ON HIGH DIMENSIONAL INTERPOLATION

This paper introduces the definition of the Orthogonal Type Node Configuration and discusses the corresponding multivariate Lagrange, Hermite and Birkhoff interpolation problems in high dimensional space R s(s>2). This node configuration can be considered to be a kind of extension of the Cross Type Node Configuration , in R 2 to high dimensional spaces. And the Mixed Type Node Configuration in R s(s>2) is also discussed in this paper in an example.

Parallel-Dynamic Interpolation Algorithm of Sea Surface Height for Future 2D Altimetry Mapping of Sea Surface Height

The sea surface height data volume of the future wide-swath two-dimensional(2D)altimetric satellite is thousands of times greater than that of nadir altimetric satellites.The time complexity of the 2D altimetry mapping reaches O(n^(3)).It is challenging to map the global grid products of future 2D altimetric satellites.In this study,to improve the efficiency of global data mapping,a new algorithm called parallel-dynamic interpolation(PA-DI)was designed.Through the use of 2D data segmentation and fine-grained data mosaic methods,the parallel along-track DI processes were accelerated,and a fast and efficient spatial-temporal high-resolution and low-error enhanced mapping method was obtained.As determined from a comparison of the single-threaded DI with the PA-DI,the new algorithm optimized the time complexity from O(n^(3))to O(n^(3)/KL),which improved the mapping efficiency and achieved the expected results.According to the test results of the observing system simulation experiments,the PA-DI algorithm may provide an efficient and reliable method for future wide-swath 2D altimetric satellite mapping.

Calculation of Space NURBS Curve Interpolation Error

Aiming at the problem of low accuracy of interpolation error calculation of existing NURBS curves, an approximate method for the distance between a point and a NURBS interpolation curve is proposed while satisfying the accuracy of the solution. Firstly, the minimum parameter interval of the node vector corresponding to the data point under test in the original data point sequence is determined, and the parameter interval is subdivided according to the corresponding step size, and the corresponding parameter value is obtained. Secondly, the distance from the measured point to the NURBS curve is calculated, and the nearest distance is found out. The node interval is subdivided again on one side of the nearest distance. Finally, the distance between the data point to be measured and each subdivision point is calculated again, and the minimum distance is taken as the interpolation error between the point and the NURBS curve. The simulation results of actual tool position data show that this method can more accurately obtain the error of spatial NURBS interpolation curve.

Three-Dimensional Space Interpolation of Grey / Depth Image Sequence-A New Technique of Computer Graphics Synthesis

This paper advances a three-dimensional space interpolation method of grey / depth image sequence, which breaks free from the limit of original practical photographing route. Pictures can cruise at will in space. By using space sparse sampling, great memorial capacity can be saved and reproduced scenes can be controlled. To solve time consuming and complex computations in three-dimensional interpolation algorithm, we have studied a fast and practical algorithm of scattered space lattice and that of 'Warp' algorithm with proper depth. By several simple aspects of three dimensional space interpolation, we succeed in developing some simple and practical algorithms. Some results of simulated experiments with computers have shown that the new method is absolutely feasible.

ACCURATE COMPUTATION AND INTERPOLATION TECHNIQUE OF FINITE ANALYTIC COEFFICIENTS

The finite analytic method (FA) developed in the last decade is an effective numerical method for solving fluid flow problems. However, because of the limitation in the present computer, large round-off errors are found in calculating FA coefficients when Reynolds number is large. This paper investigates the cause of this difficulty and presents a special programming technique in making an accurate computation of FA coefficients. Then a fundamental function known as 'Pe' is tabulated by the accurate computation. In practical application the interpolation technique is employed so that the FA coefficients can be obtained reliably and quickly.

SHAPE PRESERVING INTERPOLATION USING PIECEWISE CUBIC

The papcr gives an approach to construct shape preserving piece wise cubic, where twocubic picces are allowed by inscrting at most a new knot in each data subinterval, and these cubicpieees is C2 continuous at each new knot. Two numerical examples show that the method is effec.tive and visually pleasing.

ANGULAR VELOCITY INTERPOLATION USING QUATERNION

In simulation,sometimes we wish to stipulate a specified angular velocity applied to a given frame.Although position,linear velocity and orientation interpolations are well studied,less attention is paid on angular velocity interpolation.In this paper,a new method to smoothly interpolate angular velocity using quaternions is presented.This method can be easily incorporated into a key frame animation system.The angular velocity at an arbitrary time can be calculated easily by our method.This method can also be generalized to smoothly interpolate orientations.

