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Journal articles on the topic 'Interpolation'
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1
Earshia V., Diana, and Sumathi M. "Interpolation of Low-Resolution Images for Improved Accuracy Using an ANN Quadratic Interpolator." International Journal on Recent and Innovation Trends in Computing and Communication 11, no. 4s (April 3, 2023): 135–40. http://dx.doi.org/10.17762/ijritcc.v11i4s.6319.
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The era of digital imaging has transitioned into a new one. Conversion to real-time, high-resolution images is considered vital. Interpolation is employed in order to increase the number of pixels per image, thereby enhancing spatial resolution. Interpolation's real advantage is that it can be deployed on user end devices. Despite raising the number of pixels per inch to enhances the spatial resolution, it may not improve the image's clarity, hence diminishing its quality. This strategy is designed to increase image quality by enhancing image sharpness and spatial resolution simultaneously. Proposed is an Artificial Neural Network (ANN) Quadratic Interpolator for interpolating 3-D images. This method applies Lagrange interpolating polynomial and Lagrange interpolating basis function to the parameter space using a deep neural network. The degree of the polynomial is determined by the frequency of gradient orientation events within the region of interest. By manipulating interpolation coefficients, images can be upscaled and enhanced. By mapping between low- and high-resolution images, the ANN quadratic interpolator optimizes the loss function. ANN Quadratic interpolator does a good work of reducing the amount of image artefacts that occur during the process of interpolation. The weights of the proposed ANN Quadratic interpolator are seeded by transfer learning, and the layers are trained, validated, and evaluated using a standard dataset. The proposed method outperforms a variety of cutting-edge picture interpolation algorithms..
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Gashnikov, M. V. "Parameterized interpolation for fusion of multidimensional signals of various resolutions." Computer Optics 44, no. 3 (June 2020): 436–40. http://dx.doi.org/10.18287/2412-6179-co-696.
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Parameterized interpolation algorithms are adapted to fusion of multidimensional signals of various resolutions. Interpolating functions, switching rules for them and local features are specified, based on which the interpolating function is selected at each point of the signal. Parameterized interpolation algorithms are optimized based on minimizing the interpolation error. The recurrent interpolator optimization scheme is considered for the situation of inaccessibility of interpolated samples at the stage of setting up the interpolation procedure. Computational experiments are carried out to study the proposed interpolators for fusion of real multidimensional signals of various types. It is experimentally confirmed that the use of parameterized interpolators allows one to increase the accuracy of signal fusion.
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Xu, Weizhi. "Elements of Bi-cubic Polynomial Natural Spline Interpolation for Scattered Data: Boundary Conditions Meet Partition of Unity Technique." Statistics, Optimization & Information Computing 8, no. 4 (December 2, 2020): 994–1010. http://dx.doi.org/10.19139/soic-2310-5070-1083.
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This paper investigates one kind of interpolation for scattered data by bi-cubic polynomial natural spline, in which the integral of square of partial derivative of two orders to x and to y for the interpolating function is minimal (with natural boundary conditions). Firstly, bi-cubic polynomial natural spline interpolations with four kinds of boundary conditions are studied. By the spline function methods of Hilbert space, their solutions are constructed as the sum of bi-linear polynomials and piecewise bi-cubic polynomials. Some properties of the solutions are also studied. In fact, bi-cubic natural spline interpolation on a rectangular domain is a generalization of the cubic natural spline interpolation on an interval. Secondly, based on bi-cubic polynomial natural spline interpolations of four kinds of boundary conditions, and using partition of unity technique, a Partition of Unity Interpolation Element Method (PUIEM) for fitting scattered data is proposed. Numerical experiments show that the PUIEM is adaptive and outperforms state-of-the-art competitions, such as the thin plate spline interpolation and the bi-cubic polynomial natural spline interpolations for scattered data.
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Parker, Joshua, Dionne Ibarra, and David Ober. "Logarithm-Based Methods for Interpolating Quaternion Time Series." Mathematics 11, no. 5 (February 24, 2023): 1131. http://dx.doi.org/10.3390/math11051131.
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In this paper, we discuss a modified quaternion interpolation method based on interpolations performed on the logarithmic form. This builds on prior work that demonstrated this approach maintains C2 continuity for prescriptive rotation. However, we develop and extend this method to descriptive interpolation, i.e., interpolating an arbitrary quaternion time series. To accomplish this, we provide a robust method of taking the logarithm of a quaternion time series such that the variables θ and n^ have a consistent and continuous axis-angle representation. We then demonstrate how logarithmic quaternion interpolation out-performs Renormalized Quaternion Bezier interpolation by orders of magnitude.
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Etherington, Thomas R. "Discrete natural neighbour interpolation with uncertainty using cross-validation error-distance fields." PeerJ Computer Science 6 (July 13, 2020): e282. http://dx.doi.org/10.7717/peerj-cs.282.
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Interpolation techniques provide a method to convert point data of a geographic phenomenon into a continuous field estimate of that phenomenon, and have become a fundamental geocomputational technique of spatial and geographical analysts. Natural neighbour interpolation is one method of interpolation that has several useful properties: it is an exact interpolator, it creates a smooth surface free of any discontinuities, it is a local method, is spatially adaptive, requires no statistical assumptions, can be applied to small datasets, and is parameter free. However, as with any interpolation method, there will be uncertainty in how well the interpolated field values reflect actual phenomenon values. Using a method based on natural neighbour distance based rates of error calculated for data points via cross-validation, a cross-validation error-distance field can be produced to associate uncertainty with the interpolation. Virtual geography experiments demonstrate that given an appropriate number of data points and spatial-autocorrelation of the phenomenon being interpolated, the natural neighbour interpolation and cross-validation error-distance fields provide reliable estimates of value and error within the convex hull of the data points. While this method does not replace the need for analysts to use sound judgement in their interpolations, for those researchers for whom natural neighbour interpolation is the best interpolation option the method presented provides a way to assess the uncertainty associated with natural neighbour interpolations.
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Gashnikov, M. V. "Interpolation based on context modeling for hierarchical compression of multidimensional signals." Computer Optics 42, no. 3 (July 25, 2018): 468–75. http://dx.doi.org/10.18287/2412-6179-2018-42-3-468-475.
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Context algorithms for interpolation of multidimensional signals in the compression problem are researched. A hierarchical compression method for arbitrary dimension signals is considered. For this method, an interpolation algorithm based on the context modeling is proposed. The algorithm is based on optimizing parameters of the interpolating function in a local neighborhood of the interpolated sample. At the same time, locally optimal parameters found for more decimated scale signal levels are used to interpolate samples of less decimated scale signal levels. The context interpolation algorithm is implemented programmatically as part of a hierarchical compression method. Computational experiments have shown that using a context interpolator instead of an average interpolator makes it possible to significantly improve the efficiency of hierarchical compression.
