Journal articles: 'Interpolation transition'

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Liu, Chao, and Hui Wang. "A real-time predictor-modification-evaluation–corrector-modification-evaluation parametric interpolator for numerical control transition curves." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 234, no. 1-2 (June 18, 2019): 95–107. http://dx.doi.org/10.1177/0954405419856951.

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A real-time parametric interpolator based on a predictor-modification-evaluation–corrector-modification-evaluation algorithm is proposed in this article, which is utilized to efficiently calculate the reference points of transition curves. Meanwhile, the stable calculation is guaranteed by analyzing the convergence condition of the predictor-modification-evaluation–corrector-modification-evaluation algorithm. Under the convergence condition, the proposed parametric interpolator and traditional line interpolators are simultaneously implemented to interpolate a two-dimensional butterfly path, which consists of quintic Bézier transition curves and line segments. Simulation and experiments are carried out, and the results demonstrate that the proposed real-time predictor-modification-evaluation–corrector-modification-evaluation parametric interpolator achieves the highest accuracy and the light stripe on the tool path is further reduced and hardly observed. Compared with other parametric interpolators, the proposed real-time predictor-modification-evaluation–corrector-modification-evaluation parametric interpolator is capable of achieving a good balance between interpolation accuracy and interpolation efficiency.

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Lee, Byung Ho, Soon Woo Park, Soojin Jo, and Moon Ki Kim. "Protein conformational transitions explored by a morphing approach based on normal mode analysis in internal coordinates." PLOS ONE 16, no. 11 (November 4, 2021): e0258818. http://dx.doi.org/10.1371/journal.pone.0258818.

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Large-scale conformational changes are essential for proteins to function properly. Given that these transition events rarely occur, however, it is challenging to comprehend their underlying mechanisms through experimental and theoretical approaches. In this study, we propose a new computational methodology called internal coordinate normal mode-guided elastic network interpolation (ICONGENI) to predict conformational transition pathways in proteins. Its basic approach is to sample intermediate conformations by interpolating the interatomic distance between two end-point conformations with the degrees of freedom constrained by the low-frequency dynamics afforded by normal mode analysis in internal coordinates. For validation of ICONGENI, it is applied to proteins that undergo open-closed transitions, and the simulation results (i.e., simulated transition pathways) are compared with those of another technique, to demonstrate that ICONGENI can explore highly reliable pathways in terms of thermal and chemical stability. Furthermore, we generate an ensemble of transition pathways through ICONGENI and investigate the possibility of using this method to reveal the transition mechanisms even when there are unknown metastable states on rough energy landscapes.

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Luo, Jun, and Ying Chen. "Colour Restoration of Image Obtained from CCD Sensor Directly." Cybernetics and Information Technologies 14, no. 2 (July 15, 2014): 81–91. http://dx.doi.org/10.2478/cait-2014-0021.

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Abstract The original image data obtained from Charge-coupled Device (CCD) can be called original data, which is lack of color information. In order to restore the color of original image, firstly, we design a Bayer color filter array, and then we use bilinear interpolation algorithm and smooth hue transition interpolation algorithm to restore the color of original image. However, the hues of adjacent pixels change abruptly by the bilinear interpolation, therefore, we use smooth hue transition interpolation to enhance the edge of original image, and finally we identify the ultimate performance of these interpolation algorithms.

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Zemlyakova, Irina A. "Interpolation of an Incomplete Market by a Complete One for a Trinomial Model in the Quantile Hedging Problem." UNIVERSITY NEWS. NORTH-CAUCASIAN REGION. NATURAL SCIENCES SERIES, no. 4-1 (216-1) (December 28, 2022): 21–28. http://dx.doi.org/10.18522/1026-2237-2022-4-1-21-28.

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The transition from an incomplete market to a complete market is considered using Haar interpolating filtering. With Haar interpolation, in the case of a transition from the current level of the tree to the next, only one atom is split into two parts, while the remaining atoms do not change. In the course of this interpolation, a complete market arises, for which the martingale measure is already unique. The question arises related to the choice of a single martingale measure for the resulting complete market. As this measure, one of the extreme martingale measures is chosen, the distance from which to the market measure will be the smallest. The Kullback-Leibler distance is chosen as a tool for determining the measure of distance of the extreme martingale measure from the market one. A solution to the quantile hedging problem is constructed for the full market obtained in the course of interpolation. This solution is based on the duality theory of linear programming. The study of the problem of quantile hedging for the trinomial model continues. A computational experiment is proposed, during which there is a transition from an incomplete market to a complete one and the problem of quantile hedging is solved for the resulting complete market. The conclusion about the possibility of reducing the trinomial model to the binomial one is obtained.

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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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Imanian, Hanifeh, Hamidreza Shirkhani, Abdolmajid Mohammadian, Juan Hiedra Hiedra Cobo, and Pierre Payeur. "Spatial Interpolation of Soil Temperature and Water Content in the Land-Water Interface Using Artificial Intelligence." Water 15, no. 3 (January 25, 2023): 473. http://dx.doi.org/10.3390/w15030473.

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The distributed measured data in large regions and remote locations, along with a need to estimate climatic data for point sites where no data have been recorded, has encouraged the implementation of spatial interpolation techniques. Recently, the increasing use of artificial intelligence has become a promising alternative to conventional deterministic algorithms for spatial interpolation. The present study aims to evaluate some machine learning-based algorithms against conventional strategies for interpolating soil temperature data from a region in southeast Canada with an area of 1000 km by 550 km. The radial basis function neural networks (RBFN) and the deep learning approach were used to estimate soil temperature along a railroad after the spline deterministic spatial interpolation method failed to interpolate gridded soil temperature data on the desired locations. The spline method showed weaknesses in interpolating soil temperature data in areas with sudden changes. This limitation did not improve even by increasing the spline nonlinearity. Although both radial basis function neural networks and the deep learning approach had successful performances in interpolating soil temperature data even in sharp transition areas, deep learning outperformed the former method with a normalized RMSE of 9.0% against 16.2% and an R-squared of 89.2% against 53.8%. This finding was confirmed in the same investigation on soil water content.

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Liu, Xiao-Ming, Jun Jiang, Ling Hong, Zigang Li, and Dafeng Tang. "Fuzzy Noise-Induced Codimension-Two Bifurcations Captured by Fuzzy Generalized Cell Mapping with Adaptive Interpolation." International Journal of Bifurcation and Chaos 29, no. 11 (October 2019): 1950151. http://dx.doi.org/10.1142/s0218127419501517.

