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Journal articles on the topic 'Surface interpolation'

Author: Grafiati

Published: 4 June 2021

Last updated: 6 September 2023

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1

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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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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Wang, Bolun, Xin Jiang, Guanying Huo, Cheng Su, Dongming Yan, and Zhiming Zheng. "Key-Point Interpolation: A Sparse Data Interpolation Algorithm based on B-splines." Journal of Physics: Conference Series 2068, no. 1 (October 1, 2021): 012010. http://dx.doi.org/10.1088/1742-6596/2068/1/012010.

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Abstract B-splines are widely used in the fields of reverse engineering and computer-aided design, due to their superior properties. Traditional B-spline surface interpolation algorithms usually assume regularity of the data distribution. In this paper, we introduce a novel B-spline surface interpolation algorithm: KPI, which can interpolate sparsely and non-uniformly distributed data points. As a two-stage algorithm, our method generates the dataset out of the sparse data using Kriging, and uses the proposed KPI (Key-Point Interpolation) method to generate the control points. Our algorithm can be extended to higher dimensional data interpolation, such as reconstructing dynamic surfaces. We apply the method to interpolating the temperature of Shanxi Province. The generated dynamic surface accurately interpolates the temperature data provided by the weather stations, and the preserved dynamic characteristics can be useful for meteorology studies.

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4

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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5

Li, Ning, Xianqing Lv, and Jicai Zhang. "Application of Surface Spline Interpolation Method in Parameter Estimation of a PM2.5 Transport Adjoint Model." Mathematical Problems in Engineering 2018 (July 5, 2018): 1–11. http://dx.doi.org/10.1155/2018/6231271.

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A new method for the estimation of initial conditions (ICs) in a PM2.5 transport adjoint model is proposed in this paper. In this method, we construct the field of ICs by interpolating values at independent points using the surface spline interpolation. Compared to the traditionally used linear interpolation, the surface spline interpolation has an advantage for reconstructing continuous smooth surfaces. The method is verified in twin experiments, and the results indicate that this method can produce better inverted ICs and less simulation errors. In practical experiments, simulation results show good agreement with the ground-level observations during the 22nd Asia-Pacific Economic Cooperation summit period, demonstrating that the new method is effective in practical application fields.

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6

Pentland, Alex P. "Surface Interpolation Networks." Neural Computation 5, no. 3 (May 1993): 430–42. http://dx.doi.org/10.1162/neco.1993.5.3.430.

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Orthogonal wavelets can be used as models for receptive fields in the human visual system. They may also be used to solve spatial interpolation problems formulated either as regularization or 2-D Kalman filtering. The solutions take the form of simple feedback networks, and only a few iterations are required for convergence.

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7

Xu, Zhiming. "Discrete interpolation surface." Journal of Computer Science and Technology 5, no. 4 (October 1990): 329–32. http://dx.doi.org/10.1007/bf02945285.

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8

Lounsbery, M., S. Mann, and T. DeRose. "Parametric surface interpolation." IEEE Computer Graphics and Applications 12, no. 5 (September 1992): 45–52. http://dx.doi.org/10.1109/38.156012.

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9

Sun, W. T., Yong Xian Liu, G. M. Sun, and Y. C. Zhang. "DSP Curve Surface Interpolator Research Based on Open Platform." Applied Mechanics and Materials 10-12 (December 2007): 471–75. http://dx.doi.org/10.4028/www.scientific.net/amm.10-12.471.

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For the improvement of the system real-time capability, the DSP Curve Surface interpolator has been designed to ensure high speed, high precision requirement for the machining of complexity curve surface. The hardware and software has been designed. The changeable feedrate interpolation algorithm of limit curve error has been studied. Furthermore, the algorithm has been applied to the interpolation and has well real-time capability to satisfy the requirement of high capability CNC by experimentation.