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Richard, William D., and R. Martin Arthur. "Real-Time Ultrasonic Scan Conversion via Linear Interpolation of Oversampled Vectors." Ultrasonic Imaging 16, no. 2 (April 1994): 109–23. http://dx.doi.org/10.1177/016173469401600204.
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Scan conversion is required in order to display conventional B-mode ultrasonic signals, which are acquired along radii at varying angles, on standard Cartesian-coordinate video monitors. For real-time implementations, either nearest-neighbor or bilinear interpolation is usually used in scan conversion. If the sampling rate along each radius is high enough, however, the gray-scale value of a given pixel can be interpolated accurately using the nearest samples on two adjacent vectors. The required interpolation then reduces to linear interpolation. Oversampling by a factor of 2 along with linear interpolation was superior to bilinear interpolation of vectors sampled to match pixel-to-pixel spacing in 6 representative B-mode images. A novel 8-bit linear interpolation algorithm was implemented as a CMOS VLSI circuit using a readily available, high-level synthesis tool. The circuit performed 30 million interpolations per second. Arithmetic results produced by the 8-bit interpolator on 7-bit samples were virtually identical to IEEE-format, single-precision, floating-point results.
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Arana, Daniel, Fabricio dos Santos Prol, Paulo de Oliveira Camargo, and Gabriel do Nascimento Guimarães. "ERRORS MEASUREMENT OF INTERPOLATION METHODS FOR GEOID MODELS: STUDY CASE IN THE BRAZILIAN REGION." Boletim de Ciências Geodésicas 24, no. 1 (March 2018): 44–57. http://dx.doi.org/10.1590/s1982-21702018000100004.
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Abstract: The geoid is an equipotential surface regarded as the altimetric reference for geodetic surveys and it therefore, has several practical applications for engineers. In recent decades the geodetic community has concentrated efforts on the development of highly accurate geoid models through modern techniques. These models are supplied through regular grids which users need to make interpolations. Yet, little information can be obtained regarding the most appropriate interpolation method to extract information from the regular grid of geoidal models. The use of an interpolator that does not represent the geoid surface appropriately can impair the quality of geoid undulations and consequently the height transformation. This work aims to quantify the magnitude of error that comes from a regular mesh of geoid models. The analysis consisted of performing a comparison between the interpolation of the MAPGEO2015 program and three interpolation methods: bilinear, cubic spline and neural networks Radial Basis Function. As a result of the experiments, it was concluded that 2.5 cm of the 18 cm error of the MAPGEO2015 validation is caused by the use of interpolations in the 5'x5' grid.
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Shen, Hai Ming, Kun Qi Wang, and Yong You Tian. "Design of Interpolation Algorithm in the Multi-Axis Motion Control System." Advanced Materials Research 411 (November 2011): 259–63. http://dx.doi.org/10.4028/www.scientific.net/amr.411.259.
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This paper describes an interpolation algorithm in the multi-axis motion control system, which can achieve six-axis interpolation operations, greatly improving the processing efficiency. Using modular design idea on the Quartus II platform, by DDA interpolation theory, interpolation modules are built through VHDL. And these interpolator modules are connected into schematic diagrams. By those schematic diagrams a linear interpolator, a circular interpolator and a composite interpolator are formed. The corresponding functions of those interpolators have been simulated on the Quartus II platform. The simulation shows that this interpolation algorithm is effective to complex multi-axis motion control system.
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Barker, Paul M., and Trevor J. McDougall. "Two Interpolation Methods Using Multiply-Rotated Piecewise Cubic Hermite Interpolating Polynomials." Journal of Atmospheric and Oceanic Technology 37, no. 4 (April 2020): 605–19. http://dx.doi.org/10.1175/jtech-d-19-0211.1.
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AbstractTwo interpolation methods are presented, both of which use multiple Piecewise Cubic Hermite Interpolating Polynomials (PCHIPs). The first method is based on performing 16 PCHIPs on 8 rotated versions of the plot of the data versus an independent variable (such as pressure or time). These 16 PCHIPs are then used to form 8 interpolations of the original data, and finally, these 8 are averaged. When the original data are unevenly spaced with respect to the independent variable, we show that it is best to perform the Multiply-Rotated PCHIP (MR-PCHIP) method using the “data index” as the independent variable, and then to subsequently perform one last PCHIP of the data index with respect to the original independent variable. This MR-PCHIP method avoids the flat spots that are a feature of the PCHIP method when the data have multiple values approximately equal to a local extreme value. The MR-PCHIP interpolated data have continuous first derivatives at the data points. This method also avoids the unrealistic overshoots that can occur when using the standard cubic spline interpolation procedure. The second interpolation method is designed specifically for hydrographic data with the aim of minimizing the formation of unrealistic water masses by the interpolation procedure. This is achieved by applying a Piecewise Cubic Hermite Interpolating Polynomial to each of 8 rotations of the salinity versus temperature plot (Multiply-Rotated Salinity–Temperature PCHIP, MRST-PCHIP) with bottle number (that is, data index) as the vertical interpolating coordinate, thereby making the MRST-PCHIP method independent of the heave of a water column. This method is equivalent to interpolating in the salinity–temperature diagram, and MRST-PCHIP proves very effective at avoiding the production of anomalous water masses that otherwise occur when interpolating temperature and salinity separately.
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Guo, Jing Jie, and Wei Tang. "Design of Pythagorean Hodograph Curve Interpolator Based on NiosII Embedded Processor and FPGA." Advanced Materials Research 383-390 (November 2011): 6868–72. http://dx.doi.org/10.4028/www.scientific.net/amr.383-390.6868.
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In this paper, a novel architecture of Pythagorean Hodograph (PH) curve interpolator based on Nios Ⅱ embedded processor and FPGA is proposed. The whole interpolator including NiosⅡ processor is built in a single FPGA chip. The interpolator uses a two-stage interpolation scheme to reduce the computational burden of PH curve interpolator. The Nios Ⅱ embedded processor implements 1st-stage interpolation, the FPGA receives the command from the Nios Ⅱ processor and implements 2nd-stage interpolation simultaneously. Therefore, the interpolator can implement the real-time PH curve interpolation algorithm steadily to meet the needs of high-speed and high-precision machining.
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Lho, T.-J., and S.-J. Na. "A Study on an Improved Direct Search Interpolation Method for Two-Axis CNC Thermal Cutting Systems." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 206, no. 1 (February 1992): 67–76. http://dx.doi.org/10.1243/pime_proc_1992_206_057_02.