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In this paper, the Fuzzy Generalized Cell Mapping (FGCM) method is developed with the help of the Adaptive Interpolation (AI) in the space of fuzzy parameters. The adaptive interpolation on the set-valued fuzzy parameter is introduced in computing the one-step transition membership matrix to enhance the efficiency of the FGCM. For each of initial points in the state space, a coarse database is constructed at first, and then interpolation nodes are inserted into the database iteratively each time errors are examined with the explicit formula of interpolation error until the maximal errors are just under the error bound. With such an adaptively expanded database on hand, interpolating calculations assure the required accuracy with maximum efficiency gains. The new method is termed as Fuzzy Generalized Cell Mapping with Adaptive Interpolation (FGCM with AI), and is used to investigate codimension-two bifurcations in two-dimensional and three-dimensional nonlinear dynamical systems with fuzzy noise. It is found that global changes in fuzzy dynamics are dominated by the underlying deterministic counterparts, and the fuzzy attractor expands along the unstable manifold leading to a collision with a saddle when a bifurcation occurs. The examples show that the FGCM with AI has a thirtyfold to fiftyfold efficiency over the traditional FGCM to achieve the same analyzing accuracy.

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Fudge, T. J., E. D. Waddington, H. Conway, J. M. D. Lundin, and K. Taylor. "Interpolation methods for Antarctic ice-core timescales: application to Byrd, Siple Dome and Law Dome ice cores." Climate of the Past 10, no. 3 (June 19, 2014): 1195–209. http://dx.doi.org/10.5194/cp-10-1195-2014.

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Abstract. Antarctic ice cores have often been dated by matching distinctive features of atmospheric methane to those detected in annually dated ice cores from Greenland. Establishing the timescale between these tie-point ages requires interpolation. While the uncertainty at tie points is relatively well described, uncertainty of the interpolation is not. Here we assess the accuracy of three interpolation schemes using data from the WAIS Divide ice core in West Antarctica; we compare the interpolation methods with the annually resolved timescale for the past 30 kyr. Linear interpolation yields large age errors (up to 380 years) between tie points, abrupt changes in duration of climate events at tie points, and an age bias. Interpolations based on the smoothest accumulation rate (ACCUM) or the smoothest annual-layer thickness (ALT) yield timescales that more closely agree with the annually resolved timescale and do not have abrupt changes in duration at tie points. We use ALT to assess the uncertainty in existing timescales for the past 30 kyr from Byrd, Siple Dome, and Law Dome. These ice-core timescales were developed with methods similar to linear interpolation. Maximum age differences exceed 1000 years for Byrd and Siple Dome, and 500 years for Law Dome. For the glacial–interglacial transition (21 to 12 kyr), the existing timescales are, on average, older than ALT by 40 years for Byrd, 240 years for Siple Dome, and 150 years for Law Dome. Because interpolation uncertainty is often not considered, age uncertainties for ice-core records are often underestimated.

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Liu, Xiao-Ming, Jun Jiang, Ling Hong, and Dafeng Tang. "Studying the Global Bifurcation Involving Wada Boundary Metamorphosis by a Method of Generalized Cell Mapping with Sampling-Adaptive Interpolation." International Journal of Bifurcation and Chaos 28, no. 02 (February 2018): 1830003. http://dx.doi.org/10.1142/s0218127418300033.

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In this paper, a new method of Generalized Cell Mapping with Sampling-Adaptive Interpolation (GCMSAI) is presented in order to enhance the efficiency of the computation of one-step probability transition matrix of the Generalized Cell Mapping method (GCM). Integrations with one mapping step are replaced by sampling-adaptive interpolations of third order. An explicit formula of interpolation error is derived for a sampling-adaptive control to switch on integrations for the accuracy of computations with GCMSAI. By applying the proposed method to a two-dimensional forced damped pendulum system, global bifurcations are investigated with observations of boundary metamorphoses including full to partial and partial to partial as well as the birth of fully Wada boundary. Moreover GCMSAI requires a computational time of one thirtieth up to one fiftieth compared to that of the previous GCM.

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Huang, Jian, Ai Ping Song, Jian Ming Tao, and Dan Ping Yi. "Method of Corner Smooth Transition Based on Interpolation Spline." Advanced Materials Research 655-657 (January 2013): 1260–66. http://dx.doi.org/10.4028/www.scientific.net/amr.655-657.1260.

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Adjustable form cubic interpolation spline curve, changing its form adjustment coefficient can adjust the curvature radius and shape. Using this spline curve can realize the high-speed smooth connecting between adjacent processing trajectory during NC movement. To internal outline corner transition, use cambered spline transfer curve; To external outline corner transition, can use cambered or toroidal spline transfer curve. During the corner transition process, keep the speed constant, adjust the curvature the curvature radius to control the value of acceleration. Corner smooth transition based on the interpolation spline, can effectively reduce the mutation of acceleration, improve processing efficiency, and weaken the impact to the machine tool.

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Ashraf, G., and K. C. Wong. "Generating Consistent Motion Transition via Decoupled Framespace Interpolation." Computer Graphics Forum 19, no. 3 (September 2000): 447–56. http://dx.doi.org/10.1111/1467-8659.00437.

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Guo, Yuanjie, Jihong Yan, and Xingbo Wang. "Toolpath Smoothing Based on Controlled NURBS Interpolation." Journal of Engineering Research and Reports 25, no. 12 (December 18, 2023): 60–75. http://dx.doi.org/10.9734/jerr/2023/v25i121041.

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Based on cubic non-uniform B-spline curve constrained with tolerance band, a tool path smoothing approach is proposed for the purpose to achieve high-speed and high-precision machining of consecutive short line segments. According to a given tolerance band, the approach calculates the control polygon of the non-uniform cubic B-spline curve to transition the corners of the short line segments and obtains a GC2 continuous smooth transition for the tool path near the corners. The paper also designs an algorithm to realize the transition procedure. Compared with the reported similar approaches, this paper’s approach has advantages in reducing the fluctuations of machining speed and acceleration, enhancing machining quality, and improving the processing efficiency and motion stability of machine tools. This approach is helpful for CNC system development, as well as CAD and CAM.

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Qin, Chengjin, Jianfeng Tao, and Chengliang Liu. "A novel stability prediction method for milling operations using the holistic-interpolation scheme." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 13 (January 19, 2019): 4463–75. http://dx.doi.org/10.1177/0954406218815716.

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Currently, accurate and efficient determination of chatter-free cutting conditions is becoming increasingly important. This paper proposes a semi-analytical stability prediction method for milling processes using the holistic-interpolation scheme. The dynamics considering regeneration effect for milling operations is formulated as delay differential equations with time-periodic coefficients. The period of milling dynamic system is divided into two time periods according to the value of the coefficient matrix. On each small time interval for the forced vibration time period, the holistic-interpolation method is utilized by approximating the state term, the delay term, and the time-periodic parameter matrix as a whole unit with the second-order Lagrange interpolating polynomials. Then the Floquet transition matrix can be semi-analytically constructed for milling stability prediction according to Floquet theory. Finally, the benchmark examples of milling models are utilized to validate the effectiveness of the proposed method, which shows that the proposed algorithm achieves both high computational accuracy and efficiency.

