Traditional Interpolation Research Articles

Ultra-precision machining of Fresnel lens mould by single-point diamond turning based on axis B rotation

To promote the machining precision of Fresnel lens mould, a true circle processing method with a single-point diamond turning (SPDT) was proposed. In this method, the arc-curved surface of Fresnel lens mould grooves was processed with axis B rotation, and the frequent servo feed of each axis in the processing with traditional interpolation method was avoided. Moreover, the distribution of the arc-curved surface of the Fresnel lens mould was analyzed. All the centers of the arc-curved surfaces were distributed on the lens axle. The method was realized to process the Fresnel lens mould by combing the processing performance of a four-axis ultra-precision machine tool using axis Z to aid movement and axis B rotation. The straight blade of the tool was replaced by a circular curve by optimizing a single-point diamond tool shape according to the Fresnel lens mould characteristic to reduce the cutting force of the tip of the main cutting edge. Machining experiment on the Fresnel lens mould was studied. A mould with the diameter of 46 mm and curvature radius of 90 mm was processed. Surface of the Fresnel lens was measured using a scanning white-light interferometer. The mould surface roughness was Ra 7.3 nm. The grooves of the lens mould were sharp, and the mould teeth were accordant. Experimental results showed that the machining precision by the proposed Fresnel lens mould with the true circle turning method was high.

Frequency estimation by iterative interpolation based on leakage compensation

An iterative interpolation method for estimation parameters that characterize a linear combination of sinusoids is presented. It is based on the analysis of the generation principle of the spectrum leakage, picket fence effect and an interpolation scheme applied to the discrete Fourier transform, and is described as follows: (1) Estimate parameters by traditional interpolation method; (2) obtain the leakage compensation factors; (3) re-calculate parameters by interpolation method based on leakage compensation; Repeat (2) and (3) until obtain the high precision result. The simulation results show that the proposed iterative method has the better estimation accuracy and stability under noise and the severe long-range leakage situation, and has fast convergence rate. It can be used as an alternative method to improve parameter estimation accuracy of the discrete Fourier transform.

An Effective Technique for Enhancing Direction Finding Performance of Virtual Arrays

The array interpolation technology that is used to establish a virtual array from a real antenna array is widely used in direction finding. The traditional interpolation transformation technology causes significant bias in the directional-of-arrival (DOA) estimation due to its transform errors. In this paper, we proposed a modified interpolation method that significantly reduces bias in the DOA estimation of a virtual antenna array and improves the resolution capability. Using the projection concept, this paper projects the transformation matrix into the real array data covariance matrix; the operation not only enhances the signal subspace but also improves the orthogonality between the signal and noise subspace. Numerical results demonstrate the effectiveness of the proposed method. The proposed method can achieve better DOA estimation accuracy of virtual arrays and has a high resolution performance compared to the traditional interpolation method.

Single-slice reconstruction method for helical cone-beam differential phase-contrast CT

X-ray phase-contrast computed tomography (PC-CT) can provide the internal structure information of biomedical specimens with high-quality cross-section images and has become an invaluable analysis tool. Here a simple and fast reconstruction algorithm is reported for helical cone-beam differential PC-CT (DPC-CT), which is called the DPC-CB-SSRB algorithm. It combines the existing CB-SSRB method of helical cone-beam absorption-contrast CT with the differential nature of DPC imaging. The reconstruction can be performed using 2D fan-beam filtered back projection algorithm with the Hilbert imaginary filter. The quality of the results for large helical pitches is surprisingly good. In particular, with this algorithm comparable quality is obtained using helical cone-beam DPC-CT data with a normalized pitch of 10 to that obtained using the traditional inter-row interpolation reconstruction with a normalized pitch of 2. This method will push the future medical helical cone-beam DPC-CT imaging applications.

A method of vertical and horizontal plus cubic spline interpolation for Mie scattering lidar profile data

Since the traditional spatial data interpolation method has its limits in describing the RHI (range-height indicator) graph for Mie scattering lidar scanning profile, it cannot be applied to the visualization of Mie scattering lidar space-time scan data, and it is also difficult to achieve the continuity in atmospheric parameters evolution process. This paper analyzes the space-position relations in lidar scanning profile data based on the scanning elevation and spatial distribution characteristics of the atmospheric parameters, chooses the reference data rationally of vertical and horizontal positions, and gives the position relevant weight. The smoothness of data is revised by a cubic spline function and the missing data are replenished by interpolation finally. Results show that this method can improve effectively the accuracy of atmospheric lidar scanning data space interpolation, produce few errors; and the RHI graph becomes smooth, thus it conforms to the overall change rule of atmospheric parameters.