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A microcomputer-based reference pulse software interpolator, which can be effectively applied for two-axis computer numerical control (CNC) systems such as those used in plasma arc cutting and laser beam cutting machines, is proposed in the present study. The proposed interpolation method is based upon searching in two or three directions for the minimum path error, while the axes of motion do not move simultaneously in the stairs approximation method and the basis for selecting an interpolating point is not related to any criteria of path error in the digital differential analyses (DDA) method. Accordingly, this method has many advantages over the other two competing methods, such as small maximum path error of only a half basic length unit (BLU), uniform velocity along the cutter path, high degree of path smoothness and maximum velocity allowable. Since the velocity of the proposed CNC system is controlled through adjusting two interrupt interval times at each interpolation step, a constant velocity can be maintained along any cutting path. The proposed interpolation algorithm is very simple and can be easily applied for the practical CNC systems, since it is based on transforming the interpolating paths in all interpolating cases to those in one typical case.
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Xie, S. H., Qiu Liao, and S. R. Qin. "Sub-Pixel Edge Detection for Precision Measurement Based on Canny Criteria." Key Engineering Materials 295-296 (October 2005): 711–16. http://dx.doi.org/10.4028/www.scientific.net/kem.295-296.711.
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A new nonlinear intensity interpolation algorithm is presented to realize sub-pixel edge detection. The interpolation algorithm based on the Canny criteria makes full use of grads information attained by Canny edge detection to perform special interpolation in the grads direction. When the resolution is enhanced, the interpolated image by the new interpolation scheme can efficiently preserve high frequency component in the original image. The edge detection of interpolated image permits high precision localization. The new interpolation algorithm is more effective in reserving the grads information of the step edge of the initial image than the usual linear interpolations. It requires simpler computation than the present non-linear interpolations.
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Wang, Ren-Hong, and Jing-Xin Wang. "Quasi-interpolations with interpolation property." Journal of Computational and Applied Mathematics 163, no. 1 (February 2004): 253–57. http://dx.doi.org/10.1016/j.cam.2003.08.070.
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Charnsamorn, Chapkit, and Suphongsa Khetkeeree. "Symmetric quadratic tetration interpolation using forward and backward operation combination." International Journal of Electrical and Computer Engineering (IJECE) 12, no. 2 (April 1, 2022): 1893. http://dx.doi.org/10.11591/ijece.v12i2.pp1893-1903.
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The existed interpolation method, based on the second-order tetration polynomial, has the asymmetric property. The interpolation results, for each considering region, give individual characteristics. Although the interpolation performance has been better than the conventional methods, the symmetric property for signal interpolation is also necessary. In this paper, we propose the symmetric interpolation formulas derived from the second-order tetration polynomial. The combination of the forward and backward operations was employed to construct two types of the symmetric interpolation. Several resolutions of the fundamental signals were used to evaluate the signal reconstruction performance. The results show that the proposed interpolations can be used to reconstruct the fundamental signal and its peak signal to noise ratio (PSNR) is superior to the conventional interpolation methods, except the cubic spline interpolation for the sine wave signal. However, the visual results show that it has a small difference. Moreover, our proposed interpolations converge to the steady-state faster than the cubic spline interpolation. In addition, the option number increasing will reinforce their sensitivity.
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Essanhaji, A., and M. Errachid. "Lagrange Multivariate Polynomial Interpolation: A Random Algorithmic Approach." Journal of Applied Mathematics 2022 (March 14, 2022): 1–8. http://dx.doi.org/10.1155/2022/8227086.
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The problems of polynomial interpolation with several variables present more difficulties than those of one-dimensional interpolation. The first problem is to study the regularity of the interpolation schemes. In fact, it is well-known that, in contrast to the univariate case, there is no universal space of polynomials which admits unique Lagrange interpolation for all point sets of a given cardinality, and so the interpolation space will depend on the set Z of interpolation points. Techniques of univariate Newton interpolating polynomials are extended to multivariate data points by different generalizations and practical algorithms. The Newton basis format, with divided-difference algorithm for coefficients, generalizes in a straightforward way when interpolating at nodes on a grid within certain schemes. In this work, we propose a random algorithm for computing several interpolating multivariate Lagrange polynomials, called RLMVPIA (Random Lagrange Multivariate Polynomial Interpolation Algorithm), for any finite interpolation set. We will use a Newton-type polynomials basis, and we will introduce a new concept called Z , z -partition. All the given algorithms are tested on examples. RLMVPIA is easy to implement and requires no storage.
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Fan, Xi Ying, Yong Huan Guo, Shun Cai Li, and Xiu Ping Su. "New Digital Differential Analyzer Linear Interpolation Program and Error Analysis." Advanced Materials Research 314-316 (August 2011): 1769–72. http://dx.doi.org/10.4028/www.scientific.net/amr.314-316.1769.
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Common digital differential analyzer（DDA）linear interpolation error is lower than a pulse equivalent, and the output pulse along each axis is not uniform. New DDA linear interpolation flow chart was obtained by combining a quick algorithm of DDA interpolation and interpolating algorithm for pulses uniformization with common DDA linear interpolation principle. The relationship between interpolation error and pulse equivalent was demonstrated in detail. As the results shows, the new DDA with high precision machining but simple algorithm, increased interpolating speed; the new algorithm make the generation of uniform pulse series come true, which is of great importance to keep stepping motor rotating steadily without missing steps; At coordinate origin, interpolation error is lower than 0.42 pulse equivalent, while the interpolation point is not at coordinate origin, interpolation error is lower than 0.5 pulse equivalent.
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Flannigan, M. D., and B. M. Wotton. "A study of interpolation methods for forest fire danger rating in Canada." Canadian Journal of Forest Research 19, no. 8 (August 1, 1989): 1059–66. http://dx.doi.org/10.1139/x89-161.
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Canadian fire control agencies use either simple interpolation methods or none at all in estimating fire danger between weather stations. We compare several methods of interpolation and use the fire weather index in the North Central Region of Ontario as a case study. Our work shows that the second order least square polynomial, the smoothed cubic spline, and the weighted interpolations had the lowest residual sum of squares in our verification scheme. These methods fit the observed data at both high and low fire weather index values. The highly variable nature of the spatial distribution of summer precipitation amount is the biggest problem in interpolating between stations. This factor leads to highly variable fire weather index fields that are the most difficult to interpolate. The use of radar and (or) satellite data could help resolve precipitation patterns with greater precision. These interpolation methods could easily be implemented by fire control agencies to gain a better understanding of fire danger in the region.
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Gashnikov, M. V. "Interpolation of multidimensional signals using the reduction of the dimension of parametric spaces of decision rules." Information Technology and Nanotechnology, no. 2391 (2019): 31–40. http://dx.doi.org/10.18287/1613-0073-2019-2391-31-40.
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In this paper, we consider the interpolation of multidimensional signals problem. We develop adaptive interpolators that select the most appropriate interpolating function at each signal point. Parameterized decision rule selects the interpolating function based on local features at each signal point. We optimize the adaptive interpolator in the parameter space of this decision rule. For solving this optimization problem, we reduce the dimension of the parametric space of the decision rule. Dimension reduction is based on the parameterization of the ratio between local differences at each signal point. Then we optimize the adaptive interpolator in parametric space of reduced dimension. Computational experiments to investigate the effectiveness of an adaptive interpolator are conducted using real-world multidimensional signals. The proposed adaptive interpolator used as a part of the hierarchical compression method showed a gain of up to 51% in the size of the archive file compared to the smoothing interpolator.
