Relevant bibliographies by topics / Interpolation

Academic literature on the topic 'Interpolation'

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Published: 4 June 2021
Last updated: 7 September 2024

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Journal articles on the topic "Interpolation"

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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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Gashnikov, M. V. "Parameterized interpolation for fusion of multidimensional signals of various resolutions." Computer Optics 44, no. 3 (June 2020): 436–40. http://dx.doi.org/10.18287/2412-6179-co-696.

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Parameterized interpolation algorithms are adapted to fusion of multidimensional signals of various resolutions. Interpolating functions, switching rules for them and local features are specified, based on which the interpolating function is selected at each point of the signal. Parameterized interpolation algorithms are optimized based on minimizing the interpolation error. The recurrent interpolator optimization scheme is considered for the situation of inaccessibility of interpolated samples at the stage of setting up the interpolation procedure. Computational experiments are carried out to study the proposed interpolators for fusion of real multidimensional signals of various types. It is experimentally confirmed that the use of parameterized interpolators allows one to increase the accuracy of signal fusion.
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Xu, Weizhi. "Elements of Bi-cubic Polynomial Natural Spline Interpolation for Scattered Data: Boundary Conditions Meet Partition of Unity Technique." Statistics, Optimization & Information Computing 8, no. 4 (December 2, 2020): 994–1010. http://dx.doi.org/10.19139/soic-2310-5070-1083.

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This paper investigates one kind of interpolation for scattered data by bi-cubic polynomial natural spline, in which the integral of square of partial derivative of two orders to x and to y for the interpolating function is minimal (with natural boundary conditions). Firstly, bi-cubic polynomial natural spline interpolations with four kinds of boundary conditions are studied. By the spline function methods of Hilbert space, their solutions are constructed as the sum of bi-linear polynomials and piecewise bi-cubic polynomials. Some properties of the solutions are also studied. In fact, bi-cubic natural spline interpolation on a rectangular domain is a generalization of the cubic natural spline interpolation on an interval. Secondly, based on bi-cubic polynomial natural spline interpolations of four kinds of boundary conditions, and using partition of unity technique, a Partition of Unity Interpolation Element Method (PUIEM) for fitting scattered data is proposed. Numerical experiments show that the PUIEM is adaptive and outperforms state-of-the-art competitions, such as the thin plate spline interpolation and the bi-cubic polynomial natural spline interpolations for scattered data.
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Parker, Joshua, Dionne Ibarra, and David Ober. "Logarithm-Based Methods for Interpolating Quaternion Time Series." Mathematics 11, no. 5 (February 24, 2023): 1131. http://dx.doi.org/10.3390/math11051131.

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In this paper, we discuss a modified quaternion interpolation method based on interpolations performed on the logarithmic form. This builds on prior work that demonstrated this approach maintains C2 continuity for prescriptive rotation. However, we develop and extend this method to descriptive interpolation, i.e., interpolating an arbitrary quaternion time series. To accomplish this, we provide a robust method of taking the logarithm of a quaternion time series such that the variables θ and n^ have a consistent and continuous axis-angle representation. We then demonstrate how logarithmic quaternion interpolation out-performs Renormalized Quaternion Bezier interpolation by orders of magnitude.
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Etherington, Thomas R. "Discrete natural neighbour interpolation with uncertainty using cross-validation error-distance fields." PeerJ Computer Science 6 (July 13, 2020): e282. http://dx.doi.org/10.7717/peerj-cs.282.

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Interpolation techniques provide a method to convert point data of a geographic phenomenon into a continuous field estimate of that phenomenon, and have become a fundamental geocomputational technique of spatial and geographical analysts. Natural neighbour interpolation is one method of interpolation that has several useful properties: it is an exact interpolator, it creates a smooth surface free of any discontinuities, it is a local method, is spatially adaptive, requires no statistical assumptions, can be applied to small datasets, and is parameter free. However, as with any interpolation method, there will be uncertainty in how well the interpolated field values reflect actual phenomenon values. Using a method based on natural neighbour distance based rates of error calculated for data points via cross-validation, a cross-validation error-distance field can be produced to associate uncertainty with the interpolation. Virtual geography experiments demonstrate that given an appropriate number of data points and spatial-autocorrelation of the phenomenon being interpolated, the natural neighbour interpolation and cross-validation error-distance fields provide reliable estimates of value and error within the convex hull of the data points. While this method does not replace the need for analysts to use sound judgement in their interpolations, for those researchers for whom natural neighbour interpolation is the best interpolation option the method presented provides a way to assess the uncertainty associated with natural neighbour interpolations.
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Gashnikov, M. V. "Interpolation based on context modeling for hierarchical compression of multidimensional signals." Computer Optics 42, no. 3 (July 25, 2018): 468–75. http://dx.doi.org/10.18287/2412-6179-2018-42-3-468-475.