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10

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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11

Liu, Ming-min, L. Z. Li, and Jun Zhang. "Comparison of manifold learning algorithms used in FSI data interpolation of curved surfaces." Multidiscipline Modeling in Materials and Structures 13, no. 2 (August 14, 2017): 217–61. http://dx.doi.org/10.1108/mmms-07-2016-0032.

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Purpose The purpose of this paper is to discuss a data interpolation method of curved surfaces from the point of dimension reduction and manifold learning. Design/methodology/approach Instead of transmitting data of curved surfaces in 3D space directly, the method transmits data by unfolding 3D curved surfaces into 2D planes by manifold learning algorithms. The similarity between surface unfolding and manifold learning is discussed. Projection ability of several manifold learning algorithms is investigated to unfold curved surface. The algorithms’ efficiency and their influences on the accuracy of data transmission are investigated by three examples. Findings It is found that the data interpolations using manifold learning algorithms LLE, HLLE and LTSA are efficient and accurate. Originality/value The method can improve the accuracies of coupling data interpolation and fluid-structure interaction simulation involving curved surfaces.

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12

Wang, Dakang, Yulin Zhan, Tao Yu, Yan Liu, Xiaomei Jin, Xinyu Ren, Xinran Chen, and Qixin Liu. "Improving Meteorological Input for Surface Energy Balance System Utilizing Mesoscale Weather Research and Forecasting Model for Estimating Daily Actual Evapotranspiration." Water 12, no. 1 (December 18, 2019): 9. http://dx.doi.org/10.3390/w12010009.

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Using Surface Energy Balance System (SEBS) to estimate actual evapotranspiration (ET) on a regional scale generally uses gridded meteorological data by interpolating data from meteorological stations with mathematical interpolation. The heterogeneity of underlying surfaces cannot be effectively considered when interpolating meteorological station measurements to gridded data only by mathematical interpolation. This study aims to highlight the improvement of modeled meteorological data from the Weather Research and Forecasting (WRF) mesoscale numerical model which fully considers the heterogeneity of underlying surfaces over the data from mathematical interpolation method when providing accurate meteorological input for SEBS model. Meteorological data at 1 km resolution in the Hotan Oasis were simulated and then were put into SEBS model to estimate the daily actual ET. The accuracy of WRF simulation was evaluated through comparison with data collected at the meteorological station. Results found that the WRF-simulated wind speed, air temperature, relative humidity and surface pressure correlate well with the meteorological stations measurements (R2 are 0.628, 0.8242, 0.8089 and 0.8915, respectively). Comparison between ET calculated using the meteorological data simulated from the WRF (ETa-WRF) and meteorological data interpolated from measurements at met stations (ETa-STA) showed that ETa-WRF could better reflect the ET difference between different land cover, and capture the vegetation growing trend, especially in areas with sparse vegetation, where ETa-STA intends to overestimate. In addition, ETa-WRF has less noise in barren areas compared to ETa-STA. Our findings suggest that WRF can provide more reliable meteorological input for SEBS model than mathematical interpolation method.

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13

Shi, Kan-Le, Jun-Hai Yong, Jia-Guang Sun, and Jean-Claude Paul. "B-spline surface interpolation." Computer Aided Geometric Design 28, no. 6 (August 2011): 368–81. http://dx.doi.org/10.1016/j.cagd.2011.06.002.

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14

Beatson, R. K., and Z. Ziegler. "Monotonicity Preserving Surface Interpolation." SIAM Journal on Numerical Analysis 22, no. 2 (April 1985): 401–11. http://dx.doi.org/10.1137/0722024.

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15

Guo, Baining, and Joseph Liu. "Direct Visible Surface Interpolation." Computer Vision and Image Understanding 72, no. 3 (December 1998): 328–39. http://dx.doi.org/10.1006/cviu.1997.0668.

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16

Guo, Zheng, Haidong Pan, Wei Fan, and Xianqing Lv. "Application of Surface Spline Interpolation in Inversion of Bottom Friction Coefficients." Journal of Atmospheric and Oceanic Technology 34, no. 9 (September 2017): 2021–28. http://dx.doi.org/10.1175/jtech-d-17-0012.1.