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Amar, Eric. "On interpolation of interpolating sequences." Indagationes Mathematicae 18, no. 2 (2007): 177–87. http://dx.doi.org/10.1016/s0019-3577(07)00011-0.
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Wang, Jianmin, Yabo Li, Huizhong Zhu, and Tianming Ma. "Interpolation Method Research and Precision Analysis of GPS Satellite Position." Journal of Systems Science and Information 6, no. 3 (June 29, 2018): 277–88. http://dx.doi.org/10.21078/jssi-2018-277-12.
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Abstract According to the precise ephemeris has only provided satellite position that is discrete not any time, so propose that make use of interpolation method to calculate satellite position at any time. The essay take advantage of IGS precise ephemeris data to calculate satellite position at some time by using Lagrange interpolation, Newton interpolation, Hermite interpolation, Cubic spline interpolation method, Chebyshev fitting method respectively, which has a deeply analysis in the precision of five interpolations. The results show that the precision of Cubic spline interpolation method is the worst, the precision of Chebyshev fitting is better than Hermite interpolation method. Lagrange interpolation and Newton interpolation are better than other methods in precision. Newton interpolation method has the advantages of high speed and high precision. Therefore, Newton interpolation method has a certain scientific significance and practical value to get the position of the satellite quickly and accurately.
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Maksimov, A. I., and M. V. Gashnikov. "Parameter space dimension reduction of an adaptive interpolator during multidimensional signal differential compression." Information Technology and Nanotechnology, no. 2391 (2019): 23–30. http://dx.doi.org/10.18287/1613-0073-2019-2391-23-30.
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We propose a new adaptive multidimensional signal interpolator for differential compression tasks. To increase the efficiency of interpolation, we optimize its parameters space by the minimum absolute interpolation error criterion. To reduce the complexity of interpolation optimization, we reduce the dimension of its parameter range. The correspondence between signal samples in a local neighbourhood is parameterized. Besides, we compare several methods for such parameterization. The developed adaptive interpolator is embedded in the differential compression method. Computational experiments on real multidimensional signals confirm that the use of the proposed interpolator can increase the compression ratio.
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Poghosyan, Arnak. "On a Fast Convergence of the Rational-Trigonometric-Polynomial Interpolation." Advances in Numerical Analysis 2013 (March 21, 2013): 1–13. http://dx.doi.org/10.1155/2013/315748.
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We consider the convergence acceleration of the Krylov-Lanczos interpolation by rational correction functions and investigate convergence of the resultant parametric rational-trigonometric-polynomial interpolation. Exact constants of asymptotic errors are obtained in the regions away from discontinuities, and fast convergence of the rational-trigonometric-polynomial interpolation compared to the Krylov-Lanczos interpolation is observed. Results of numerical experiments confirm theoretical estimates and show how the parameters of the interpolations can be determined in practice.
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Liang, Chang Chun, Liu Qun Fan, Dang Jin Qi, Gang Yi, and Zhuang Miao. "Optimal Interpolation Algorithm Research Based on Quasi-Hermite Space Curve." Advanced Materials Research 317-319 (August 2011): 215–21. http://dx.doi.org/10.4028/www.scientific.net/amr.317-319.215.
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According to the principle of parametric curve paths CNC interpolating, a real-time interpolation algorithm based on algebraic index of the micro-segment spline is presented. It’s used to solve the problems of Hermite polynomial interpolation algorithm, which are commonly slow recursive algorithm, poor accuracy of approximation and the limitations of constant parameters increment interpolation. And the constant interpolation is achieved by fitting a first-order Taylor Formula. Simulation results show that the algorithm shortens the interpolation time and also improve the interpolation accuracy; meanwhile, it maintains the stability of the feed rate.
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Aziz, Siti Hawa. "Polynomial Interpolation in Matlab." Journal of Engineering and Science Research 2, no. 4 (August 10, 2018): 12–19. http://dx.doi.org/10.26666/rmp.jesr.2018.4.3.
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The problem of constructing such a continuous function is called data fitting. Many times, data given only at discrete points. With interpolation, we seek a function that allows us to approximate f(x) such that functional values between the original data set values may be determined. The process of finding such a polynomial is called interpolation and one of the most important approaches used are Lagrange interpolating formula. In this study, researcher determining the polynomial interpolation by using Lagrange interpolating formula. Then, a mathematical modelling was built by using MATLAB programming to determine the polynomial interpolation for a given points using the Lagrange method. The result of the study showed that the manual calculating and the MATLAB mathematical modelling will give the same answer for evaluated x and graph.
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Zou, You-Yun, Yu-Cheng Tian, D. M. Li, Xu-Bao Luo, and Bin Liu. "On Interpolative Meshless Analysis of Orthotropic Elasticity." Buildings 13, no. 2 (January 31, 2023): 387. http://dx.doi.org/10.3390/buildings13020387.
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As one possible alternative to the finite element method, the interpolation characteristic is a key property that meshless shape functions aspire to. Meanwhile, the interpolation meshless method can directly impose essential boundary conditions, which is undoubtedly an advantage over other meshless methods. In this paper, the establishment, implementation, and horizontal comparison of interpolative meshless analyses of orthotropic elasticity were studied. In addition, the radial point interpolation method, the improved interpolative element-free Galerkin method and the interpolative element-free Galerkin method based on the non-singular weight function were applied to solve orthotropic beams and ring problems. Meanwhile, the direct method is used to apply the displacement boundary conditions for orthotropic elastic problems. Finally, a detailed convergence study of the numerical parameters and horizontal comparison of numerical accuracy and efficiency were carried out. The results indicate that the three kinds of interpolative meshless methods showed good numerical accuracy in modelling orthotropic elastic problems, and the accuracy of the radial point interpolation method is the highest.
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Feng, Zhigang, and Heping Xie. "On Stability of Fractal Interpolation." Fractals 06, no. 03 (September 1998): 269–73. http://dx.doi.org/10.1142/s0218348x98000316.
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In this paper, a special kind of FIF (fractal interpolation function) is studied. The authors prove the stability of the fractal interpolations. When the interpolation data have a small perturbation, the corresponding FIFs also have a small perturbation.
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DeGaetano, Arthur T., Brian N. Belcher, and William Noon. "Temporal and Spatial Interpolation of the Standardized Precipitation Index for Computational Efficiency in the Dynamic Drought Index Tool." Journal of Applied Meteorology and Climatology 54, no. 4 (April 2015): 795–810. http://dx.doi.org/10.1175/jamc-d-14-0088.1.