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Context algorithms for interpolation of multidimensional signals in the compression problem are researched. A hierarchical compression method for arbitrary dimension signals is considered. For this method, an interpolation algorithm based on the context modeling is proposed. The algorithm is based on optimizing parameters of the interpolating function in a local neighborhood of the interpolated sample. At the same time, locally optimal parameters found for more decimated scale signal levels are used to interpolate samples of less decimated scale signal levels. The context interpolation algorithm is implemented programmatically as part of a hierarchical compression method. Computational experiments have shown that using a context interpolator instead of an average interpolator makes it possible to significantly improve the efficiency of hierarchical compression.
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Richard, William D., and R. Martin Arthur. "Real-Time Ultrasonic Scan Conversion via Linear Interpolation of Oversampled Vectors." Ultrasonic Imaging 16, no. 2 (April 1994): 109–23. http://dx.doi.org/10.1177/016173469401600204.

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Scan conversion is required in order to display conventional B-mode ultrasonic signals, which are acquired along radii at varying angles, on standard Cartesian-coordinate video monitors. For real-time implementations, either nearest-neighbor or bilinear interpolation is usually used in scan conversion. If the sampling rate along each radius is high enough, however, the gray-scale value of a given pixel can be interpolated accurately using the nearest samples on two adjacent vectors. The required interpolation then reduces to linear interpolation. Oversampling by a factor of 2 along with linear interpolation was superior to bilinear interpolation of vectors sampled to match pixel-to-pixel spacing in 6 representative B-mode images. A novel 8-bit linear interpolation algorithm was implemented as a CMOS VLSI circuit using a readily available, high-level synthesis tool. The circuit performed 30 million interpolations per second. Arithmetic results produced by the 8-bit interpolator on 7-bit samples were virtually identical to IEEE-format, single-precision, floating-point results.
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Arana, Daniel, Fabricio dos Santos Prol, Paulo de Oliveira Camargo, and Gabriel do Nascimento Guimarães. "ERRORS MEASUREMENT OF INTERPOLATION METHODS FOR GEOID MODELS: STUDY CASE IN THE BRAZILIAN REGION." Boletim de Ciências Geodésicas 24, no. 1 (March 2018): 44–57. http://dx.doi.org/10.1590/s1982-21702018000100004.

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Abstract: The geoid is an equipotential surface regarded as the altimetric reference for geodetic surveys and it therefore, has several practical applications for engineers. In recent decades the geodetic community has concentrated efforts on the development of highly accurate geoid models through modern techniques. These models are supplied through regular grids which users need to make interpolations. Yet, little information can be obtained regarding the most appropriate interpolation method to extract information from the regular grid of geoidal models. The use of an interpolator that does not represent the geoid surface appropriately can impair the quality of geoid undulations and consequently the height transformation. This work aims to quantify the magnitude of error that comes from a regular mesh of geoid models. The analysis consisted of performing a comparison between the interpolation of the MAPGEO2015 program and three interpolation methods: bilinear, cubic spline and neural networks Radial Basis Function. As a result of the experiments, it was concluded that 2.5 cm of the 18 cm error of the MAPGEO2015 validation is caused by the use of interpolations in the 5'x5' grid.
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Shen, Hai Ming, Kun Qi Wang, and Yong You Tian. "Design of Interpolation Algorithm in the Multi-Axis Motion Control System." Advanced Materials Research 411 (November 2011): 259–63. http://dx.doi.org/10.4028/www.scientific.net/amr.411.259.

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This paper describes an interpolation algorithm in the multi-axis motion control system, which can achieve six-axis interpolation operations, greatly improving the processing efficiency. Using modular design idea on the Quartus II platform, by DDA interpolation theory, interpolation modules are built through VHDL. And these interpolator modules are connected into schematic diagrams. By those schematic diagrams a linear interpolator, a circular interpolator and a composite interpolator are formed. The corresponding functions of those interpolators have been simulated on the Quartus II platform. The simulation shows that this interpolation algorithm is effective to complex multi-axis motion control system.
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Barker, Paul M., and Trevor J. McDougall. "Two Interpolation Methods Using Multiply-Rotated Piecewise Cubic Hermite Interpolating Polynomials." Journal of Atmospheric and Oceanic Technology 37, no. 4 (April 2020): 605–19. http://dx.doi.org/10.1175/jtech-d-19-0211.1.