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Chomputawat, Anuthep, and Watchara Chatwiriya. "Comparative Efficiency Analysis of Data Fusion Methods for Vehicle Trajectory Reconstruction." Applied Mechanics and Materials 886 (January 2019): 182–87. http://dx.doi.org/10.4028/www.scientific.net/amm.886.182.

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This article compares the efficiency of vehicle trajectory analysis methods based on data fusion from multiple cameras, monitoring the same area from different views under the condition having detection errors, which causes incorrectly localized and, in some cases, undetected vehicle during the movement. The experiment used the simulation of detection and localization of vehicle moving in straight, curved, zigzag and arbitrary trajectories, with localization errors and multi-level loss of data. By comparing Kalman-filter-based method and Linear-interpolation-based method for analyzing and reconstructing vehicle trajectory, the result shows that the data loss robustness of Kalman-filter-based method is higher than that of Linear-interpolation-based method, with data loss around 97% 97% and 90% for straight, curved and zigzag trajectories respectively. However, for arbitrary trajectory, the Linear-interpolation-based method is better than Kalman-filter-based method in all levels of data loss. In conclusion, Kalman-filter-based method is effective in the case of unchanged or slight transition of direction, while Linear-interpolation-based method is effective in the case of sudden transition of direction.

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Huang, Zhui Liang, Shu Wen Lin, and Dao Ying Jiang. "High-Precision Positioning and Speed Smooth Transition Control Algorithm for Terminal Point of Micro-Line Segment." Advanced Materials Research 305 (July 2011): 19–24. http://dx.doi.org/10.4028/www.scientific.net/amr.305.19.

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In allusion to the problem of data sampling interpolation error which exists in continuous micro-line segments interpolation algorithm with acceleration /deceleration control, this paper proposes a high-precision positioning and speed smooth transition control algorithm for terminal point of micro-line segment. The linear acceleration/deceleration mode was taken as an example to derive a motion control algorithm, which can eliminate the rounding error of the interpolation with fine adjusting the reserved parameters of acceleration /deceleration process when micro-line segment starting point and terminal point velocity are not zero. Simulation analysis and experiments of motion control shows that the algorithm greatly improves the control accuracy of the joint point position of micro-line segments, achieves the continuous smooth transition at the feed speed of the joint point of adjacent line segments and the uniformity of the velocity in specific line segment.

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Shi, Jing, Qing Zhen Bi, Yu Han Wang, and Gang Liu. "Development of Real-Time Look-Ahead Methodology Based on Quintic PH Curve with G² Continuity for High-Speed Machining." Applied Mechanics and Materials 464 (November 2013): 258–64. http://dx.doi.org/10.4028/www.scientific.net/amm.464.258.

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Curving tool paths composed of straight lines, which are often represented as G01 blocks, are still the most widespread format form in the machining process chain of CAD/CAM/CNC. At the junctions between consecutive segments, the tangency and curvature discontinuities may lead to feedrate fluctuation and acceleration oscillation, which would deteriorate the machining efficiency and quality. In this paper, a real-time look-ahead interpolation methodology is proposed, which adopts a curvature-continuous PH curve as a transition to blend corner at the junction of adjacent lines in the tool path. The blending algorithm can guarantee the approximation error exactly, and the control points of the curve can be calculated analytically. On the other hand, the arc length and the curvature of the transition curve, which are important items in speed planning, also have analytical expressions. All the advantages are the guarantee of calculation efficiency during the interpolation. Except for a curvature-continuous tool path, our look-ahead algorithm adopts a speed planning window strategy to achieve a balance between the calculation capabilities and the real-time interpolation requirements. In this window, the corner transition algorithm and speed planning are implemented simultaneously and dynamically during the interpolation. By defining the width of this window, which is actually the number of linear segments contained in this window, can adjust the time consuming of speed planning. Simulation and experiments on our own developed CNC platform are conducted. The results demonstrate the feasibility and efficiency of the proposed algorithms.

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Zhang, Lei, and Jinhai Zhang. "Local wavefield refinement using Fourier interpolation and boundary extrapolation for finite-element method based on domain reduction method." GEOPHYSICS 87, no. 3 (April 18, 2022): T251—T263. http://dx.doi.org/10.1190/geo2021-0503.1.

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The domain reduction method based on the finite-element method (FEM) is promising for multiscale seismic wave simulations for local complex structures and rough topography. However, a transition region is required to refine the wavefields from coarse to fine grids, which may lead to strong artifacts. Traditional wavefield interpolation methods can only handle a small upsampling ratio due to their low accuracy. Here, we propose a high accuracy upsampling method using Fourier interpolation and boundary extrapolation. It requires that the wavefield in the transition region is evenly sampled, which may slightly reduce the flexibility of FEMs. Fortunately, this constraint only exists in two layers of nodes, in which the coarse and fine grids are collocated. To further apply our interpolation method to the wavefield upsampling on the nonuniform grid, we adopt cubic interpolation within the local region of interest, which is adequate in accuracy for regularizing the wavefield on the fine nonuniform grid. For a topographic surface, we perform wavefield extrapolation on the ground surface to avoid abnormal amplitude variations below and beyond the surface, which can greatly reduce potential artifacts caused by the Fourier interpolation. Numerical experiments find that our method is superior to traditional interpolation methods in accuracy, especially for large upsampling ratios. Its relative error is less than 2% even for a 40-time upsampling; in contrast, the relative error of linear and cubic interpolation is up to 90% and 41% in the same situation, respectively. We further verify the feasibility of our method for 3D heterogeneous models with rough topography, multilayer heterogeneity, and random perturbations of background models. The proposed method yields a significant speeding of the multiscale seismic simulation using the FEM for 3D models with complex local structures and topographies while being highly accurate.

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Du, Jinfeng, Liqiang Zhang, and Tian Gao. "Acceleration smoothing algorithm for global motion in high-speed machining." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 233, no. 8 (September 24, 2018): 1844–58. http://dx.doi.org/10.1177/0954405418798870.

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When machining a series of short linear segments, the computer numerical control system interpolates the machining path with the pre-specified spline curve to obtain continuous feed motion. However, to obtain adequate smooth tool-paths to smooth the feed velocity and acceleration, the computer-aided manufacturing system needs to use a higher order spline curve, which will be limited by some technical bottlenecks. In this article, a new real-time interpolation algorithm is proposed from the perspective of kinematics to achieve uninterrupted feed motion throughout the global tool-path. At the same time, the acceleration profile achieves G2 continuous to avoid unnecessary feed frustration and inertial impact, reaching the balance between time-optimal and motion performance. First, the jounce-limited acceleration curve is blended at the corner of the machining path, and the optimal cornering transition velocity is obtained by adding the velocity, acceleration and contour error constraints to the corner transition motion. Then, according to the linear segments with different lengths between the corners, combined with the feed motion around the corner, a look-ahead interpolation algorithm is proposed to calculate the maximum feed rate with the constraint of the linear segment length and kinematic boundary conditions. At last, for the linear segments whose corner contours overlap with each other after interpolation, the smooth transition between the two corners can be realized by mixing the feed motion of the next corner. Compared with non-uniform rational B-spline interpolation algorithm, the proposed algorithm reduces the total machining time by 14% and the computer numerical control system improves the computational efficiency by 11%. It proves that the proposed algorithm has better application value in the manufacturing of complex parts.