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AbstractThe feasibility of interpolating gamma-distribution parameters between different precipitation accumulation intervals (durations) is statistically evaluated. The interpolation of these parameters for a specific accumulation interval, but ending on different dates, is similarly assessed. Such interpolation increases the computational efficiency of drought-monitoring tools that require calculation of the standardized precipitation index (SPI) for any user-specified accumulation period on any given day. Spatial interpolation of the distribution parameters is also assessed. Given a 60-yr period of record, few statistically significant differences were found between gamma-distribution percentiles interpolated between fixed base durations and those computed directly. Shorter interpolation intervals (generally 30 days) were required for the shortest (e.g., 30 days) durations, whereas interpolation over periods of as long as 180 days could be used for the longest (between 360 and 720 days) durations. Interpolating the distribution parameters to different ending dates on the basis of those computed for the end of each month was also appropriate. The spatial interpolation of gamma-distribution parameters, although viable in practice for monitoring large-scale drought conditions, was associated with larger SPI differences than was the spatial interpolation of the SPI index itself or the interpolation of historical precipitation and the subsequent calculation of gamma-distribution parameters on the basis of these values.
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Kiani, M. "Spherical approximating and interpolating moving least squares in geodesy and geophysics: a case study for deriving gravity acceleration at sea surface in the Persian Gulf." Journal of Geodetic Science 10, no. 1 (January 1, 2020): 124–35. http://dx.doi.org/10.1515/jogs-2020-0112.
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Abstract This paper is aimed at introducing the concept of Spherical Interpolating Moving Least Squares to the problems in geodesy and geophysics. Based on two previously known methods, namely Spherical Moving Least Squares and Interpolating Moving Least Squares, a simple theory is formulated for using Spherical Moving Least Squares as an interpolant. As an application, a case study is presented in which gravity accelerations at sea surface in the Persian Gulf are derived, using both the approximation and interpolation mode of the Spherical Moving Least Squares. The roles of the various elements in the methods-weight function, scaling parameter, and the degree of spherical harmonics as the basis functions-are investigated. Then, the results of approximation and interpolation are compared with the field data at sea surface, collected by shipborne gravimetry approach. Finally, the results are compared with another independent interpolation method-spline interpolation. It is shown that in this particular problem, SMLS approximation and SIMLS interpolation present a better accuracy than spherical splines.
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Chen, Hao, You Peng You, Jun He, and Xue Feng Yang. "A Separated-Axis Interpolator with Variable Period for Stepping Systems." Key Engineering Materials 431-432 (March 2010): 61–64. http://dx.doi.org/10.4028/www.scientific.net/kem.431-432.61.
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In motion systems driven by stepping motors, reference word interpolation is usually used with a constant period T, in which the existing position quantization errors will inevitably result in the trouble of velocity quantization errors. A separated-axis interpolator with variable period is proposed to deal with these troubles. The reassignment module of displacement and time is the key of the interpolator. In the module, the interpolation period of each axis can be separately adjusted upon its quantized displacement, thus resulting in almost ideal velocity profile and moving smoothness. Simulation and machining results are given and show that the proposed interpolator is effective in the improvement of motion stability and interpolation accuracy.
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Zhu, Li Da, Gang Li, and Wan Shan Wang. "Research on Interpolation Algorithm of Three-Links Hybrid Machine Tool." Advanced Materials Research 97-101 (March 2010): 3124–27. http://dx.doi.org/10.4028/www.scientific.net/amr.97-101.3124.
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Aiming at the characteristics of structure and control of three-links hybrid machine tool, the interpolation strategy of CNC system is proposed in this paper. Coarse interpolation in workspace and fine interpolation in joint-space are expatiated. The trajectory points are transformed into discrete points by coarse interpolation mapping from workspace to joint-space. At the same time, the plans of trajectory, velocity and acceleration of discrete points in workspace are got, and then joint discrete points are realized by joint fitting smooth function. In order to meet the design demand and enhance effectively interpolation precision, the five polynomial interpolations will be thinning discrete points, and geometric locus will be very smooth.
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Jiang, Hong Fei. "Triangle Interpolation on Discrete Point Set." Applied Mechanics and Materials 580-583 (July 2014): 2872–75. http://dx.doi.org/10.4028/www.scientific.net/amm.580-583.2872.
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An algorithm for triangle interpolation on discrete points is presented in the paper. It creates a square mesh which covers all the discrete points, then puts the points into the mesh and records the relationship between grids and points. When interpolating elevation of an interpolation point, it can fast find the discrete points which are near the interpolation point and these discrete points can be used to create a special triangle which contains the interpolation point. The elevation of the interpolation point can be obtained from the triangle. The method has the advantage of fast speed, high precision and needing less memory.
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You, You Peng, and Jun He. "A Parametric Interpolator with Smooth Kinematic Profiles for High Speed Machining." Key Engineering Materials 315-316 (July 2006): 169–73. http://dx.doi.org/10.4028/www.scientific.net/kem.315-316.169.
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Smooth kinematic profiles are very important for high speed curve machining. During parametric interpolation, simple adaptive feedrate with confined contour error may cause acceleration and jerk to fluctuate acutely. To avoid the undesirable influence, an interpolation algorithm for parametric curves with smooth kinematic profiles is presented. The interpolator consists of three parts, look-ahead module, feedrate planning module and interpolation module. In look-ahead module, a pre-interpolator is designed to produce the required feedrate profile considering chord error. By feedrate planning, a smooth feedrate profile with confined acceleration and jerk is schemed based on bell-shape ACC/DEC profile by feedrate profile matching and feedrate profile synthesis. Then the parametric curve can be interpolated with the planned feedrate in interpolation module. Simulation results have been also provided to illustrate that the proposed interpolator can generate smooth kinematic profiles required for the high tracking accuracy at high speed with confined chord error, acceleration and jerk, and can be used for high speed and precision curve machining.
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Caloiero, Tommaso, Gaetano Pellicone, Giuseppe Modica, and Ilaria Guagliardi. "Comparative Analysis of Different Spatial Interpolation Methods Applied to Monthly Rainfall as Support for Landscape Management." Applied Sciences 11, no. 20 (October 14, 2021): 9566. http://dx.doi.org/10.3390/app11209566.
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Landscape management requires spatially interpolated data, whose outcomes are strictly related to models and geostatistical parameters adopted. This paper aimed to implement and compare different spatial interpolation algorithms, both geostatistical and deterministic, of rainfall data in New Zealand. The spatial interpolation techniques used to produce finer-scale monthly rainfall maps were inverse distance weighting (IDW), ordinary kriging (OK), kriging with external drift (KED), and ordinary cokriging (COK). Their performance was assessed by the cross-validation and visual examination of the produced maps. The results of the cross-validation clearly evidenced the usefulness of kriging in the spatial interpolation of rainfall data, with geostatistical methods outperforming IDW. Results from the application of different algorithms provided some insights in terms of strengths and weaknesses and the applicability of the deterministic and geostatistical methods to monthly rainfall. Based on the RMSE values, the KED showed the highest values only in April, whereas COK was the most accurate interpolator for the other 11 months. By contrast, considering the MAE, the KED showed the highest values in April, May, June and July, while the highest values have been detected for the COK in the other months. According to these results, COK has been identified as the best method for interpolating rainfall distribution in New Zealand for almost all months. Moreover, the cross-validation highlights how the COK was the interpolator with the best least bias and scatter in the cross-validation test, with the smallest errors.