A wavelet-based baseline drift correction method for grounded electrical source airborne transient electromagnetic signals

A grounded electrical source airborne transient electromagnetic (GREATEM) system on an airship enjoys high depth of prospecting and spatial resolution, as well as outstanding detection efficiency and easy flight control. However, the movement and swing of the front-fixed receiving coil can cause severe baseline drift, leading to inferior resistivity image formation. Consequently, the reduction of baseline drift of GREATEM is of vital importance to inversion explanation. To correct the baseline drift, a traditional interpolation method estimates the baseline ‘envelope’ using the linear interpolation between the calculated start and end points of all cycles, and obtains the corrected signal by subtracting the envelope from the original signal. However, the effectiveness and efficiency of the removal is found to be low. Considering the characteristics of the baseline drift in GREATEM data, this study proposes a wavelet-based method based on multi-resolution analysis. The optimal wavelet basis and decomposition levels are determined through the iterative comparison of trial and error. This application uses the sym8 wavelet with 10 decomposition levels, and obtains the approximation at level-10 as the baseline drift, then gets the corrected signal by removing the estimated baseline drift from the original signal. To examine the performance of our proposed method, we establish a dipping sheet model and calculate the theoretical response. Through simulations, we compare the signal-to-noise ratio, signal distortion, and processing speed of the wavelet-based method and those of the interpolation method. Simulation results show that the wavelet-based method outperforms the interpolation method. We also use field data to evaluate the methods, compare the depth section images of apparent resistivity using the original signal, the interpolation-corrected signal and the wavelet-corrected signal, respectively. The results confirm that our proposed wavelet-based method is an effective, practical method to remove the baseline drift of GREATEM signals and its performance is significantly superior to the interpolation method.

A new method for interpolating yield curve data, with applications to the South African market

This paper presents a method for interpolating yield curve data in a manner that ensures positive and continuous forward curves. As shown by Hagan and West (2006), traditional interpolation methods suffer from problems: they posit unreasonable expectations, or are not necessarily arbitrage-free. The method presented in this paper, which we refer to as the “monotone preserving r(t)t method", stems from the work done in the field of shape preserving cubic Hermite interpolation, by authors such as Akima (1970), de Boor and Swartz (1977), and Fritsch and Carlson (1980). In particular, the monotone preserving r(t)t method applies shape preserving cubic Hermite interpolation to the log capitalisation function. We present some examples of South African swap and bond curves obtained under the monotone preserving r(t)t method.

A numerical method to generate high temporal resolution precipitation time series by combining weather radar measurements with a nowcast model

The topic of this paper is temporal interpolation of precipitation observed by weather radars. Precipitation measurements with high spatial and temporal resolution are, in general, desired for urban drainage applications. An advection-based interpolation method is developed which uses methods for vector field estimation already known from short-term weather radar nowcasting. However, instead of forecasting the weather radar rainfall, the proposed interpolation method exploits the advection of the rainfall in the interpolation. The interpolated rainfall fields are validated by measurements at ground level from laser disdrometers. The proposed interpolation method performs better when compared to traditional interpolation of weather radar rainfall where the radar observation is considered constant in time between measurements. It is demonstrated that the advection-based interpolation method reconstructs a significant part of the temporal variations of the rainfall. Moreover, the interpolated precipitation fields estimate accumulated rain depths more accurately.

Simulation and Implementation of an Improved Inscribed Chord Interpolation Algorithm

In order to improve the shortcomings of the realization of the traditional quadratic curve interpolation inscribed chord method, this paper proposes an improved internal chord interpolation algorithm. The program flow chart of the algorithm achievement and the interpolation method of circular arc interpolation and linear interpolation of a detailed operation process is given in this paper. Finally through a calculation example the simulation is conducted, and the point by point comparison method were compared. The simulation results show the improvement on the quadratic curve interpolation in the inner string interpolation speed, good flexibility, and it worth popularizing in the interpolation algorithm for real time interpolation.