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AbstractA new method for the inversion of bottom friction coefficients (BFCs) in a two-dimensional tidal model is proposed in this study. In this method, the field of BFCs is constructed by interpolating values at independent points using a surface spline. The surface spline interpolation has an advantage: that the constructed surface is smoother than the surface constructed by the traditionally used linear interpolation, which has unrealistic extrema. The method is validated in twin experiments where the prescribed nonlinear distribution of BFCs are better inverted with the surface spline interpolation. In practical experiments, the BFCs are inverted and the M2 tide in the Bohai Sea is simulated by assimilating the TOPEX/Poseidon (T/P) data. The small errors between the simulation results and the observations, as well as the accurate cotidal charts, demonstrate the feasibility of the new method in practical application.

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17

Jiang, Lei, and Yu Lan Wang. "The NURBS Interpolation Based on Machining Dynamics." Advanced Materials Research 422 (December 2011): 401–5. http://dx.doi.org/10.4028/www.scientific.net/amr.422.401.

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This article presents a new NURBS interpolation of tool path according to the requirements of machining dynamics, so the NURBS interpolation can satisfies the dynamics condition of the machine. The experimental results confirm that the proposed NURBS interpolator is capable of achieving a satisfactory performance, reducing the impact, machine vibration of feed, and improving the surface accuracy and quality of machining.

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18

Xu, Tianle, Venkatesh Merwade, and Zhiquan Wang. "Interpolating Hydrologic Data Using Laplace Formulation." Remote Sensing 15, no. 15 (August 2, 2023): 3844. http://dx.doi.org/10.3390/rs15153844.

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Spatial interpolation techniques play an important role in hydrology, as many point observations need to be interpolated to create continuous surfaces. Despite the availability of several tools and methods for interpolating data, not all of them work consistently for hydrologic applications. One of the techniques, the Laplace Equation, which is used in hydrology for creating flownets, has rarely been used for data interpolation. The objective of this study is to examine the efficiency of Laplace formulation (LF) in interpolating data used in hydrologic applications (hydrologic data) and compare it with other widely used methods such as inverse distance weighting (IDW), natural neighbor, and ordinary kriging. The performance of LF interpolation with other methods is evaluated using quantitative measures, including root mean squared error (RMSE) and coefficient of determination (R2) for accuracy, visual assessment for surface quality, and computational cost for operational efficiency and speed. Data related to surface elevation, river bathymetry, precipitation, temperature, and soil moisture are used for different areas in the United States. RMSE and R2 results show that LF is comparable to other methods for accuracy. LF is easy to use as it requires fewer input parameters compared to inverse distance weighting (IDW) and Kriging. Computationally, LF is faster than other methods in terms of speed when the datasets are not large. Overall, LF offers a robust alternative to existing methods for interpolating various hydrologic data. Further work is required to improve its computational efficiency.

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Xiao, Xiao Ping, Zi Sheng Li, and Wei Gong. "Fuzzy Fractal Interpolation Surface and its Applications." Advanced Materials Research 542-543 (June 2012): 1141–44. http://dx.doi.org/10.4028/www.scientific.net/amr.542-543.1141.

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Tackling of uncertain data is a major problem in analysis, modeling and simulation. Fractal interpolation surface and fuzzy set method are employed to solve the issue of uncertainty in modeling irregular surface. Initial interpolation data grid point is used as the kernel of Gaussian fuzzy membership function and its fuzzy numbers can be calculated by specifying λ of λ-cut set. These fuzzy numbers are used as uncertain data, which are the boundaries of the fluctuation of initial grid, and defined as a new kind of fuzzy interpolation grids. With these interpolation grids fractal interpolation surface algorithm is applied to act on. By these definitions, experimental data for modeling rock surface is illustrated to show that how the interpolation scheme proposed in this paper enhances the controllability for manipulating uncertain data.