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Zhu, Dantong, Zhenhao Zhong, Minghao Zhang, Suqin Wu, Kefei Zhang, Zhen Li, Qingfeng Hu, Xianlin Liu, and Junguo Liu. "An Improved Principal Component Analysis Method for the Interpolation of Missing Data in GNSS-Derived PWV Time Series." Remote Sensing 15, no. 21 (October 28, 2023): 5153. http://dx.doi.org/10.3390/rs15215153.
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Missing data in precipitable water vapor derived from global navigation satellite systems (GNSS-PWV) is commonly a large hurdle in climatical applications, since continuous PWV is an important prerequisite. Interpolation using principal component analysis (PCA) is typically used to resolve this problem. However, the popular PCA-based interpolating methods, e.g., rank-deficient least squares PCA (RDPCA) and data interpolating empirical orthogonal function (DINEOF), often lead to unsatisfactory results. This study analyzes the relationship between missing data and PCA-based interpolation results and proposes an improved interpolation-based RDPCA (IRDPCA) that can take into account the PWV derived from ERA5 (ERA-PWV) as an additional aid. Three key steps are involved in the IRDPCA: initially interpolating missing data, estimating principal components through a functional model and optimizing the interpolation through an iterative process. Using a 6-year GNSS-PWV over 26 stations and ERA-PWV in Yunnan, China, the performance of the IRDPCA is compared with the RDPCA and DINEOF using simulation experiments based on both homogeneous data (i.e., interpolating ERA-PWV using available ERA-PWV) and heterogeneous data (i.e., interpolating GNSS-PWV using ERA-PWV). In the case of using homogeneous data, the root mean square (RMS) values of the interpolation errors are 3.45, 1.18 and 1.17 mm for the RDPCA, DINEOF and IRDPCA, respectively; while the values are 3.50, 2.50 and 1.55 mm in the heterogeneous case. These results demonstrate the superior performance of the IRDPCA in both the heterogeneous and homogeneous cases. Moreover, these methods are also applied to the interpolation of the real GNSS-PWV. The RMS, absolute bias and correlation of the GNSS-PWV are calculated by comparison with ERA-PWV. The results reveal that the interpolated GNSS-PWV using the IRDPCA is not impacted by the systematic discrepancies in the ERA-PWV and agrees well with the original data.
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Bau, David, Hendrik Himmelein, and Christoph Pörschmann. "Comparison of Non-Parametric Interpolation Techniques for Sparsely Measured Binaural Room Impulse Responses." Journal of the Audio Engineering Society 72, no. 7/8 (July 18, 2024): 479–92. http://dx.doi.org/10.17743/jaes.2022.0150.
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This study investigates different interpolation techniques for spatially upsampling Binaural Room Impulse Responses (BRIRs) measured on a sparse grid of view orientations. In this context, the authors recently presented the Spherical Array Interpolation by Time Alignment (SARITA) method for interpolating spherical microphone array signals with a limited number of microphones, which is adapted for the spatial upsampling of sparse BRIR datasets in the present work. SARITA is compared with two existing nonparametric BRIR-interpolation methods and naive linear interpolation. The study provides a technical and perceptual analysis of the interpolation performance. The results show the suitability of all interpolation methods apart from linear interpolation to achieving a realistic auralization, even for very sparse BRIR sets. For angular resolutions of 30° and real-world stimuli, most participants could not distinguish SARITA from an artifact-free reference.
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Beckers, J. M., A. Barth, I. Tomazic, and A. Alvera-Azcárate. "A method to generate fully multi-scale optimal interpolation by combining efficient single process analyses, illustrated by a DINEOF analysis spiced with a local optimal interpolation." Ocean Science 10, no. 5 (October 30, 2014): 845–62. http://dx.doi.org/10.5194/os-10-845-2014.
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Abstract. We present a method in which the optimal interpolation of multi-scale processes can be expanded into a succession of simpler interpolations. First, we prove how the optimal analysis of a superposition of two processes can be obtained by different mathematical formulations involving iterations and analysis focusing on a single process. From the different mathematical equivalent formulations, we then select the most efficient ones by analyzing the behavior of the different possibilities in a simple and well-controlled test case. The clear guidelines deduced from this experiment are then applied to a real situation in which we combine large-scale analysis of hourly Spinning Enhanced Visible and Infrared Imager (SEVIRI) satellite images using data interpolating empirical orthogonal functions (DINEOF) with a local optimal interpolation using a Gaussian covariance. It is shown that the optimal combination indeed provides the best reconstruction and can therefore be exploited to extract the maximum amount of useful information from the original data.
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Sharples, Jason J., Michael F. Hutchinson, and Damian R. Jellett. "On the Horizontal Scale of Elevation Dependence of Australian Monthly Precipitation." Journal of Applied Meteorology 44, no. 12 (December 1, 2005): 1850–65. http://dx.doi.org/10.1175/jam2289.1.
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Abstract Determination of the scale of the interaction between precipitation and topography is important for the accurate interpolation of rainfall in mountainous areas and also provides insight into the physical processes involved. In this paper, trivariate thin-plate smoothing splines are used to investigate the scale of interaction between monthly precipitation and topography by interpolating monthly rainfall over three subregions of the Australian continent, incorporating different climatic conditions and rainfall types. The interpolations are based upon elevations derived from digital elevation models (DEMs) of various resolutions. All of the DEMs are local averages of version 2.0 of the 9-s-resolution DEM of Australia. The results suggest that the optimal scale of the interaction between precipitation and topography, as it pertains to the elevation-dependent interpolation of monthly precipitation in Australia, is between 5 and 10 km. This is in agreement with results of similar studies that addressed daily precipitation over Switzerland.
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WANG, HAO, WEI ZHANG, and YANYAN LIU. "NOVEL PIPELINED INTERPOLATOR FOR REED–SOLOMON DECODER BASED ON LOW-COMPLEXITY CHASE DECODING." Journal of Circuits, Systems and Computers 22, no. 10 (December 2013): 1340037. http://dx.doi.org/10.1142/s0218126613400379.