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AbstractTwo interpolation methods are presented, both of which use multiple Piecewise Cubic Hermite Interpolating Polynomials (PCHIPs). The first method is based on performing 16 PCHIPs on 8 rotated versions of the plot of the data versus an independent variable (such as pressure or time). These 16 PCHIPs are then used to form 8 interpolations of the original data, and finally, these 8 are averaged. When the original data are unevenly spaced with respect to the independent variable, we show that it is best to perform the Multiply-Rotated PCHIP (MR-PCHIP) method using the “data index” as the independent variable, and then to subsequently perform one last PCHIP of the data index with respect to the original independent variable. This MR-PCHIP method avoids the flat spots that are a feature of the PCHIP method when the data have multiple values approximately equal to a local extreme value. The MR-PCHIP interpolated data have continuous first derivatives at the data points. This method also avoids the unrealistic overshoots that can occur when using the standard cubic spline interpolation procedure. The second interpolation method is designed specifically for hydrographic data with the aim of minimizing the formation of unrealistic water masses by the interpolation procedure. This is achieved by applying a Piecewise Cubic Hermite Interpolating Polynomial to each of 8 rotations of the salinity versus temperature plot (Multiply-Rotated Salinity–Temperature PCHIP, MRST-PCHIP) with bottle number (that is, data index) as the vertical interpolating coordinate, thereby making the MRST-PCHIP method independent of the heave of a water column. This method is equivalent to interpolating in the salinity–temperature diagram, and MRST-PCHIP proves very effective at avoiding the production of anomalous water masses that otherwise occur when interpolating temperature and salinity separately.
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Dissertations / Theses on the topic "Interpolation"

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Rabut, Christophe. "B-splines polyharmoniques cardinales : interpolation, quasi-interpolation, filtrage." Toulouse 3, 1990. http://www.theses.fr/1990TOU30046.

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Les B-splines polynomiales sont couramment utilisées pour définir simplement une fonction spline qui passe "près" de points donnés. Dans le cas où les données sont régulièrement réparties, on apporte, par un traitement préalable des données (convolution avec certains vecteurs à support borné), plus de souplesse à cette opération : on peut alors obtenir une fonction qui passe très près des points -on parle alors de quasi-interpolation- ou au contraire qui filtre les bruits inhérents à ces données on parle alors de filtrage. On montre comment utiliser la méthode de validation croisée pour choisir de façon optimale la force d'un filtrage, qui peut être adaptative, et on propose une méthode de réduction de données, le taux de réduction étant lié à la bande passante du filtre. Ces notions sont ensuite généralisées en dimension quelconque par l'utilisation des B-splines polyharmoniques : après avoir defini les splines polyharmoniques pour des données qui peuvent être en nombre infini, on en donne une expression numériquement plus stable que celle généralement utilisée, et on montre un lien entre splines polyharmoniques d'ordre ou de dimension différents. On définit alors les B-splines polyharmoniques, et on présente leurs propriétés essentielles, très voisines de celles des B-splines polynomiales. On propose l'utilisation de ces B-splines d'une part pour quasi-interpoler ou filtrer des données régulièrement réparties, d'autre part pour déterminer rapidement, par une méthode de subdivision, la spline d'interpolation de ces données. On envisage enfin la généralisation de cette notion de B-spline à des noeuds quelconques et à toute famille de fonctions satisfaisant certaines équations différentielles.
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Ramesh, Gayatri. "FRACTAL INTERPOLATION." Master's thesis, University of Central Florida, 2008. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/3128.