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Song, Ai Ping, Jian Huang, Jian Ming Tao, and Dan Ping Yi. "Describing NC Smooth Path Based on the Adjustable Form of the Cubic Spline Interpolation Function." Applied Mechanics and Materials 215-216 (November 2012): 1158–64. http://dx.doi.org/10.4028/www.scientific.net/amm.215-216.1158.

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In order to describe the NC processing path better, and easy to realize path in a smooth transition of inflection point, this paper puts forward a kind of adjustable form of the cubic spline interpolation function; using the function can describe line, arc and freecurve, and realize smooth transition of inflection point through the control points which near the inflexion point. The spline function is of cubic polynomial, which calculation is simple, and it is easy to realize the operation of fast interpolation; it not only can describe various of NC paths, but also can be easy to realize the high speed of smooth processing between the NC orbit segments, which meets the needs of modern numerical control system for high speed, stability and flexible.

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Savinykh, I. S., and D. A. Chemasov. "Computing efficiency of the three-stage interpolated low pass filters." Radio industry 28, no. 4 (November 27, 2018): 21–27. http://dx.doi.org/10.21778/2413-9599-2018-28-4-21-27.

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Undoubted advantages of finite impulse response filters are their unconditional stability, the absence of limit cycles and the possibility of implementing a filter that does not introduce phase distortion. The disadvantage of such filters is the large cost required to compute the response. This paper considers three-stage interpolated finite impulse response low-pass filters. The maximum values of the interpolation factors are determined. Dependences of the coefficient of computational efficiency and the coefficient of increase in the registers of the three-stage interpolated low-pass filter on the values of the interpolation factors, the widths of the passband and the transition band are obtained. Relations for determining the optimal values of interpolation factors corresponding to the maximal value of computational efficiency coefficient are obtained. In addition, the dependencies of the maximum coefficient of computational efficiency and the optimal coefficient of increase in the registers of the three-stage interpolated low-pass filter on the widths of the passband and the transition band at the optimum values of the interpolation factors are obtained. Considered three-stage interpolated low-pass filters should be used in the case when the required stopband is significantly less than the sampling rate. In this case, three- stage interpolated filters require less computational resources for calculating the response than the two-stage interpolated filters or filter implemented by the transversal structure.

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Ratsamee, Photchara, Pudit Tempattarachoke, Laphonchai Jirachuphun, Masafumi Miwa, and Komsoon Somprasong. "Point Cloud Estimation During Aerial-Aquatic Transition in Monocular Camera-Based Localization and Mapping." Journal of Robotics and Mechatronics 35, no. 6 (December 20, 2023): 1645–54. http://dx.doi.org/10.20965/jrm.2023.p1645.

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This paper presents a multi-box interpolation method to estimate point clouds during aerial-aquatic transition. Our proposed method is developed based on an investigation of noise characteristics of aerial point clouds and aquatic point clouds. To evaluate the performance of realistic point cloud estimation, we compare the interpolation method with the Gaussian mixture method. We also investigate how single-box and multi-box approaches deal with noise in point cloud estimation. The simulation and the experimental results show that the estimated point cloud is accurate even when the aerial and aquatic point clouds contain noise. Also, the multi-box concept helps the algorithm to avoid taking unwanted noise into consideration when predicting point clouds.

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Ahmad, Azhar. "Pembinaan lengkungan peralihan berbentuk C yang memuaskan Data Interpolasi Hermite G2." Journal of Science and Mathematics Letters 8, no. 2 (April 7, 2020): 39–50. http://dx.doi.org/10.37134/jsml.vol8.2.6.2020.

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Makalah ini membincangkan satu kaedah pembinaan lengkungan peralihan berbentuk C yang memenuhi syarat-syarat data interpolasi Hermite Lengkungan peralihan ini dibina berasaskan gabungan dua pilin kuadratik nisbah Bezier atau gabungan bersama satu segmen garis lurus bagi mencapai keselanjaran pada keseluruhan binaan. Kaedah analisis geometri bersama syarat kemonotonan suatu lengkungan kuadratik nisbah Bezier telah digunakan bagi mencapai objektif kajian. Hasil kajian yang dicapai adalah satu teknik pembinaan yang membolehkan kita memperolehi lengkungan peralihan secara terus, mudah diaplikasikan serta tanpa perlu menggunakan sebarang prosedur tranformasi affin. Syarat untuk lengkungan peralihan ini terhasil ditentukan oleh data Hermite yang diberi dan kepelbagaiannya pula dikawal oleh panjang segmen garis lurus yang menghubungkan kedua-dua pilin berkenaan. Keupayaan memenuhi sifat-sifat interpolasi ini memberi banyak kelebihan dan amat sesuai untuk aplikasi tertentu di dalam CAGD (Computer Aided Geometric Design), umpamanya rekabentuk produk industri, trajektori robot non-holonomic, serta rekabentuk mendatar landasan keretapi dan lebuhraya. Oleh kerana kuadratik nisbah Bezier merupakan sebahagian daripada perwakilan NURBS (Nonuniform Rational B-splines) maka adalah mudah bagi kita mengabungjalinkan formulasi lengkungan peralihan yang dicadangkan ini ke dalam kebanyakan sistem pengaturcara CAD (Computer Aided Design).

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Zhao, Peng, FeiYang Gao, Kai Guo, EnYuan Zhang, and Song Li. "Trajectory optimization of B-splines interpolation based on dynamic error adjustment." Journal of Physics: Conference Series 2760, no. 1 (May 1, 2024): 012038. http://dx.doi.org/10.1088/1742-6596/2760/1/012038.

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Abstract In this paper, we propose a motion planning algorithm based on the five-fold B-spline curve for multi-axis motion control systems with non-smooth trajectories, acceleration, plus acceleration over the limit, etc. We construct a smooth transition model for the micro-line segment G3 of the continuous five-fold B-spline curve. A derivation of the corresponding theoretical equation is given. Using the transition model, we propose an optimization method for dynamic adjustment of motion trajectory errors based on the velocity forward planning constraints by smoothing the transition after the trajectory of the micro-line segment for the forward planning velocity. Finally, the design flow for the forward planning of the velocity is given. Finally, the above algorithm is used to perform simulation experiments for the optimization algorithm. Experimental results show that the proposed optimization improves the accuracy of fitting motion trajectories under the constraints of acceleration and deceleration addition, which validates the proposed algorithm.