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Reed–Solomon (RS) codes are widely used in digital communication and storage systems. Algebraic soft-decision (ASD) decoding of RS codes can obtain significant coding gain over hard-decision decoding. Compared with other ASD algorithms, the low-complexity chase (LCC) decoding algorithm needs less computation complexity with similar or better coding gain. To reduce the latency of the interpolation, multiple interpolators can be applied. However, the interpolator has to finish the forward interpolation (FI) which costs more iterations before it turns to the unified-backward–forward interpolator (UBFI). In this paper, FI and UBFI are carried out by two different interpolators. A novel pipelined interpolator (NPI) architecture is proposed which includes a parallel forward interpolator (PFI) and a reduced-complexity multi-interpolator (RCMI). For the (255, 239) RS code with η = 5, the interpolation latency and the efficiency will be 44% and 1.76 times of the previous design, respectively.
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Celis, Oliver Salazar. "Numerical continued fraction interpolation." Ukrains’kyi Matematychnyi Zhurnal 74, no. 4 (April 26, 2024): 568–80. http://dx.doi.org/10.3842/umzh.v74i4.7349.
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UDC 517.524 We show that highly accurate approximations can often be obtained by constructing Thiele interpolating continued fractions by a Greedy selection of the interpolation points together with an early termination condition. The obtained results are comparable with the outcome of state-of-the-art rational interpolation techniques based on the barycentric form.
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Al-Jawfi, Rashad A. "3D Fractal Interpolation Functions." Nanoscience and Nanotechnology Letters 12, no. 1 (January 1, 2020): 120–23. http://dx.doi.org/10.1166/nnl.2020.3081.
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For visualizing one, two- and/or three-dimensional data, reconstruction mechanism is generally considered. In the present study, I have examined the application of iterated function systems in interpolation. I have also presented new fractal interpolation derivations for three-dimensional scalar data. The interpolations can indicate uncertainty of the data, allow tenability from the data, represent the data statistically at different scales, and may also more accurately facilitate data analysis.
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Zou, Le, Liangtu Song, Xiaofeng Wang, Thomas Weise, Yanping Chen, and Chen Zhang. "A New Approach to Newton-Type Polynomial Interpolation with Parameters." Mathematical Problems in Engineering 2020 (November 16, 2020): 1–15. http://dx.doi.org/10.1155/2020/9020541.
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Newton’s interpolation is a classical polynomial interpolation approach and plays a significant role in numerical analysis and image processing. The interpolation function of most classical approaches is unique to the given data. In this paper, univariate and bivariate parameterized Newton-type polynomial interpolation methods are introduced. In order to express the divided differences tables neatly, the multiplicity of the points can be adjusted by introducing new parameters. Our new polynomial interpolation can be constructed only based on divided differences with one or multiple parameters which satisfy the interpolation conditions. We discuss the interpolation algorithm, theorem, dual interpolation, and information matrix algorithm. Since the proposed novel interpolation functions are parametric, they are not unique to the interpolation data. Therefore, its value in the interpolant region can be adjusted under unaltered interpolant data through the parameter values. Our parameterized Newton-type polynomial interpolating functions have a simple and explicit mathematical representation, and the proposed algorithms are simple and easy to calculate. Various numerical examples are given to demonstrate the efficiency of our method.
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Janett, Gioele, Oskar Steiner, Ernest Alsina Ballester, Luca Belluzzi, and Siddhartha Mishra. "A novel fourth-order WENO interpolation technique." Astronomy & Astrophysics 624 (April 2019): A104. http://dx.doi.org/10.1051/0004-6361/201834761.
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Context. Several numerical problems require the interpolation of discrete data that present at the same time (i) complex smooth structures and (ii) various types of discontinuities. The radiative transfer in solar and stellar atmospheres is a typical example of such a problem. This calls for high-order well-behaved techniques that are able to interpolate both smooth and discontinuous data. Aims. This article expands on different nonlinear interpolation techniques capable of guaranteeing high-order accuracy and handling discontinuities in an accurate and non-oscillatory fashion. The final aim is to propose new techniques which could be suitable for applications in the context of numerical radiative transfer. Methods. We have proposed and tested two different techniques. Essentially non-oscillatory (ENO) techniques generate several candidate interpolations based on different substencils. The smoothest candidate interpolation is determined from a measure for the local smoothness, thereby enabling the essentially non-oscillatory property. Weighted ENO (WENO) techniques use a convex combination of all candidate substencils to obtain high-order accuracy in smooth regions while keeping the essentially non-oscillatory property. In particular, we have outlined and tested a novel well-performing fourth-order WENO interpolation technique for both uniform and nonuniform grids. Results. Numerical tests prove that the fourth-order WENO interpolation guarantees fourth-order accuracy in smooth regions of the interpolated functions. In the presence of discontinuities, the fourth-order WENO interpolation enables the non-oscillatory property, avoiding oscillations. Unlike Bézier and monotonic high-order Hermite interpolations, it does not degenerate to a linear interpolation near smooth extrema of the interpolated function. Conclusion. The novel fourth-order WENO interpolation guarantees high accuracy in smooth regions, while effectively handling discontinuities. This interpolation technique might be particularly suitable for several problems, including a number of radiative transfer applications such as multidimensional problems, multigrid methods, and formal solutions.
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Bedi, S., I. Ali, and N. Quan. "Advanced Interpolation Techniques for N.C. Machines." Journal of Engineering for Industry 115, no. 3 (August 1, 1993): 329–36. http://dx.doi.org/10.1115/1.2901668.
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This paper describes two methods for curve and surface interpolation. The layout of the machine and the implementation of these methods on an N.C. machine are discussed. The requirement for additional computational power to implement these interpolation methods is addressed by a network of computers called transputers. The interface between the controller and the network is described. This network also provides the ability to do interference checking in real time using the subdivision technique. The advantage of this implementation is that it enhances the ability of the conventional controller and avoids problems such as communication errors, jerky motion, gouging, and closed architecture. The method used to determine the accuracy of the interpolator is described and some results are given. Curved surfaces described as a series of B-spline curves can be machined using the curve interpolator, whereas a B-spline surface can be machined with the surface interpolator. Sample surfaces are machined to show the ability of the controller in both the curve interpolation and surface interpolation modes.
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Hakim, Denny. "Calderon's Complex Interpolation of Morrey Spaces." Journal of the Indonesian Mathematical Society 26, no. 1 (March 1, 2020): 137–64. http://dx.doi.org/10.22342/jims.26.1.818.137-164.
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In this note we will discuss some results related to complex interpolation of Morreyspaces. We first recall the Riesz-Thorin interpolation theorem in Section 1.After that, we discuss a partial generalization of this theorem in Morrey spaces proved in \cite{St}.We also discuss non-interpolation property of Morrey spaces given in \cite{BRV99, RV}.In Section 3, we recall the definition of Calder\'on's complex interpolation method andthe description of complex interpolation of Lebesgue spaces.In Section 4, we discuss the description of complex interpolation of Morrey spaces given in\cite{CPP98, HS2, Lemarie, LYY}. Finally, we discuss the description of complex interpolationof subspaces of Morrey spaces in the last section.This note is a summary of the current research about interpolation of Morrey spaces,generalized Morrey spaces, and their subspaces in\cite{CPP98, HS, HS2, H, H4, Lemarie, LYY}.