An efficient large-scale mesh deformation method based on MPI/Open MP hybrid parallel radial basis function interpolation

An efficient MPI/OpenMP hybrid parallel Radial Basis Function (RBF) strategy for both continuous and discontinuous large-scale mesh deformation is proposed to reduce the computational cost and memory consumption.Unlike the conventional parallel methods in which all processors use the same surface displacement and implement the same operation,the present method employs different surface points sets and influence radius for each volume point movement,accompanied with efficient geometry searching strategy.The deformed surface points,also called Control Points (CPs),are stored in each processor.The displacement of spatial points is interpolated by using only 20-50 nearest control points,and the local influence radius is set to 5-20 times the maximum displacement of control points.To shorten the searching time for the nearest control point clouds,an Alternating Digital Tree (ADT) algorithm for 3D complex geometry is designed based on an iterative bisection technique.Besides,an MPI/OpenMP hybrid parallel approach is developed to reduce the memory cost in each High-Performance Computing (HPC) node for large-scale applications.Three 3D cases,including the ONERA-M6 wing and a commercial transport airplane standard model with up to 2.5 billion hybrid elements,are used to test the present mesh deformation method.The robustness and high parallel efficiency are demonstrated by a wing deflection case with a maximum bending angle of 450 and more than 80% parallel efficiency with 1024 MPI processors.In addition,the availability for both continuous and discontinuous surface deformation is verified by interpolating the projecting displacement with opposite directions surface points to the spatial points.

Interpolation and approximation for data living on manifold surfaces

Meshed surfaces are ubiquitous in digital geometry processing and computer graphics. The set of attributes associated with each vertex such as the vertex locations, curvature, temperature, pressure or saliency, can be recognized as data living on mani- fold surfaces. So interpolation and approximation for these data are of general interest. This paper presents two approaches for mani- fold data interpolation and approximation through the properties of Laplace-Beltrami operator （Laplace operator defined on a mani- fold surface）. The first one is to use Laplace operator minimizing the membrane energy of a scalar function defined on a manifold. The second one is to use bi-Laplace operator minimizing the thin plate energy of a scalar function defined on a manifold. These two approaches can process data living on high genus meshed surfaces. The approach based on Laplace operator is more suitable for manifold data approximation and can be applied manifold data smoothing, while the one based on bi-Laplace operator is more suit- able for manifold data interpolation and can be applied image extremal envelope computation. All the application examples demon- strate that our procedures are robust and efficient.

OBTAINING EXACT INTERPOLATION MULTIVARIATE POLYNOMIAL BY APPROXIMATION

In some fields such as Mathematics Mechanization, automated reasoning and Trustworthy Computing, etc., exact results are needed. Symbolic computations are used to obtain the exact results. Symbolic computations are of high complexity. In order to improve the situation, exact interpolating methods are often proposed for the exact results and approximate interpolating methods for the ap- proximate ones. In this paper, the authors study how to obtain exact interpolation polynomial with rational coefficients by approximate interpolating methods.

C^2 quartic spline surface interpolation

This paper discusses the problem of constructing C2 quartic spline surface interpolation. Decreasing the continuity of the quartic spline to C2 offers additional freedom degrees that can be used to adjust the precision and the shape of the interpolation surface. An approach to determining the freedom degrees is given, the continuity equations for constructing C2 quartic spline curve are discussed, and a new method for constructing C2 quartic spline surface is presented. The advantages of the new method are that the equations that the surface has to satisfy are strictly row diagonally dominant, and the discontinuous points of the surface are at the given data points. The constructed surface has the precision of quartic polynomial. The comparison of the interpolation precision of the new method with cubic and quartic spline methods is included.

Toolpath Interpolation and Smoothing for Computer Numerical Control Machining of Freeform Surfaces: A Review

Driven by the ever increasing demand in function integration,more and more next generation high value-added products,such as head-up displays,solar concentrators and intra-ocular-lens,etc.,are designed to possess freeform(i.e.,non-rotational symmetric)surfaces.The toolpath,composed of high density of short linear and circular segments,is generally used in computer numerical control(CNC)systems to machine those products.However,the discontinuity between toolpath segments leads to high-frequency fluctuation of feedrate and acceleration,which will decrease the machining efficiency and product surface finish.Driven by the ever-increasing need for high-speed high-precision machining of those products,many novel toolpath interpolation and smoothing approaches have been proposed in both academia and industry,aiming to alleviate the issues caused by the conventional toolpath representation and interpolation methods.This paper provides a comprehensive review of the state-of-the-art toolpath interpolation and smoothing approaches with systematic classifications.The advantages and disadvantages of these approaches are discussed.Possible future research directions are also offered.

Fast regularized image interpolation method

The regularized image interpolation method is widely used based on the vector interpolation model in which down-sampling matrix has very large dimension and needs large storage consumption and higher computation complexity. In this paper, a fast algorithm for image interpolation based on the tensor product of matrices is presented, which transforms the vector interpolation model to matrix form. The proposed algorithm can extremely reduce the storage requirement and time consumption. The simulation results verify their validity.

Motion-compensated interpolation for face-centered-orthorhombic sampled video sequence

Face-centered orthorhombic（FCO） sampling can be implemented more easily on CMOS image sensors than on other video acquisition devices.The sampling efficiency of FCO is the highest among all threedimensional（3D） sampling schemes.However,interpolation of FCO-sampled data is inevitable in bridging human perception and machine-vision algorithms.In this letter,the concept of motion compensation is borrowed from deinterlacing,which displays interlaced videos on progressively scanned devices.The combination of motion estimation based on intrafield interpolated frames and motion-compensated interfield interpolation is found to provide the best performance by evaluating different combinations of motion estimation and interpolation.