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This thesis is devoted to a study about Fractals and Fractal Polynomial Interpolation. Fractal Interpolation is a great topic with many interesting applications, some of which are used in everyday lives such as television, camera, and radio. The thesis is comprised of eight chapters. Chapter one contains a brief introduction and a historical account of fractals. Chapter two is about polynomial interpolation processes such as Newton s, Hermite, and Lagrange. Chapter three focuses on iterated function systems. In this chapter I report results contained in Barnsley s paper, Fractal Functions and Interpolation. I also mention results on iterated function system for fractal polynomial interpolation. Chapters four and five cover fractal polynomial interpolation and fractal interpolation of functions studied by Navascués. Chapter five and six are the generalization of Hermite and Lagrange functions using fractal interpolation. As a concluding chapter we look at the current applications of fractals in various walks of life such as physics and finance and its prospects for the future.
M.S.
Department of Mathematics
Sciences
Mathematical Science MS
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Goggins, Dan. "Constraint-based interpolation /." Diss., CLICK HERE for online access, 2005. http://contentdm.lib.byu.edu/ETD/image/etd976.pdf.

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Yeung, R. Kacheong. "Stable rational interpolation." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape7/PQDD_0021/NQ46952.pdf.

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Christ, Jürgen [Verfasser], and Andreas [Akademischer Betreuer] Podelski. "Interpolation modulo theories." Freiburg : Universität, 2015. http://d-nb.info/1119805767/34.

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Fang, Quanlei. "Multivariable Interpolation Problems." Diss., Virginia Tech, 2008. http://hdl.handle.net/10919/28311.

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In this dissertation, we solve multivariable Nevanlinna-Pick type interpolation problems. Particularly, we consider the left tangential interpolation problems on the commutative or noncommutative unit ball. For the commutative setting, we discuss left-tangential operator-argument interpolation problems for Schur-class multipliers on the Drury-Arveson space and for the noncommutative setting, we discuss interpolation problems for Schur-class multipliers on Fock space. We apply the Krein-space geometry approach (also known as the Grassmannian Approach). To implement this approach J-versions of Beurling-Lax representers for shift-invariant subspaces are required. Here we obtain these J-Beurling-Lax theorems by the state-space method for both settings. We see that the Krein-space geometry method is particularly simple in solving the interpolation problems when the Beurling-Lax representer is bounded. The Potapov approach applies equally well whether the representer is bounded or not.
Ph. D.
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Merrell, Jacob Porter. "Generalized Constrained Interpolation." Diss., CLICK HERE for online access, 2008. http://contentdm.lib.byu.edu/ETD/image/etd2360.pdf.

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Goggins, Daniel David. "Constraint-Based Interpolation." BYU ScholarsArchive, 2005. https://scholarsarchive.byu.edu/etd/610.

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Image reconstruction is the process of converting a sampled image into a continuous one prior to transformation and resampling. This reconstruction can be more accurate if two things are known: the process by which the sampled image was obtained and the general characteristics of the original image. We present a new reconstruction algorithm known as Constraint-Based Interpolation, which estimates the sampling functions found in cameras and analyzes properties of real world images in order to produce quality real-world image magnifications. To accomplish this, Constraint-Based Interpolation uses a sensor model that pushes the pixels in an interpolation to more closely match the data in the sampled image. Real-world image properties are ensured with a level-set smoothing model that smooths "jaggies" and a sharpening model that alleviates blurring. This thesis describes the three models, their methods and constraints. The effects of the various models and constraints are also shown, as well as a human observer test. A variation of a previous interpolation technique, Quad-based Interpolation, and a new metric, gradient weighted contour curvature, is presented and analyzed.
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Ameur, Yacin. "Interpolation of Hilbert spaces." Doctoral thesis, Uppsala universitet, Matematiska institutionen, 2002. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-1753.