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Wang, Geng Zhu. "The Real-Time Look-Ahead NURBS Curve Interpolation Algorithm." Advanced Engineering Forum 2-3 (December 2011): 523–26. http://dx.doi.org/10.4028/www.scientific.net/aef.2-3.523.

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To ensure a given chord error, through the division of the cusp, the NURBS (Non-Uniform Rational B-Splins) curve is divided into several sections and the speed of the various sections is planned accordingly. The acceleration and deceleration time period is recalculated, which results in a smooth speed transition curve.

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Fudge, T. J., E. D. Waddington, H. Conway, J. M. D. Lundin, and K. Taylor. "Interpolation methods for Antarctic ice-core timescales: application to Byrd, Siple Dome and Law Dome ice cores." Climate of the Past Discussions 10, no. 1 (January 7, 2014): 65–104. http://dx.doi.org/10.5194/cpd-10-65-2014.

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Abstract. Antarctic ice cores have often been dated by matching distinctive features of atmospheric methane to those detected in annually dated ice cores from Greenland. Establishing the timescale between these tie-point ages requires interpolation. While the uncertainty at tie points is relatively well described, uncertainty of the interpolation is not. Here we assess the accuracy of three interpolation schemes using data from the WAIS Divide ice core in West Antarctica; we compare the interpolation methods with the annually resolved timescale for the past 30 kyr. Linear interpolation yields large age errors (up to 380 yr) between tie points, abrupt changes in duration at tie points, and an age bias. Interpolation based on the smoothest accumulation rate (ACCUM) or the smoothest annual-layer thickness (ALT) yield timescales that more closely agree with the annually resolved timescale and do not have abrupt changes in duration at the tie points. We use ALT to assess the uncertainty in existing timescales for the past 30 kyr from Byrd, Siple Dome, and Law Dome. These ice-core timescales were developed with methods similar to linear interpolation. Maximum age differences exceed 1000 yr for Byrd and Siple Dome, and 500 yr for Law Dome. For the glacial-interglacial transition (21 to 12 kyr), the existing timescales are, on average, older than ALT by 40 yr for Byrd, 240 yr for Siple Dome, and 150 yr for Law Dome. Because interpolation uncertainty is often not considered, age uncertainties for ice-core records are often underestimated.

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Chen, Yanjun, Shengye Wang, and Wei Liu. "Data-Driven Transition Models for Aeronautical Flows with a High-Order Numerical Method." Aerospace 9, no. 10 (October 5, 2022): 578. http://dx.doi.org/10.3390/aerospace9100578.

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Over the past years, there has been innovative ideas about data-driven turbulence modeling proposed by scholars all over the world. This paper is a continuity of these significant efforts, with the aim of offering a better representation for turbulence physics. Previous works mainly focus on turbulence viscosity or Reynolds stress, while there are few works for turbulence transition. In our work, two mapping functions between average flow parameters and transition intermittency, a virtual physical quantity describing the amount of turbulence at a given position, are refactored, respectively, with neuron networks and random forests. These two functions are then coupled with the Spalart–Allmaras (SA) model to reconstitute two models for transition prediction. To demonstrate that these two coupled models provide improved prediction accuracy on transition compared with previous SA models, we conduct test cases all under a high-order weighted compact nonlinear scheme (WCNS). The prediction results of both coupled models significantly improved the capture of natural transitions occurring in the flows. Furthermore, the interpolation generalisation and extrapolation generalisation abilities of the coupled models are also demonstrated in this paper. The results emphasize the potential for machine learning as a supplementary in turbulence transition modeling.

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Gladkov, Aleksandr Vjacheslavovich, Yury Vjacheslavovich Sivets, and Ksenya Yuryevna Avdeeva. "NEW APPROACH TO APPLICATION OF MATHEMATICAL APPARATUS FOR THE CONSTRUCTION OF THREE-DIMENSIONAL SPINE MODEL." Hirurgiâ pozvonočnika, no. 1 (March 14, 2005): 100–104. http://dx.doi.org/10.14531/ss2005.1.100-104.

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The paper presents a mathematical model with graphic visualization, which describes spine geometric parameters and conditions of their changes in time and space. Reduction of data file size necessary for reproduction of vertebra shape and storage of this structure in a computer with the least losses is achieved with algorithm of geometrical interpolation and vertebral body shape reconstruction – with trigonometric interpolation sums (TIS). The developed spine model is based on three concepts. A spline interpolation is used for reproduction of the whole spine. The spline polynomial is built on data received by calculation of transition matrices. This requires the parameters of not each point, but only of three key ones (in the basic spine levels). Application of spline interpolation considerably reduces time expenses for transition matrices calculation. The developed model takes into account the geometrical features of human vertebra, and changes of its kinematic characteristics in space and time. The model will allow observation of deformation of the whole spine caused by change of one or several randomly chosen parameters. Thus the geometrical characteristics necessary to calculate matrix chain of the second model are the results of the first model calculations. Having a set of the statistical data, the given model can be used for observation of spine response to various disturbing factors. After assigning initial spine parameters a graphic interpretation of the model will enable to receive a three-dimensional spine image, to shift and rotate it, to assign a direction of load application, to trace the changes in the spine shape during physiological movements and walking.

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Stasik, Paweł M., and Julian Balcerek. "Extensible Implementation of Reliable Pixel Art Interpolation." Foundations of Computing and Decision Sciences 44, no. 2 (June 1, 2019): 213–39. http://dx.doi.org/10.2478/fcds-2019-0011.

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Abstract Pixel art is aesthetics that emulates the graphical style of old computer systems. Graphics created with this style needs to be scaled up for presentation on modern displays. The authors proposed two new modifications of image scaling for this purpose: a proximity-based coefficient correction and a transition area restriction. Moreover a new interpolation kernel has been introduced. The presented approaches are aimed at reliable and flexible bitmap scaling while overcoming limitations of existing methods. The new techniques were introduced in an extensible. NET application that serves as both an executable program and a library. The project is designed for prototyping and testing interpolation operations and can be easily expanded with new functionality by adding it to the code or by using the provided interface.

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Lekshmi, Ajayan, and C. Christopher Seldev. "Shadow Removal Using Inpainting and Interpolation Technique." Applied Mechanics and Materials 626 (August 2014): 32–37. http://dx.doi.org/10.4028/www.scientific.net/amm.626.32.

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Shadows are viewed as undesired information that strongly affects images. Shadows may cause a high risk to present false color tones, to distort the shape of objects, to merge, or to lose objects. This paper proposes a novel approach for the detection and removal of shadows in an image. Firstly the shadow and non shadow region of the original image is identified by HSV color model. The shadow removal is based on exemplar based image inpainting. Finally, the border between the reconstructed shadow and the non shadow areas undergoes bilinear interpolation to yield a smooth transition between them. They would lead to a better fitting of the shadow and non shadow classes, thus resulting in a potentially better reconstruction quality.