The Construction of the SGW-Based Bar-Beam Elements

PsdVoigt2 function was used to fit SGW function and a series of bar beam elements based on the theory of SGW and wavelet finite element were constructed. Traditional finite element polynomial interpolation was replaced by the SGW scaling function and transformation matrix was utilized to transform wavelet interpolation coefficients to physical space. Thereby the shape function and element were constructed. The precision of a series of bar beam elements constructed with the SGW scale function as the interpolation function were verified by the calculation cases. The calculation results showed that the precision of the SGW-based element constructed was higher in calculating the deformation and strain. And the SGW-based bar beam element constructed enriched the element library of wavelet-finite element method.

A Fast Interpolation Algorithm Based on the Fractal in the Digital Speckle Sub-Pixel Displacement Measurement

The Digital Speckle Correlation Method is a non-contact in-plane displacement measurement method based on machine vision. The spline, the linear or the bi-cubic interpolation algorithm is often used in the sub-pixel algorithm. The block effect or the edges blurring, however, could occur in these algorithms. Therefore, a fast interpolation algorithm based on fractal theory is proposed in this paper. The results indicate that this algorithm can overcome either the blocking effect or the edge blurring caused by the traditional interpolation algorithm. In addition, with the same sub-pixel accuracy, the shortest time is required.

An interpolation algorithm using center coordinates of pixels for converting SDTV images to HDTV images

How to guarantee high image quality is the key point when converting standard-definition television (SDTV) images to high-definition television (HDTV) images. The change of pixel shape from rectangular to square makes traditional interpolation methods inappropriate because traditional methods are based on integer coordinates. In this paper, we propose a novel interpolation algorithm using center coordinates of pixels (IAUCCP). This method revises the color value of each pixel on HDTV images by correcting the pixels’ xy coordinates. After that, considering the huge enlarging multiples, sharpening treatment is done to the HDTV images. Experiments show that our method greatly improves the HDTV image quality comparing with traditional interpolation algorithms.

Optimal Kinematics of a Looped Filament

New kinematics of supercoiling of closed filaments as solutions of the elastic energy minimization are proposed. The analysis is based on the thin rod approximation of the linear elastic theory, under conservation of the self-linking number. The elastic energy is evaluated by means of bending contribution and torsional influence. Time evolution functions are described by means of piecewise polynomial transformations based on cubic spline functions. In contrast with traditional interpolation, the parameters, which define the cubic splines representing the evolution functions, are considered as the unknowns in a nonlinear optimization problem. We show how the coiling process is associated with conversion of mean twist energy into bending energy through the passage by an inflexional configuration in relation to geometric characteristics of the filament evolution. These results provide new insights on the folding mechanism and associated energy contents and may find useful applications in folding of macromolecules and DNA packing in cell biology.

An improved method for head-related transfer function interpolation and grid matching

Today, there exists a growing number of HRTF datasets available with each set often proposing a unique variation on the spatial discretization measurement grid. These differing grids, typically determined by the mechanical system employed, result in datasets, which are not directly comparable or exploitable. To alleviate the limitation of incompatible grids and assist in the adaptation of measurements performed on one grid to another, facilitating the inter-exchange of HRTF sets, a fixed radius HRTF interpolation method is proposed. The approach is based on decomposition of the sound field using spherical harmonics, allowing for a global spatial recomposition. The frequency domain HRTF is separated into its complex components and interpolations are performed independently before reconstitution. Spherical harmonic truncation order is chosen to provide a system which is roughly square, improving matrix inversion with Tikhonov regularization. A high spatial density HRTF was used as a test case for evaluating the interpolation method. A series of measures are employed to quantitatively compare the quality of the interpolation as compared to traditional interpolation methods in both the time and frequency domains.

INTERPOLATION TECHNIQUES FOR SCATTERED DATA BY LOCAL RADIAL BASIS FUNCTION DIFFERENTIAL QUADRATURE METHOD

Interpolation techniques based on the local radial basis function differential quadrature (LRBF-DQ) method are proposed to interpolate the field values with arbitrarily given scattered data. The interpolation of more unknown field data from the limited known data is becoming an important research subject nowadays for the large-scale engineering analysis and design problems. Three new methods that utilize the field gradient, the governing equation, and both of them are undertaken. The geometric characteristics of the field values can therefore be taken into consideration by the field gradient. In the meantime the physical principle is able to be satisfied with the introduction of the governing equation whose merit is absent in the traditional interpolation techniques, such as the linear polynomial fitting (LPF) and the quadratic polynomial fitting (QPF) methods. The last method will take the advantages of both the methods of gradient and governing equation, namely the geometric characteristics and physical laws. Two numerical examples governed respectively by the three-dimensional (3D) Poisson and the 3D advection–diffusion equations are performed to demonstrate the accuracy and the stability of the present methods. The results are compared with those by the LPF and the QPF methods which show the current interpolation methods are more accurate and robust than the conventional ones.

