation is not only reliable but also can save the amount of calculation by nearly 36%. Large amount of calculation and lacking strict theoretical bas is has been th e two disadvantage of direct method by new. If this defect is not overcome, they will not only s eriously affect the application of this method, but also hinder its further rese arch. Based on sufficient calculation practice, this article has made a primary discussion about the theory and method of reducing the amount of calculation, an d has achieved some satisfactory results.

Direction Finding Using Cumulant in Multipath Environment with an Arbitrary Array

In this paper, the problem of estimating the direction of arrival of signals of which some may be perfectly correlated is considered. This method can be applied in the situation that the non-Gaussian independent and coherent signals coexist with unknown Gaussian noise. In this method at first via mappings, the virtual uniform linear array (ULA) and also the shifted versions of this virtual ULA by assuming that all the DOAs are located in one section are constructed. In order to avoid coloring the noise because of these mappings we use a cumulant matrix instead of a covariance ones. In this method since we construct all the subarrays virtually for detection of coherent signals we do not need the array with regular configuration. The advantages of this method are: increasing the array aperture, having the ability to find the DOAs with fewer sensors and also avoiding the coupling between sensors as much as possible in contrast to conventional spatial smoothing.

基于非对称幅度插值的二维来波方位估计

幅度插值方位估计法通过对少数几个波束采样插值得到来波方位,避免了密集的方位搜索,在工程中有广泛的应用。目前该方法大多基于一维,且使用对称函数进行插值,估计误差较高。本文通过解耦的方式将该方法由一维推广至二维任意阵,并考虑真实方位谱在偏离0°后左右波束不对称的情况,利用左右波束斜率比作为求解条件,使用非对称函数进行幅度插值。进一步,针对二维非对称插值中出现的角度失配问题,提出了迭代插值的解决方法。最后仿真分析了插值方法、迭代插值以及信噪比对插值精度的影响,所提出方法的插值精度优于传统对称插值方法;且通过千岛湖实验数据验证,所提方法以10°间隔插值得到的估计精度可以比拟常规波束形成以0.01°进行密集扫描的估计精度。所提方法能够在满足一些工程应用中对实时性要求的同时达到较高的方位估计精度。

考虑扬声器指向性补偿的声场再现方法研究

在实验室环境下精准再现基于测试或仿真的声环境,对降噪优化设计与声品质评价研究具有重要意义。常用的基于扬声器阵列的声场再现方法能在特定的空间区域内再现原始声场分布,提供更为真实的临场感和沉浸感,但扬声器的指向性特性较差会降低声场再现的精度。本文提出一种考虑扬声器指向性补偿的声场再现方法用于提高声场再现的精度。该方法基于扬声器指向性的声压表达模型,利用坐标变换的方法将空间观测点转换到以扬声器为中心的局部坐标系下,并采用插值的方法实现空间观测点的指向性补偿;最后采用声压匹配的方法求解扬声器驱动权重,实现声场的精准再现。开展基于仿真指向性补偿和实测指向性补偿的声场再现试验,结果表明考虑指向性补偿比不考虑补偿的声场再现精度平均提高了约22.37%,验证了所提声场再现方法的有效性。

阵列流形向量映射的虚拟稀疏阵测向方法

方位估计技术用于获得空间中的目标方位,阵列自由度表征阵列最多可分辨的目标个数,增加阵列自由度是方位估计的关键技术。稀疏阵的差分阵列可以实现利用较少的阵元个数,分辨更多的目标个数。但是为了降低稀疏阵的方位估计技术的难度,只选取稀疏阵差分阵列中最大连续的均匀直线阵进行方位估计,造成了阵元信息的浪费,且经常无法有效提高阵列自由度。为了进一步提高自由度,本文提出一种阵列流形向量映射的虚拟稀疏阵方位估计方法,利用虚拟阵列技术,在实际稀疏阵中增加虚拟阵元,使得虚拟稀疏阵差分阵列的最大连续均匀直线阵具有更多阵元,从而增加阵列自由度,理论分析与仿真结果证明了该方法的有效性。

一种整数抽取结合小数插值重采样技术研究

射频直采技术近年来在雷达、通信、电子对抗尤其是一体化接收等领域得到了广泛的应用。然而射频采样数据率极高,导致后续信号传输与实时处理难度变大。数字重采样技术能够在数字域降低采样率,从而减轻射频直采带来的信号处理压力。本文针对数字重采样技术开展研究,提出一种整数抽取结合小数插值重采样方法,推导了理论模型,给出了相应的参数递推解算方法,仿真验证了方法的有效性。采用本文所提方法,既可解决在射频高采样率下,直接进行小数插值带来的数字信号实时处理压力,又可在保证信号质量的情况下,解决特殊场景下精确变采样率处理的需求,进而实现对大范围任意分数倍抽取。

一种基于粗网格的多算子模拟成像方法

对于已知速度模型,传统的叠前深度偏移成像方法都是以快速获得高精度偏移剖面为目的。基于成像算子的模拟叠前深度偏移成像方法无需进行波场正演和偏移处理便可快速得到偏移结果,但成像算子却是根据单一散射点散射向量构建的,只能对散射点附近的局部区域进行精准模拟成像。为了提高直接模拟成像结果的可靠性和兼顾直接模拟成像计算效率高的优势,先在粗网格离散原速度模型的前提下建立粗点扩散算子,在波数域对粗点扩散算子进行不同插值方法测试,测试不同尺寸粗网格以及不同插值方法对模拟成像结果的影响。在此基础上,又提出一种多算子协同模拟成像,设置多个局部偏移成像窗,每个窗内布置散射点并求取射线路径,分区构建较为精准的控制局部成像的成像算子,使模拟成像结果能更好地体现观测系统对不同区域的理论成像结果的影响。该方法不仅保留了快速成像的高计算效率,同时得到控制局部成像的成像算子,可以模拟不同区域在同一观测系统的理论模拟成像结果,并检测观测系统对全局成像的影响,可以直接展示观测系统对不同区域理论成像的控制。

B样条拟插值算子在Orlicz空间中的逼近

为了研究B样条拟插值算子在Orlicz空间的逼近性质,根据m阶B样条算子所构造出的B样条拟插值算子的定义,利用B样条算子的基本性质、Orliz空间的相关性质和光滑模、K泛函及其等价性质等工具,参照B样条拟插值算子在Lp空间逼近的研究方法对B样条拟插值算子进行了研究,得到B样条拟插值算子的有界性,最后得出B样条拟插值算子在Orlicz空间的逼近正定理。

比例方向阀静态特性仿真与实验

比例方向阀是电液控制技术中最基础的元件之一,其作用是对液压执行机构的速度、方向、位置和输出力进行连续控制。在比例方向阀使用过程中,发现电压指令相同时,当比例方向阀阀口的压差较大时,随着压差的增加,流量出现了不增反减的现象。为了解释该现象,建立两种比例方向阀的静态仿真模型:第一种静态仿真模型基于液动力和阀口流量的经验公式;第二种静态仿真模型基于通过ANSYS Fluent流场数值计算得到的液动力和阀口流量插值公式。静态仿真结果表明:阀口流量不增反减的原因在于当压差增大时,液动力增加导致阀芯位移减小,进而使流量减小。实验结果证明:相比传统的经验公式,使用基于流场仿真数据得出的稳态液动力和阀口流量插值公式时,静态仿真结果更接近实验结果。