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(i) We prove that intermediate Banach spaces A, B with respect to arbitrary Hilbert couples H, K are exact interpolation iff they are exact K-monotonic, i.e. the condition f0∊A and the inequality K(t,g0;K)≤K(t,f0;H), t>0 imply g0∊B and ||g0||B≤||f0||A (K is Peetre's K-functional). It is well-known that this property is implied by the following: for each ρ>1 there exists an operator T : H→K such that Tf0=g0, and K(t,Tf;K)≤ρK(t,f;H), f∊H0+H1, t>0.Verifying the latter property, it suffices to consider the "diagonal" case where H=K is finite-dimensional. In this case, we construct the relevant operators by a method which allows us to explicitly calculate them. In the strongest form of the theorem, it is shown that the statement remains valid when substituting ρ=1. (ii) A new proof is given to a theorem of W. F. Donoghue which characterizes certain classes of functions whose domain of definition are finite sets, and which are subject to certain matrix inequalities. The result generalizes the classical Löwner theorem on monotone matrix functions, and also yields some information with respect to the finer study of monotone functions of finite order. (iii) It is shown that with respect to a positive concave function ψ there exists a function h, positive and regular on ℝ+ and admitting of analytic continuation to the upper half-plane and having positive imaginary part there, such that h≤ψ≤ 2h. This fact is closely related to a theorem of Foiaş, Ong and Rosenthal, which states that regardless of the choice of a concave function ψ, and a weight λ, the weighted l2-space l2(ψ(λ)) is c-interpolation with respect to the couple (l2,l2(λ)), where we have c≤√2 for the best c. It turns out that c=√2 is best possible in this theorem; a fact which is implicit in the work of G. Sparr. (iv) We give a new proof and new interpretation (based on the work (ii) above) of Donoghue's interpolation theorem; for an intermediate Hilbert space H* to be exact interpolation with respect to a regular Hilbert couple H it is necessary and sufficient that the norm in H* be representable in the form ||f||*= (∫[0,∞] (1+t-1)K2(t,f;H)2dρ(t))1/2 with some positive Radon measure ρ on the compactified half-line [0,∞]. (v) The theorem of W. F. Donoghue (item (ii) above) is extended to interpolation of tensor products. Our result is related to A. Korányi's work on monotone matrix functions of several variables.
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Ameur, Yacin. "Interpolation of Hilbert spaces /." Uppsala : Matematiska institutionen, Univ. [distributör], 2001. http://publications.uu.se/theses/91-506-1531-9/.

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Books on the topic "Interpolation"

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A, Brudnyĭ I͡U. Interpolation functors and interpolation spaces. Amsterdam: North-Holland, 1991.

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Mastroianni, Giuseppe, and Gradimir V. Milovanović. Interpolation Processes. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-68349-0.

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Lunardi, Alessandra. Interpolation Theory. Pisa: Scuola Normale Superiore, 2018. http://dx.doi.org/10.1007/978-88-7642-638-4.

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Bennett, Colin. Interpolation of operators. Boston: Academic Press, 1987.

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Lorentz, Rudolph A. Multivariate Birkhoff Interpolation. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/bfb0088788.

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Karl, Maurer. Interpolation in Thucydides. Leiden: E.J. Brill, 1995.

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Lorentz, Rudoph A. Multivariate Birkhoff interpolation. Berlin: New York, 1992.

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Bennett, Colin. Interpolation of operators. Boston: Academic Press, 1988.

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Stein, Michael L. Interpolation of Spatial Data. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-1494-6.

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Dym, H., V. Katsnelson, B. Fritzsche, and B. Kirstein, eds. Topics in Interpolation Theory. Basel: Birkhäuser Basel, 1997. http://dx.doi.org/10.1007/978-3-0348-8944-5.

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Book chapters on the topic "Interpolation"

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Peuter, Dennis, Viorica Sofronie-Stokkermans, and Sebastian Thunert. "On P-Interpolation in Local Theory Extensions and Applications to the Study of Interpolation in the Description Logics $$\mathcal{E}\mathcal{L}, \mathcal{E}\mathcal{L}^+$$." In Automated Deduction – CADE 29, 419–37. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-38499-8_24.

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AbstractWe study the P-interpolation property for certain local theory extensions, and use these results for proving $$\le $$ ≤ -interpolation in classes of semilattices with monotone operators. For computing the $$\le $$ ≤ -interpolating terms, we use a hierarchic approach. We use these results for the study of $$\sqsubseteq $$ ⊑ -interpolation in the description logics $$\mathcal{E}\mathcal{L}$$ E L and $$\mathcal{E}\mathcal{L}^+$$ E L + .
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Siemon, Klaus Dieter. "Interpolation." In HOAI-Praxis bei Architektenleistungen, 41–42. Wiesbaden: Vieweg+Teubner Verlag, 2004. http://dx.doi.org/10.1007/978-3-322-93967-8_7.

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Schwarz, Hans Rudolf. "Interpolation." In Numerische Mathematik, 94–149. Wiesbaden: Vieweg+Teubner Verlag, 1993. http://dx.doi.org/10.1007/978-3-322-94127-5_3.

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Opfer, Gerhard. "Interpolation." In Numerische Mathematik für Anfänger, 37–84. Wiesbaden: Vieweg+Teubner Verlag, 2002. http://dx.doi.org/10.1007/978-3-322-94286-9_3.