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20

Fantoni, C., J. D. Hilger, W. Gerbino, and P. J. Kellman. "Surface interpolation and 3D relatability." Journal of Vision 5, no. 8 (March 16, 2010): 341. http://dx.doi.org/10.1167/5.8.341.

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Hilger, J. D., C. Fantoni, W. Gerbino, and P. J. Kellman. "Surface interpolation and slant anisotropy." Journal of Vision 6, no. 6 (March 18, 2010): 334. http://dx.doi.org/10.1167/6.6.334.

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Fantoni, Carlo, James D. Hilger, Walter Gerbino, and Philip J. Kellman. "Surface interpolation and 3D relatability." Journal of Vision 8, no. 7 (November 7, 2008): 29. http://dx.doi.org/10.1167/8.7.29.

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23

Sprynski, N., N. Szafran, B. Lacolle, and L. Biard. "Surface reconstruction via geodesic interpolation." Computer-Aided Design 40, no. 4 (April 2008): 480–92. http://dx.doi.org/10.1016/j.cad.2008.01.005.

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Oumellal, Fatima, and Abdellah Lamnii. "Curve and Surface Construction Using Hermite Trigonometric Interpolant." Mathematical and Computational Applications 26, no. 1 (January 29, 2021): 11. http://dx.doi.org/10.3390/mca26010011.

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In this paper, the constructions of both open and closed trigonometric Hermite interpolation curves while using the derivatives are presented. The combination of tension, continuity, and bias control is used as a very powerful type of interpolation; they are applied to open and closed Hermite interpolation curves. Surface construction utilizing the studied trigonometric Hermite interpolation is explored and several examples obtained by the C1 trigonometric Hermite interpolation surface are given to show the usefulness of this method.

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Balasubramani, N., M. Guru Prem Prasad, and S. Natesan. "Constrained and convex interpolation through rational cubic fractal interpolation surface." Computational and Applied Mathematics 37, no. 5 (August 27, 2018): 6308–31. http://dx.doi.org/10.1007/s40314-018-0689-0.

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Rimon, Y., E. R. Graber, and A. Furman. "Interpolation of extensive routine water pollution monitoring datasets: methodology and discussion of implications for aquifer management." Hydrology and Earth System Sciences Discussions 10, no. 7 (July 17, 2013): 9363–87. http://dx.doi.org/10.5194/hessd-10-9363-2013.

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Abstract. A large fraction of the fresh water available for human use is stored in groundwater aquifers. Since human activities such as mining, agriculture, industry and urbanization often result in incursion of various pollutants to groundwater, routine monitoring of water quality is an indispensable component of judicious aquifer management. Unfortunately, groundwater pollution monitoring is expensive and usually cannot cover an aquifer with the spatial resolution necessary for making adequate management decisions. Interpolation of monitoring data between points is thus an important tool for supplementing measured data. However, interpolating routine groundwater pollution data poses a special problem due to the nature of the observations. The data from a producing aquifer usually includes many zero pollution concentration values from the clean parts of the aquifer but may span a wide range (up to a few orders of magnitude) of values in the polluted areas. This manuscript presents a methodology that can cope with such datasets and use them to produce maps that present the pollution plumes but also delineates the clean areas that are fit for production. A method for assessing the quality of mapping in a way which is suitable to the data's dynamic range of values is also presented. Local variant of inverse distance weighting is employed to interpolate the data. Inclusion zones around the interpolation points ensure that only relevant observations contribute to each interpolated concentration. Using inclusion zones improves the accuracy of the mapping but results in interpolation grid points which are not assigned a value. That inherent trade-off between the interpolation accuracy and coverage is demonstrated using both circular and elliptical inclusion zones. A leave-one-out cross testing is used to assess and compare the performance of the interpolations. The methodology is demonstrated using groundwater pollution monitoring data from the Coastal aquifer along the Israeli shoreline.