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Tao, Jian Ming, Ai Ping Song, and Dan Ping Yi. "Description and Smoothing of NC Motion Path Based on the Cubic Trigonometric Interpolation Spline." Applied Mechanics and Materials 365-366 (August 2013): 515–21. http://dx.doi.org/10.4028/www.scientific.net/amm.365-366.515.

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In order to better describe the complex motion path of NC machining and realize the smooth transition between path segments, a kind of cubic trigonometric interpolation spline curve was put forward based on a set of special basis function. The spline curve which with adjustable shape satisfies the C1 continuity and it can accurately describe some common engineering curves such as straight line, circular arc and free curve. According to the given information of control points, different shapes of interpolation spline curve can be gotten by changing the adjustment coefficients. Through selecting proper control points and shape adjustment coefficients near the corner, insert the spline curve can realize the smooth transition at the corner of adjacent NC motion path segments, which can ensure the stability of motion path and the continuous of feed speed. Meanwhile, it also can reduce the impact to NC machine.

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Ruffhead, Andrew Carey. "Enhancement of inverse-distance-weighting 2D interpolation using accelerated decline." Reports on Geodesy and Geoinformatics 116, no. 1 (August 25, 2023): 9–14. http://dx.doi.org/10.2478/rgg-2023-0006.

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Abstract Two-dimensional interpolation – or surface fitting – is an approximation tool with applications in geodetic datum transformations, terrain modelling and geoid determination. It can also be applied to many other forms of geographic point data, including rainfall, chemical concentrations and noise levels. The problem of fitting of a smooth continuous interpolant to a bivariate function is particularly difficult if the dataset of control points is scattered irregularly. A typical approach is a weighted sum of data values where the sum of the weights is always unity. Weighting by inverse distance to a power is one approach, although a power greater than 1 is needed to ensure smooth results. One advantage over other methods is that data values can be incorporated into the interpolated surface. One disadvantage is the influence of distant points. A simple cut-off limit on distance would affect continuity. This study proposes a transition range of accelerated decline by means of an adjoining polynomial. This preserves smoothness and continuity in the interpolating surface. Case studies indicate accuracy advantages over standard versions of inverse-distance weighting.

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Liu, Xiongding, Guangjie Lin, and Wu Wei. "Adaptive Transition Gait Planning of Snake Robot Based on Polynomial Interpolation Method." Actuators 11, no. 8 (August 5, 2022): 222. http://dx.doi.org/10.3390/act11080222.

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This paper mainly studies the transition gait planning by updating the parameters of snack robot motion control function through ROS nodes, including a straight running gait into a turning gait. In the practical scenario, when changing the control parameters, the joint angle of the snake robot will increase or decrease sharply, and the angular velocity and angular acceleration of the driving joints will also change, which results in oscillation and sideslip of the body. In the turning scene, the visual tracking will loss if the head joint of the snake robot causes the lateral movement and oscillation. To solve those problems, firstly, the dynamic model of the snake robot’s gait of serpentine movement is established. Then, we propose a method based on polynomial interpolation compensation to solve the body oscillation and sideslip caused by nodes updating. To further improve the efficiency of snake robot’s gait switching, an optimal dichotomy interpolation time search is proposed to realize the snake robot’s adaptive transition gait. Finally, some simulation experiments are verified the effectiveness of the proposed method.

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Nie, Yahui, Yinfei Du, Zhuo Xu, Zimiao Zhang, and Yang Qi. "RBF Interpolation Algorithm for FTS Tool Path Generation." Mathematical Problems in Engineering 2021 (February 2, 2021): 1–10. http://dx.doi.org/10.1155/2021/6689200.

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Freeform optics are defined as nonrotational symmetric optical surfaces in the manufacturing industry. Freeform optics are extensively applied to many areas in order to improve system performance. Fast tool servo (FTS) assisting single-point diamond turning technology has high application prospects in freeform optics machining. This paper discusses the interpolation algorithm for tool path generation of FTS through the application of a radial basis function (RBF) algorithm. For this purpose, a positive definite RBF with compact support was employed as the interpolant. The existence is mathematically proven. Numerical simulations were performed to compare the performances of the RBF algorithm and commonly used algorithms for satisfying the requirements of existence, smoothness, and accuracy. Machining experiments were also conducted to validate the applicability of the algorithm. The simulation results showed that the RBF interpolation algorithm outperformed other algorithms in terms of smoothness. The RBF algorithm also provided the highest interpolation accuracy. Furthermore, the RBF interpolation algorithm exhibited the highest accuracy for error distribution, with large errors distributed mainly in transition areas. The machining results were also in general agreement with the simulation results although obvious practical errors were observed. Overall, RBF interpolation can provide higher accuracy and better smoothness in the tool path generation of FTS.

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Ryuh, B. S., and G. R. Pennock. "Accurate Motion of a Robot End-Effector Using the Curvature Theory of Ruled Surfaces." Journal of Mechanisms, Transmissions, and Automation in Design 110, no. 4 (December 1, 1988): 383–88. http://dx.doi.org/10.1115/1.3258934.

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In robotics, there are two methods of trajectory planning: the joint interpolation method which is appropriate for fast transition of the robot end-effector; and the cartesian interpolation method which is appropriate for slower motion of the end-effector along straight path segments. Neither method, however, is sufficient to allow a smooth, differentiable, transition of position and orientation of the end-effector. In this paper, we propose a method of trajectory planning that will permit more accurate motion of a robot end-effector. The method is based on the curvature theory of a ruled surface generated by a line fixed in the end-effector, referred to as the tool line. The orientation of the end-effector about the tool line is included in the analysis to completely describe the six degree-of-freedom motion of the end-effector. The linear and angular properties of motion of the end-effector, determined from the differential properties of the ruled surface, are utilized in the trajectory planning.

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Trivedi, R. K., Uma Shrivastava, V. K. Hinge, and B. D. Shrivastava. "Calculation of Coster-Kronig energies and transition probabilities by linear interpolation method." Journal of Physics: Conference Series 755 (October 2016): 012014. http://dx.doi.org/10.1088/1742-6596/755/1/012014.

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Dembo, Amir, Jian Ding, Jason Miller, and Yuval Peres. "Cut-off for lamplighter chains on tori: dimension interpolation and Phase transition." Probability Theory and Related Fields 173, no. 1-2 (November 20, 2018): 605–50. http://dx.doi.org/10.1007/s00440-018-0883-4.

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Cardenas-Lailhacar, Cristian, and Michael C. Zerner. "Generalized symmetry-adapted interpolation procedure for finding transition states in internal rotations." International Journal of Quantum Chemistry 75, no. 4-5 (1999): 563–76. http://dx.doi.org/10.1002/(sici)1097-461x(1999)75:4/5<563::aid-qua21>3.0.co;2-z.