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Glumov, N. I., and M. V. Gashnikov. "Adaptive interpolation of multidimensional signals for compression on board an aircraft." Information Technology and Nanotechnology, no. 2391 (2019): 97–102. http://dx.doi.org/10.18287/1613-0073-2019-2391-97-102.
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We consider the compression of multidimensional signals on the aircraft board. We describe the data of such signals as a hypercube, which is "rotated" in a special way. To compress this hypercube, we use a hierarchical compression method. As one of the stages of this method, we use an adaptive interpolation algorithm. The adaptive algorithm automatically switches between different interpolating functions at each signal point. We perform computational experiments in real-world multidimensional signals. Computational experiments confirm that the use of proposed adaptive interpolator allows increasing (up to 31%) the compression ratio of the “rotated” hypercube corresponding to multidimensional hyperspectral signals.
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Ren, Xiao Zhong, Ya Hui Wang, and Jian Xin Su. "Research on NC Dressing of Involute Grinding Wheel." Key Engineering Materials 455 (December 2010): 132–36. http://dx.doi.org/10.4028/www.scientific.net/kem.455.132.
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Aiming at the dressing of involute grinding wheel, the mathematical model of involute interpolation is established. Taking the normal tolerance δ as accuracy index, the dense degree of interpolation points can be changed constantly with the change of developable angle increment △θ so that the numbers of interpolation points can meet the requirements not only for interpolating accuracy, but for interpolating efficiency. The wheel dressing software developed by using VC++ as programming tool can be applied for dressing the involute grinding wheel which can be used to grind involute gears with different teeth and modules. The results of simulation experiment verify the feasibility and correctness of the software.
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Jin, Yong Qiao, Yu Han Wang, and Jian Guo Yang. "Real-Time B-Spline Interpolator with Look-Ahead Scheme for High-Speed CNC Machine Tools." Key Engineering Materials 455 (December 2010): 599–605. http://dx.doi.org/10.4028/www.scientific.net/kem.455.599.
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NC tool paths of digital CAD models are currently generated as a set of discrete data points. The CNC interpolator must convert these points into continuous machine tool axis motions. In order to achieve high-speed and high-accuracy machining, the development of a real-time interpolation algorithm is really indispensable, which can deal with a large number of short blocks and still maintain smooth interpolation with an optimal speed. In this paper, a real-time local cubic B-spline interpolator with look-ahead scheme is proposed for consecutive micro-line blocks interpolation. First, the consecutive micro-line blocks that satisfy the bi-chord error constraints are fitted into a C1 continuous cubic B-spline curve. Second, machining dynamics and tool path contour constrains are taken into consideration. Third, local cubic B-spline interpolator with an optimal look-ahead scheme is proposed to generate the optimal speed profile. Simulation and experiment are performed in real-time environment to verify the effectiveness of the proposed method. Compared with the conventional interpolation algorithm, the proposed algorithm reduces the machining time by 70%.
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Liu, Zhiqiang, Bo Xu, Bo Cheng, and Xiaomei Hu. "Interpolation Parameters in Inverse Distance-Weighted Interpolation Algorithm on DEM Interpolation Error." Journal of Sensors 2021 (December 24, 2021): 1–14. http://dx.doi.org/10.1155/2021/3535195.
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Although DEM occupies an important basic position in spatial analysis, so far, the quality of DEM modeling has still not reached a satisfactory accuracy. This research mainly discusses the influence of interpolation parameters in the inverse distance-weighted interpolation algorithm on the DEM interpolation error. The interpolation parameters to be studied in this paper are the number of search points, the search direction, and the smoothness factor. In order to study the optimization of IDW parameters, the parameters that have uncertain effects on DEM interpolation are found through analysis, such as the number of search points and smoothing factor. This paper designs an experiment for the optimization of the interpolation parameters of the polyhedral function and finds the optimal interpolation parameters through experimental analysis. Of course, the “optimum” here is not the only one, but refers to different terrain areas, which makes the interpolation results relatively good. The selection of search points will be one of the research focuses of this article. After determining the interpolation algorithm, the kernel function is also one of the important factors that affect the accuracy of DEM. The value of the smoothing factor in the kernel function has always been the focus of DEM interpolation research. Different terrains, different interpolations, and functions will have different optimal smoothing factors. The search direction is to ensure that the sampling points are distributed in all directions when the sampling points are sparse and to improve the contribution rate of the sampling points to the interpolation points. The selection of search shape is to improve computing efficiency and has no effect on DEM accuracy; the search radius is mainly controlled by the number of search points, and there are two methods: adaptive search radius and variable length search radius. When the weight coefficient k = 1 , 2 , 3 , 4 , the number of sampling points involved in the interpolation calculation is different, and the error in the residual varies greatly, and both increase with the increase of the number of sampling points in the parameter interpolation calculation. This research will help improve the quality evaluation of DEM.
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Pu, Yasong, Yaoyao Shi, Xiaojun Lin, Yuan Hu, and Zhishan Li. "C2-Continuous Orientation Planning for Robot End-Effector with B-Spline Curve Based on Logarithmic Quaternion." Mathematical Problems in Engineering 2020 (July 22, 2020): 1–16. http://dx.doi.org/10.1155/2020/2543824.
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Smooth orientation planning is beneficial for the working performance and service life of industrial robots, keeping robots from violent impacts and shocks caused by discontinuous orientation planning. Nevertheless, the popular used quaternion interpolations can hardly guarantee C2 continuity for multiorientation interpolation. Aiming at the problem, an efficient quaternion interpolation methodology based on logarithmic quaternion was proposed. Quaternions of more than two key orientations were expressed in the exponential forms of quaternion. These four-dimensional quaternions in space S3, when logarithms were taken for them, could be converted to three-dimensional points in space R3 so that B-spline interpolation could be applied freely to interpolate. The core formulas that B-spline interpolated points were mapped to quaternion were founded since B-spline interpolated point vectors were decomposed to the product of unitized forms and exponents were taken for them. The proposed methodology made B-spline curve applicable to quaternion interpolation through dimension reduction and the high-order continuity of the B-spline curve remained when B-spline interpolated points were mapped to quaternions. The function for reversely finding control points of B-spline curve with zero curvature at endpoints was derived, which helped interpolation curve become smoother and sleeker. The validity and rationality of the principle were verified by the study case. For comparison, the study case was also analyzed by the popular quaternion interpolations, Spherical Linear Interpolation (SLERP) and Spherical and Quadrangle (SQUAD). The comparison results demonstrated the proposed methodology had higher smoothness than SLERP and SQUAD and thus would provide better protection for robot end-effector from violent impacts led by unreasonable multiorientation interpolation. It should be noted that the proposed methodology can be extended to multiorientation quaternion interpolation with higher continuity than the second order.