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Liang, Ying Chun, Ming Jun Chen, Ya Zhou Sun, and W. X. Guo. "Machining Simulation and Experimental Research of Complex Surface Parts Based on the PMAC." Key Engineering Materials 315-316 (July 2006): 753–57. http://dx.doi.org/10.4028/www.scientific.net/kem.315-316.753.

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In order to machine the complex free surface, in this paper, NC interpolation of any complex surface is realized used the recursive reconstruction algorithm. The interpolating errors of this algorithm are controllable, and its applicability is relatively wide. Then, these NC codes of the complex human’s free surface are obtained with data exchange of the manufacturing module in the software UG, and machining simulation is obtained used NC codes. Finally, these NC codes are entered into the NC micro-machine tool, which is controlled by the PMAC and developed by ourselves, and the experimental research of the human’s free surface has been finished on this machine tool. The experimental results show that the NC interpolation accuracy of this recursive reconstruction algorithm is very high, and the machining simulation and machining experiments of the complex human’s surface are completely consistent. The study result shows that the complex surface molding is smooth and continuous, and the machined surface is satisfactory.

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Xu, L. J. "Study on the Magnetic Abrasive Finishing Based on 5-DOF Machine Tool." Materials Science Forum 628-629 (August 2009): 317–22. http://dx.doi.org/10.4028/www.scientific.net/msf.628-629.317.

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Magnetic abrasive finishing (MAF) is one of the advanced finishing processes, which produces a high level of surface quality. The technology is researched and applied just in recent years and it has good effect at the complex surface product manufacturing due to its flexibility and self-adaptability. Based on research about the theory and characteristic of magnetic abrasive finishing and 5-DOF Machine Tool, this study set up the interpolation mathematic model and space-line interpolations and circular arc interpolations of the tool-path for magnetic abrasive finishing were researched.

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Wu, Zhaohao, Lin Bi, Deyun Zhong, Ju Zhang, Qiwang Tang, and Mingtao Jia. "Orebody Modeling Method Based on the Coons Surface Interpolation." Minerals 12, no. 8 (August 6, 2022): 997. http://dx.doi.org/10.3390/min12080997.

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This paper presents a surface modeling method for interpolating orebody models based on a set of cross-contour polylines (geological polylines interpreted from the raw geological sampling data) using the bi-Coons surface interpolation method. The method is particularly applicable to geological data with cross-contour polylines acquired during the geological and exploration processes. The innovation of this paper is that the proposed method can automatically divide the closed loops and automatically combine the sub-meshes. The method solves the problem that it is difficult to divide closed loops from the cross-contour polylines with complex shapes, and it greatly improves the efficiency of modeling based on complex cross-contour polylines. It consists of three stages: (1) Divide closed loops using approximate planes of contour polylines; each loop is viewed as a polygon combined with several polylines, that is the n-sided region. (2) After processing the formed n-sided regions, Coons surface interpolation is improved to complete the modeling of every single loop (3) Combine all sub-meshes to form a complete orebody model. The corresponding algorithm was implemented using the C++ programing language on 3D modeling software. Experimental results show that the proposed orebody modeling method is useful for efficiently recovering complex orebody models from a set of cross-contour polylines.

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TANJUNG, MAULINA, SAUMI SYAHREZA, and MUHAMMAD RUSDI. "Comparison of interpolation methods based on Geographic Information System (GIS) in the spatial distribution of seawater intrusion." Jurnal Natural 20, no. 2 (June 16, 2020): 24–30. http://dx.doi.org/10.24815/jn.v20i2.16440.