Design of a novel hybrid quantum deep neural network in INEQR images classification

We redesign the parameterized quantum circuit in the quantum deep neural network, construct a three-layer structure as the hidden layer, and then use classical optimization algorithms to train the parameterized quantum circuit, thereby propose a novel hybrid quantum deep neural network(HQDNN) used for image classification. After bilinear interpolation reduces the original image to a suitable size, an improved novel enhanced quantum representation(INEQR) is used to encode it into quantum states as the input of the HQDNN. Multi-layer parameterized quantum circuits are used as the main structure to implement feature extraction and classification. The output results of parameterized quantum circuits are converted into classical data through quantum measurements and then optimized on a classical computer. To verify the performance of the HQDNN, we conduct binary classification and three classification experiments on the MNIST(Modified National Institute of Standards and Technology) data set. In the first binary classification, the accuracy of 0 and 4 exceeds98%. Then we compare the performance of three classification with other algorithms, the results on two datasets show that the classification accuracy is higher than that of quantum deep neural network and general quantum convolutional neural network.

基于Bezier曲线的功率车人机交互系统设计

针对功率车在使用过程中骑行体验感较差的问题,提出了一种具有人机交互功能的功率车训练系统。该系统的下位机由功率车、霍尔传感器、单片机和伺服电机等模块组成,功率车的阻力通过设计的新型磁阻装置进行无级连续调节。基于贝塞尔曲线对上位机的骑行路径进行优化,结合实时插值、等距插值和非等距插值算法,提升了场景跟踪效果。实验结果表明,基于贝塞尔曲线的实时插值算法生成的路径能够满足体感一致性,确保人机交互过程中场景的流畅性与稳定性。

基于Delaunay三角网的克里金并行算法优化

当采样点数据量较大时,可以采用Delaunay三角剖分建立三角网来使用局部邻域采样点进行克里金插值.但是该算法需要对每个插值点拟合半变异函数,插值点规模大时造成巨大开销.为此,本文提出了一种以三角形为单位拟合半变异函数的克里金插值方法,采用CPU-GPU负载均衡将部分计算优化,充分考虑不均匀样本对克里金插值效果的影响.结果表明,本文算法能够保证不均匀样本集的插值效果,提升了计算性能且能够保证较高的精度.

基于计算机视觉和视频插帧的结构振动测试与模态识别

结构振动测试和模态参数识别是基于结构动态特性进行结构健康监测(SHM)的基本方法。为克服传统接触式测试的不便,引入了非接触式计算机视觉方法,其中以智能手机为数据采集装置的方法受到越来越多的关注。然而智能手机相机往往因为性能受限无法满足需求,从而导致测量结果精度下降。为此,提出一种改进的视频插帧算法EQVI-T与改进的边缘检测算法,通过提高原始视频的帧率和提出的特征点追踪方法共同提升计算精度。为验证这一方法的有效性,将其应用于试验室模型的位移响应监测和模态参数识别,并进行了定量和定性评估。结果表明,所提方法在提高测量精度和准确性方面具有显著优势,展示了其在结构振动测试中的潜在应用价值。

基于三次样条插值的M-QAM载波相位估计

在基于高阶调制的相干光通信传输系统中,接收端信号受相位噪声干扰会对系统性能产生直接的影响。传统的盲相位搜索(BPS)算法具有较高的线宽容差,适用于多种调制格式,但随着调制阶数的增加,用于BPS的测试相位数量会急剧加大。针对M元正交振幅调制(M-QAM)格式,本研究提出了一种新的低复杂度载波相位估计(CPE)算法。首先利用BPS算法,得到B个测试相位和平均欧氏距离之间的关系;然后在此基础上,提出了一种基于三次样条插值(CSI)的两级BPS载波相位估计算法,得到(2B−1)个等间隔插值相位和平均欧氏距离之间的光滑曲线关系;最后取曲线的最小值处所对应的相位值为最优相位估计值。仿真结果表明,在使用少量测试相位的前提下,通过CSI算法可以有效地对载波相位进行恢复,与BPS算法相比,CSI算法乘、加法器计算复杂度分别降低了38%和42%(16-QAM),为载波相位恢复提供了新思路。

基于参数化降阶模型的非线性气动弹性高效分析

针对非线性气动弹性分析时需要在时域求解多个流场参数条件下结构运动方程而造成的计算消耗过大的问题,提出了一种适用于参数变化时非定常流场高效计算的参数化降阶模型,不仅可以应用于计算机翼等结构的总体气动力还可以得到每个时刻的结构表面的流场数据分布,并成功应用于典型机翼的跨声速颤振边界的计算,大大地提高了计算效率.结果显示,单流场条件时降阶模型的计算速度比直接使用时域分析方法提高了3倍;在计算多流场参数条件下,参数化降阶模型相比于使用单流场降阶模型计算速度提高了3.5倍,相较于时域分析方法提高了10倍.