Estimating Circulation Patterns by Combining Velocity and Tracer Observations

A method is suggested for estimating unknown velocities by combining their sparse measurements with observations of a tracer on a fine grid advected by the underlined velocity field. The dependence of the estimation error on a coarseness parameter and parameters of the flow in question is investigated numerically using synthetic velocity fields typical for real oceanic circulation. In an advanced version of the estimation procedure uncertainty in the transport equation forcing is modeled via a fuzzy sets approach. We also compare the method with a traditional interpolation which is in contrast to the developed procedure unable to capture the flow details.

DEM Densification Using Perspective Shape From Shading Through Multispectral Imagery

Although photogrammetry has long been used as the primary method to produce digital elevation models (DEMs), there are still some locations that are not covered by multiangle images because of various limitations. Moreover, traditional interpolation methods for producing denser DEMs often cause oversmoothing, particularly over rough terrain. To formulate a robust procedure that is capable of reconstructing the terrain surface using sparse ground control points in heterogeneous areas, this letter describes an improved spatial enhancement method combining perspective shape from shading (SFS) using a single optical image. This method is called SFS-based densification using multispectral information (SDMI). First, the image irradiance equation based on the perspective Lambertian model is formulated as a static Hamilton–Jacobi equation and is solved using a fast sweeping strategy. We then reconstruct the relative surface shape and apply an edge-preserved iterative interpolation method to generate a higher resolution DEM grid. Multispectral information is used to reveal the actual surface reflection properties, and the land surface is classified into several types to better estimate surface reflectance. Experiments indicate that SDMI is effective for the interpolation of a sparse grid DEM over heterogeneous terrain.

Study on the Flood Volume Investigation for Medium and Small River

The hydrological research of ungauged basins became the new topic of international hydrological plan, the flood investigation can effectively make up for the information insufficient of the contemporary remote sensing technology and traditional statistical interpolation techniques. Take Dasha River rainstorm for example, water surface slope was monitored of 8‰ by slope-area method, the peak flow was calculated of 1830 m3/s. According to the measured multi-peak flood hydrograph simulates single peak hydrograph and five points probable, the flood volume was calculated of 109 million m3, the runoff coefficient is 0.84 and runoff depth is 505 mm. The river basin has 250 mm previous rainfall, and the underlying surface was saturated, so the result indicated that it accord with runoff yield and concentration theory. The method can be extended for medium and small size river.

Research on Feedrate Planning Model for Continuous Small Lines Contour with Look-Ahead

The traditional line or arc interpolation function treats small line segments separately and conducts feedrate planning within each of them. The rather small lengths of the segments result in low machining efficiency, and the frequent acceleration and deceleration also reduce the lifetime of the motor. To solve these problems, a look-ahead feedrate planning model for the continuous small lines contour (CSLC) is proposed in this paper to implement the high speed interpolating. The feedrate planning is elaborated from the aspects of the curvature characteristic of the contour, the turning feedrate, and the federate optimization between the adjacent segments. Simulations show that the proposed algorithm can efficiently improve the machining efficiency.

Precise Magnetic Field Modeling Techniques of Rotary Machines Using Transient Finite-Element Method

A general and precise method to model rotary machines based on transient magnetic field computation using finite-element method (FEM) is presented. The merits of the proposed method are that the nonlinear iteration on the rotor position can be avoided. Formulas to predict the rotor position and speed of the machine are deduced based on Taylor's expansion. A curvilinear element is used on the two sides of the sliding surface to reduce the numerical noises arising from mesh rotation. The proposed methods for dealing with matching boundary conditions and periodic boundary conditions are very general, accurate and flexible. Typical numerical experiment shows that the numerical error of the local magnetic potentials on the motion sliding surface is only one twentieth of that of traditional interpolation method.