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The study of monitoring seawater intrusion and groundwater quality in a coastal area needs to be done regularly to prevent the clean water crisis problems in the future. Accurate and reliable interpolation of seawater intrusion over a region is the requirement of an efficient monitoring. In this study, different interpolation methods were investigated and compared to determine the best interpolation method for predicting the spatial distribution of seawater intrusion in the coastal area of Banda Aceh. Groundwater electrical conductivity (EC) was analyzed to identify the contamination of seawater intrusion into the coastal aquifers. Four interpolation methods such as Empirical Bayesian Kriging (EBK), Global Polynomial Interpolation (GPI), Inverse Distance Weighting (IDW), and Local Polynomial Interpolation (LPI), were used to create the spatial distribution of the groundwater electrical conductivity. The accuracy of interpolation methods was evaluated by using a cross-validation technique through the coefficient of determination (R2) and the Root Mean Square Error (RMSE). The results showed that IDW performed the most accurate prediction values and the best surface which were indicated by the least RMSE and the highest R2 value. It can be concluded that IDW interpolation method is the best method for interpolating the groundwater electrical conductivity associated with seawater intrusion in the coastal area of Banda Aceh.

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Zhang, Wei, Xiao Chun Tang, and Jing Wang. "Research on a Class of Multi Parameter Fractal Interpolation Curved Surface Based on Iterative Function Image Generating Method." Applied Mechanics and Materials 687-691 (November 2014): 1457–61. http://dx.doi.org/10.4028/www.scientific.net/amm.687-691.1457.

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This paper extends the polynomial function to double logarithmic function, constructing a class of multi parameters iterative function, and uses this function to calculate the fractal interpolated surface for given interpolation points, and establishes the iterative function mathematical model of multi parameters fractal interpolation. In order to verify the effectiveness and reliability of this proposed model algorithm, this paper uses MATLAB numerical simulation method to calculate, and programs the Newton iterative function of multi parameters fractal interpolation surface, finally gets calculation nephogram of multi parameters fractal interpolation curved surface through calculating. Finally, using iterative method reduces the surface grid size, increasing the smoothness of the surface, so the surface is closer to the actual surface. It provides a new computer method research of fractal interpolation function.

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RI, SONGIL. "A NEW CONSTRUCTION OF THE FRACTAL INTERPOLATION SURFACE." Fractals 23, no. 04 (December 2015): 1550043. http://dx.doi.org/10.1142/s0218348x15500437.

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In this paper, we introduce a new construction of the fractal interpolation surface (FIS) using an even more general iterated function systems (IFS) which can generate self-affine and non self-affine fractal surfaces. Here we present the general types of fractal surfaces that are based on nonlinear IFSs.

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Bender, Christian, and Matthias Thiel. "Arbitrage-free interpolation of call option prices." Statistics & Risk Modeling 37, no. 1-2 (March 1, 2020): 55–78. http://dx.doi.org/10.1515/strm-2018-0026.

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AbstractIn this paper, we introduce a new interpolation method for call option prices and implied volatilities with respect to the strike, which first generates, for fixed maturity, an implied volatility curve that is smooth and free of static arbitrage. Our interpolation method is based on a distortion of the call price function of an arbitrage-free financial “reference” model of one’s choice. It reproduces the call prices of the reference model if the market data is compatible with the model. Given a set of call prices for different strikes and maturities, we can construct a call price surface by using this one-dimensional interpolation method on every input maturity and interpolating the generated curves in the maturity dimension. We obtain the algorithm of N. Kahalé [An arbitrage-free interpolation of volatilities, Risk 17 2004, 5, 102–106] as a special case, when applying the Black–Scholes model as reference model.

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Peng, Xingxuan, Zhihong Li, and Qian Sun. "Nonnegativity Preserving Interpolation byC1Bivariate Rational Spline Surface." Journal of Applied Mathematics 2012 (2012): 1–11. http://dx.doi.org/10.1155/2012/624978.

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This paper is concerned with the nonnegativity preserving interpolation of data on rectangular grids. The function is a kind of bivariate rational interpolation spline with parameters, which isC1in the whole interpolation region. Sufficient conditions are derived on coefficients in the rational spline to ensure that the surfaces are always nonnegative if the original data are nonnegative. The gradients at the data sites are modified if necessary to ensure that the nonnegativity conditions are fulfilled. Some numerical examples are illustrated in the end of this paper.