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Ma, Junjin, Yunfei Li, Dinghua Zhang, Bo Zhao, Geng Wang, and Xiaoyan Pang. "A Novel Updated Full-Discretization Method for Prediction of Milling Stability." Micromachines 13, no. 2 (January 21, 2022): 160. http://dx.doi.org/10.3390/mi13020160.

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This paper presents an updated full-discretization method for milling stability prediction based on cubic spline interpolation. First, the mathematical model of the time-delay milling system considering regenerative chatter is represented by a dynamic delay differential equation. Then, in a single tooth passing period, the time is divided into a finite time intervals, the state item and the time-delay item are approximated in each time interval by cubic spline interpolation and third-order Newton interpolation, respectively. Afterward, a transition matrix is constructed to represent the transfer relationship of the teeth in a period. Finally, based on Floquet theory, the milling stability lobes can be obtained. Meanwhile, in order to improve computational efficiency, an optimized method is proposed based on the traditional algorithm and the proposed method has high precision without losing high efficiency. Finally, several milling experiments are conducted to verify the accuracy of the proposed method, and the results show that the predicted results agree well with the experimental results.

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Brown, Mark. "Spectral Analysis, without Eigenvectors, for Markov Chains." Probability in the Engineering and Informational Sciences 5, no. 2 (April 1991): 131–44. http://dx.doi.org/10.1017/s0269964800001972.

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The Lagrange-Sylvester interpolation polynomial approach provides a simple, eigenvector-free representation for finite diagonalizable matrices. This paper discusses the Lagrange-Sylvester methodology and applies it to skip free to the right Markov chains. It leads to relatively simple, eigenvalue-based expressions for first passage time distributions and transition probabilities.

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Feng, Jin Qian, Tao Wang, and Wei Xu. "The Noise-Induced Chaotic Transition in a Vibro-Impact Oscillator." Applied Mechanics and Materials 117-119 (October 2011): 347–50. http://dx.doi.org/10.4028/www.scientific.net/amm.117-119.347.

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The influences of noise on chaotic dynamics in a vibro-impact oscillator, modeled as Duffing Van der Pol (DVP) system with unilateral rigid barrier, are investigated. An interpolation strategy is introduced to locate the impact instants, and effective numerical method is proposed to improve the computational precision in the vibro-impact oscillator. Near the boundary crisis, the phenomenon of noise-induced chaotic transition occurs. Our studies reveal that the escape of oscillator from the boundary is responsible for this chaotic transition. The increase of noise can aggravate this escape.

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Mihalache, Raluca Maria, and Andreea Manescu. "Interpolation Grid for Local Area of Iasi City." Present Environment and Sustainable Development 8, no. 1 (May 1, 2014): 157–64. http://dx.doi.org/10.2478/pesd-2014-0014.

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Abstract Definitive transition to GNSS technology of achieving geodetic networks for cadastre implementation in cities and municipalities, enforce establishing a unique way of linking between current measurements and existing geodetic data, with a sufficient accuracy proper to urban cadastre standards. Regarding city of Iasi, is presented a different method of transformation which consist in an interpolation grid for heights system. The Romanian national height system is „Black Sea-1975” normal heights system. Founded in 1945 by Molodenski, this system uses the quasigeoid as reference surface, being in relation with the ellipsoid through the height anomalies sizes in each point. The unitary transformation between the ETRS- 89 ellipsoidal height system and the normal one, at national level is provided through the „TransdatRo” program developed by NACLR (National Agency for Cadastre and Land Registration).

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PREZIOSI, L., and L. M. DE SOCIO. "A NONLINEAR INVERSE PHASE TRANSITION PROBLEM FOR THE HEAT EQUATION." Mathematical Models and Methods in Applied Sciences 01, no. 02 (June 1991): 167–82. http://dx.doi.org/10.1142/s0218202591000101.

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This paper proposes a method for the solution of two inverse problems which are governed by the nonlinear heat equation in one space dimension. In the first case phase transition occurs at the moving interface which divides two media. In the second one a random heat source is placed at a moving point. In both cases the temperature is assigned, as a function of time and within a random error, at a given fixed point. The solution procedure leads to quantitative results and is based on the Stochastic Adaptative Interpolation method.

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Fellmuth, Bernd, and Christof Gaiser. "High-accuracy realization of temperature fixed and reference points." Review of Scientific Instruments 94, no. 1 (January 1, 2023): 011102. http://dx.doi.org/10.1063/5.0110125.

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The harmonization of international temperature measurements requires the high-accuracy realization of many different temperature reference points. This results from the feature of the intensive measurand temperature that temperatures cannot simply be divided or multiplied. Thus, the points must cover the whole range of interest, at present from 1 mK to a few 1000 K. Furthermore, instruments are necessary for the interpolation between the non-continuous guide values. This led to the establishment of International Temperature Scales (ITS). The ITS prescribe interpolation instruments and assign fixed temperature values to suitable phase transitions without uncertainty. The large temperature range can only be covered by applying very different phase transitions. This includes the classical transitions, namely triple, melting, and freezing points, but also second-order transitions, as superfluid and superconducting ones, and the very new eutectic or peritectic points of metal-carbon compositions. A high-accuracy realization requires a reliable uncertainty estimation. This is, therefore, the central topic of this review. Since a given non-ideal condition of a sample, especially the impurity content, cannot be reproduced as accurate as necessary, the fixed- and reference-point temperatures are defined for ideal substances under ideal conditions. Thus, the estimation of the uncertainty of the realizations must be based on estimating the magnitude of all physical effects influencing the observed phase-transition temperature. The application of this methodology is discussed in the paper as unifying topic independent of the individual problems to be solved. Furthermore, recommendations of the Consultative Committee for Thermometry are summarized, and own experiences are supplemented.

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Berezin, Arseniy Vladimirovich, Vadim Dmitrievich Levchenko, and Anastasia Yurievna Perepelkina. "Interpolation – free LBM on non-uniform grids with TRT collision operator." Keldysh Institute Preprints, no. 19 (2024): 1–32. http://dx.doi.org/10.20948/prepr-2024-19.

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Lattice Boltzmann method (LBM) is a modern numerical scheme for solving fluid dynamics problems. LBM is easy to implement and it has a great potential for modifications. One of the priority LBM development directions is the correct construction of such a scheme on non-uniform spatial grids. However, at the moment, it requires interpolation and often deprives the scheme of the classical LBM advantages. We developed and tested an interpolation-free method for constructing athermal node-based LBM on non-uniform meshes with the TRT collision operator. The method is based on the use of different LBM stencils near the transition boundary of a non-uniform grid, together with a two-step procedure for transformation of populations corresponding to different LBM stencils.

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Lim, Sooyeon. "Linear Interpolation Transition of Character Animation for Immediate 3D Response to User Motion." International Journal of Contents 11, no. 1 (March 28, 2015): 15–20. http://dx.doi.org/10.5392/ijoc.2015.11.1.015.