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Opfer, Gerhard. "Interpolation." In Numerische Mathematik für Anfänger, 34–82. Wiesbaden: Vieweg+Teubner Verlag, 1994. http://dx.doi.org/10.1007/978-3-322-94301-9_3.

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Kress, Rainer. "Interpolation." In Graduate Texts in Mathematics, 151–88. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-0599-9_8.

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Stoyan, Gisbert, and Agnes Baran. "Interpolation." In Compact Textbooks in Mathematics, 111–33. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-44660-8_6.

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Stoer, J., and R. Bulirsch. "Interpolation." In Introduction to Numerical Analysis, 37–124. New York, NY: Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4757-2272-7_2.

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Vince, John. "Interpolation." In Mathematics for Computer Graphics, 121–34. London: Springer London, 2014. http://dx.doi.org/10.1007/978-1-4471-6290-2_8.

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Opfer, Gerhard. "Interpolation." In Numerische Mathematik für Anfänger, 34–86. Wiesbaden: Vieweg+Teubner Verlag, 1993. http://dx.doi.org/10.1007/978-3-663-00144-7_3.

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Conference papers on the topic "Interpolation"

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Adhikary, N., and B. Gurumoorthy. "Smooth Surface Interpolation With Multiple Patches." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/dac-8555.

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Abstract This paper addresses the problem of interpolating point data with multiple patches. The specific issue addressed in this paper is the continuity between the patches used for interpolation. The procedure described in this paper maintains continuity by introducing an intermediate patch between the two patches used for interpolating the point data. This patch is formed by several Bezier patches that maintain continuity with the corresponding Bezier patches obtained by repeated knot insertion in the two interpolating patches. The blending Bezier patches are then converted to a blending B-spline patch by knot removal. It is shown that C1 continuity is obtained across the junction between each interpolating patch and the blending patch. The continuity, across each blending patch and the interpolation performance in the blending patch is also discussed. The paper presents results, of implementation on some typical surfaces.
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Moetakef Imani, Behnam, and Amirmohammad Ghandehariun. "Look-Ahead NURBS-PH Interpolation for High Speed CNC Machining." In ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2010. http://dx.doi.org/10.1115/esda2010-24426.

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Various methods for parametric interpolation of NURBS curves have been proposed in the past. However, the errors caused by the approximate nature of the NURBS interpolator were rarely taken into account. This paper proposes an integrated look-ahead algorithm for parametric interpolation along NURBS curves. The algorithm interpolates the sharp corners on the curve with the Pythagorean-hodograph (PH) interpolation. This will minimize the geometric and interpolator approximation errors simultaneously. The algorithm consists of four different modules: a sharp corner detection module, a PH construction module, a jerk-limited module, and a dynamics module. Simulations are performed to show correctness of the proposed algorithm. Experiments on an X-Y table confirm that the developed method improves tracking and contour accuracies significantly when compared to previously proposed adaptive-feedrate and curvature-feedrate algorithms.
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Ge, Q. J., Amitabh Varshney, Jai P. Menon, and Chu-Fei Chang. "Double Quaternions for Motion Interpolation." In ASME 1998 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/detc98/dfm-5755.

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Abstract This paper describes the concept of double quaternions, an extension of quaternions, and shows how they can be used for effective three-dimensional motion interpolation. Motion interpolation using double quaternions has several advantages over the method of interpolating rotation and translation independently and then combining the results. First, double quaternions provide a conceptual framework that allows one to handle rotational and translational components in a unified manner. Second, results obtained by using double quaternions are coordinate frame invariant. Third, double quaternions allow a natural way to tradeoff robustness against accuracy. Fourth, double quaternions, being a straightforward extension of quaternions, can be integrated into several existing systems that currently use quaternions with translational components, with a only small coding effort.
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Luo, Wen, Jinbo Liu, Zengrui Li, and Jiming Song. "High Order Interpolation Error Analysis Based on Triangular Interpolations." In 2020 IEEE International Conference on Computational Electromagnetics (ICCEM). IEEE, 2020. http://dx.doi.org/10.1109/iccem47450.2020.9219341.

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Chen, Chih-Hsin. "A Surface Interpolation Scheme Based on the Theory of Conjugate Surfaces." In ASME 1994 International Computers in Engineering Conference and Exhibition and the ASME 1994 8th Annual Database Symposium collocated with the ASME 1994 Design Technical Conferences. American Society of Mechanical Engineers, 1994. http://dx.doi.org/10.1115/cie1994-0455.