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Bajaj, Chanderjit L., and Insung Ihm. "Algebraic surface design with Hermite interpolation." ACM Transactions on Graphics 11, no. 1 (January 2, 1992): 61–91. http://dx.doi.org/10.1145/102377.120081.

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Fisher, John, John Lowther, and Ching-Kuang Shene. "Curve and surface interpolation and approximation." ACM SIGCSE Bulletin 36, no. 3 (September 2004): 146–50. http://dx.doi.org/10.1145/1026487.1008036.

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Li, Qiang, Chang Liu, and XueZhang Liang. "Lagrange interpolation on the conical surface." SCIENTIA SINICA Mathematica 45, no. 9 (September 1, 2015): 1573–82. http://dx.doi.org/10.1360/n012015-00047.

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Hartle, Brittney, Richard Murray, and Laurie Wilcox. "Stereoscopic surface interpolation from illusory contours." Journal of Vision 16, no. 12 (September 1, 2016): 1330. http://dx.doi.org/10.1167/16.12.1330.

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Bacchelli Montefusco, Laura, and Giulio Casciola. "Algorithm 677 C 1 surface interpolation." ACM Transactions on Mathematical Software 15, no. 4 (December 1989): 365–74. http://dx.doi.org/10.1145/76909.76914.

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Fantoni, C., M. Bertamini, and W. Gerbino. "Contour curvature polarity and surface interpolation." Vision Research 45, no. 8 (April 2005): 1047–62. http://dx.doi.org/10.1016/j.visres.2004.10.023.

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Wilcox, L. M., and P. A. Duke. "Spatial scaling of 3D surface interpolation." Journal of Vision 1, no. 3 (March 14, 2010): 177. http://dx.doi.org/10.1167/1.3.177.

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Schijvenaars, Bob J. A., Jan A. Kors, Gerard van Herpen, Fred Kornreich, and J. H. van Bemmel. "Interpolation of body surface potential maps." Journal of Electrocardiology 28 (January 1995): 104–9. http://dx.doi.org/10.1016/s0022-0736(95)80034-4.

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Low, Robert J. "Vector interpolation for surface normal calculation." Visual Computer 5, no. 3 (May 1989): 158–59. http://dx.doi.org/10.1007/bf01901390.

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Wilcox, Laurie M., and Philip A. Duke. "Stereoscopic Surface Interpolation Supports Lightness Constancy." Psychological Science 14, no. 5 (September 2003): 525. http://dx.doi.org/10.1111/1467-9280.03456.

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Galligani, Emanuele. "C 1 surface interpolation with constraints." Numerical Algorithms 5, no. 11 (November 1993): 549–55. http://dx.doi.org/10.1007/bf02113890.

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Oostendorp, Thom F., Adriaan van Oosterom, and Geertjan Huiskamp. "Interpolation on a triangulated 3D surface." Journal of Computational Physics 80, no. 2 (February 1989): 331–43. http://dx.doi.org/10.1016/0021-9991(89)90103-4.

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Piegl, L. A., and W. Tiller. "Reducing control points in surface interpolation." IEEE Computer Graphics and Applications 20, no. 5 (2000): 70–75. http://dx.doi.org/10.1109/38.865883.

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Shirman, Leon A., and Carlo H. Séquin. "Local surface interpolation with Bézier patches." Computer Aided Geometric Design 4, no. 4 (December 1987): 279–95. http://dx.doi.org/10.1016/0167-8396(87)90003-3.

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Peters, Jörg. "Local smooth surface interpolation: a classification." Computer Aided Geometric Design 7, no. 1-4 (June 1990): 191–95. http://dx.doi.org/10.1016/0167-8396(90)90030-u.

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Cheng, Fu-Hua (Frank), Feng-Tao Fan, Shu-Hua Lai, Cong-Lin Huang, Jia-Xi Wang, and Jun-Hai Yong. "Loop Subdivision Surface Based Progressive Interpolation." Journal of Computer Science and Technology 24, no. 1 (January 2009): 39–46. http://dx.doi.org/10.1007/s11390-009-9199-2.

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