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ZHANG, Xiaohui. "Corner Curve Transition Interpolation Algorithm for High Speed Machining of Micro-line Segment." Journal of Mechanical Engineering 46, no. 19 (2010): 183. http://dx.doi.org/10.3901/jme.2010.19.183.

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Beikircher, T., N. Benz, and W. Spirkl. "A Modified Temperature-Jump Method for the Transition and Low-Pressure Regime." Journal of Heat Transfer 120, no. 4 (November 1, 1998): 965–70. http://dx.doi.org/10.1115/1.2825916.

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For modeling the gas heat conduction at arbitrary Knudsen numbers and for a broad range of geometries, we propose a modified temperature-jump method. Within the modified approach, we make a distinction between an inner convex surface and an outer concave surface enclosing the inner surface. For problems, where only a single geometric length is involved, i.e., for large parallel plates, long concentric cylinders and concentric spheres, the new method coincides at any Knudsen number with the interpolation formula according to Sherman, and therefore also with the known solutions of the Boltzmann equation obtained by the four momenta method. For the general case, where more than one geometric length is involved, the modified temperature method is trivially correct in the limit of high pressure and identical with Knudsen’s formula in the limit of low pressure. For intermediate pressure, where there is a lack of known solutions of the Boltzmann equation for general geometries, we present experimental data for the special two-dimensional plate-in-tube configuration and compare it with results of the modified temperature-jump method stating good agreement. The results match slightly better compared to the standard temperature method and significantly better compared to the interpolation formula according to Sherman. For arbitrary geometries and Knudsen numbers, the modified temperature method shows no principal restrictions and may be a simple approximative alternative to the solution of the Boltzmann equation, which is rather cumbersome.

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Oliveira, Walter Alexandre A. de, Denise Guliato, Douglas Coelho Braga de Oliveira, Rodrigo Luis de Souza da Silva, and Gilson Antonio Giraldi. "New Technique for Binary Morphological Shape-Based Interpolation." International Journal of Image and Graphics 19, no. 02 (April 2019): 1950007. http://dx.doi.org/10.1142/s0219467819500074.

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In this paper we consider shape-based methods to generate additional slices in 3D binary volumes. The focused interpolation approaches, named SIMOL and BORS, are based on morphological and logical operators. Given two adjacent slices [Formula: see text] and [Formula: see text] of the binary image set, the methods iteratively generate a sequence of new slices showing a gradual transition between the corresponding shapes. First, we analyze the SIMOL and BORS techniques and highlight their problems. Then we present the main contribution of this paper: a new interpolation scheme, called SIMOL-NEW, that combines the iterative scheme of BORS and an interpolation kernel generated through SIMOL framework. Next, we compare SIMOL-NEW and BORS approaches using theoretical elements and computational experiments. The latter are executed using: (a) benchmark shapes; (b) simple volumes defined by sphere and paraboloid; (c) combination of ellipsoids; (d) a fork-like volume; (e) Cylinder Minus Sphere. The conclusion is that SIMOL-NEW performs closer to BORS for the cases (a) and (c) but it is more accurate than BORS in the tests (b) and (d). Besides, we offer comparisons of state-of-the-art approaches in shape-based interpolation and SIMOL-NEW using ground truth volumes (d) and (e). The computational experiment report that SIMOL-NEW gets outstanding results regarding the ability to recover the target volume.

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Luo, Yun Mei, Luc Chevalier, and Eric Monteiro. "Numerical Simulation of the Viscohyperelastic Behaviour of PET near the Glass Transition Temperature." Key Engineering Materials 504-506 (February 2012): 1139–44. http://dx.doi.org/10.4028/www.scientific.net/kem.504-506.1139.

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The presentation deals with the non linear strongly elastic and viscous behaviour of poly ethylene terephthalate near the glass transition temperature and biaxially stretched at high strain rates representative of the injection stretch blow moulding process. A non linear visco-hyperelastic model inspired from [1] and identified from the experimental results of the equi-biaxial tension test [2], have been developed and presented in [3] is implemented into a finite element code developed with Matlab. The thermal behaviour modelling, identification and simulation has also been managed. First, a numerical simulation of 2D plane stress case has been performed involving 2 fields (global velocity V and elastic Cauchy Green tensor Be). Rectangular finite elements with quadratic and linear interpolations have been employed for velocity and the elastic left Cauchy Green tensor. Second, an axi symmetric formulation involving 4 fields (global velocity V, lagrange multiplier p associated with the global incompressibility condition, and multiplier q associated with the incompressibility of the elastic part) has been performed using rectangular elements. Degree of interpolation have been tested for all possible combinations to test the LBB like condition. Both simulations are compared with equi biaxial or sequential biaxial testing in order to reproduce the strain hardening effect and the self-heating observed. The final goal of this work is to perform the free blowing simulation to compare with experimental data. Therefore, we should solve an iterative procedure for a thermo-mechanical equation. At each time step, a four-field approach is adopted for the mechanical part, and a classical heat transfer equation is discretised for the thermal part.

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Borkowski, Piotr, Zbigniew Pietrzykowski, and Janusz Magaj. "The Algorithm of Determining an Anti-Collision Manoeuvre Trajectory Based on the Interpolation of Ship’s State Vector." Sensors 21, no. 16 (August 6, 2021): 5332. http://dx.doi.org/10.3390/s21165332.

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The determination of a ship’s safe trajectory in collision situations at sea is one of the basic functions in autonomous navigation of ships. While planning a collision avoiding manoeuvre in open waters, the navigator has to take into account the ships manoeuvrability and hydrometeorological conditions. To this end, the ship’s state vector is predicted—position coordinates, speed, heading, and other movement parameters—at fixed time intervals for different steering scenarios. One possible way to solve this problem is a method using the interpolation of the ship’s state vector based on the data from measurements conducted during the sea trials of the ship. This article presents the interpolating function within any convex quadrilateral with the nodes being its vertices. The proposed function interpolates the parameters of the ship’s state vector for the specified point of a plane, where the values in the interpolation nodes are data obtained from measurements performed during a series of turning circle tests, conducted for different starting conditions and various rudder settings. The proposed method of interpolation was used in the process of determining the anti-collision manoeuvre trajectory. The mechanism is based on the principles of a modified Dijkstra algorithm, in which the graph takes the form of a regular network of points. The transition between the graph vertices depends on the safe passing level of other objects and the degree of departure from the planned route. The determined shortest path between the starting vertex and the target vertex is the optimal solution for the discrete space of solutions. The algorithm for determining the trajectory of the anti-collision manoeuvre was implemented in autonomous sea-going vessel technology. This article presents the results of laboratory tests and tests conducted under quasi-real conditions using physical ship models. The experiments confirmed the effective operation of the developed algorithm of the determination of the anti-collision manoeuvre trajectory in the technological framework of autonomous ship navigation.

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Journal articles on the topic 'Interpolation transition'

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