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Abstract A surface interpolation scheme is described for interpolating an array of knot points and normals. The scheme is based on the generation of interpolation surface patches by envelopment of a moving base plane which is fixed in the end effector of a robot of two revolute pairs and one prismatic pair. The initial values, the control values, and the interpolation functions of the robot motion are discussed. The equations for determining the geometrical values of an interpolation point are derived with the aid of the theory of conjugate surfaces, and are arranged in order of the corresponding algorithm. The continuity between neighboring interpolation surface patches is proved to be C1.5. The feasibility of improving the continuity by adjusting the control values of the robot motion is investigated.
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Yudilevich, E., and Henry Stark. "Interpolation from samples on a linear spiral scan." In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1987. http://dx.doi.org/10.1364/oam.1987.tuh5.

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An interpolation method useful for reconstructing an image from its Fourier plane samples on a linear spiral scan trajectory is presented. This kind of sampling arises in NMR imaging. We first present a theorem that enables exact interpolation from spiral samples to a Cartesian lattice. We then investigate two practical implementations of the theorem in which a finite number of interpolating points are used to calculate the value at a new point. Our experimental results confirm the theorem’s validity and also demonstrate that both practical implementations yield very good reconstructions. Thus the theorem and/or its practical implementation suggest the possibility of using direct Fourier reconstruction from linear spiral-scan NMR imaging.
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Ning, Lihua, and Kelu Luo. "An Interpolation Based on Cubic Interpolation Algorithm." In Proceedings of the International Conference. World Scientific Publishing Company, 2008. http://dx.doi.org/10.1142/9789812799524_0391.

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Condat, L., T. Blu, and M. Unser. "Beyond interpolation: optimal reconstruction by quasi-interpolation." In 2005 International Conference on Image Processing. IEEE, 2005. http://dx.doi.org/10.1109/icip.2005.1529680.

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Loh, Woong-Kee, Sang-Wook Kim, and Kyu-Young Whang. "Index interpolation." In the ninth international conference. New York, New York, USA: ACM Press, 2000. http://dx.doi.org/10.1145/354756.354856.

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Moss, Andrew, and Dan Page. "Program interpolation." In the 2009 ACM SIGPLAN workshop. New York, New York, USA: ACM Press, 2008. http://dx.doi.org/10.1145/1480945.1480951.

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Reports on the topic "Interpolation"

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Nolting, J., and U. Yang. Improving Interpolation in BoomerAMG. Office of Scientific and Technical Information (OSTI), September 2006. http://dx.doi.org/10.2172/894324.

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Fritsch, F. N. The LEOS Interpolation Package. Office of Scientific and Technical Information (OSTI), March 2003. http://dx.doi.org/10.2172/15005830.

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De Boor, Carl, and Amos Ron. On Multivariate Polynomial Interpolation. Fort Belvoir, VA: Defense Technical Information Center, November 1988. http://dx.doi.org/10.21236/ada204099.

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Foley, T. A. Scattered data interpolation codes. Office of Scientific and Technical Information (OSTI), February 1985. http://dx.doi.org/10.2172/5936369.

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Chen, Qi, and Ivo Babuska. Polynomial Interpolation and Approximation of Real Functions 2: Symmetrical Interpolation for the Triangle. Fort Belvoir, VA: Defense Technical Information Center, November 1993. http://dx.doi.org/10.21236/ada277345.

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Gammel, J. Tinka. EOS Interpolation and Thermodynamic Consistency. Office of Scientific and Technical Information (OSTI), November 2015. http://dx.doi.org/10.2172/1226141.

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Miller, Walter F. Short-Term Hourly Temperature Interpolation. Fort Belvoir, VA: Defense Technical Information Center, December 1990. http://dx.doi.org/10.21236/ada240489.

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Carnegie, D. W. Interpolation of Hall probe calibration data. Office of Scientific and Technical Information (OSTI), July 1992. http://dx.doi.org/10.2172/87840.

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Tannenbaum, Allen. An Interpolation Theoretic Approach to Control. Fort Belvoir, VA: Defense Technical Information Center, April 1994. http://dx.doi.org/10.21236/ada281465.

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Soanes, Royce W. Thrice Differentiable Affine Conic Spline Interpolation. Fort Belvoir, VA: Defense Technical Information Center, September 1995. http://dx.doi.org/10.21236/ada304778.

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