Automatic selection of interpolation segments for a machine tool with linear interpolator
Automatic selection of interpolation segments for machine tool with linear interpolator
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Nearest neighbor, bilinear interpolation and bicubic interpolation geographic correction effects on LANDSAT imagery
Geographical correction effects on LANDSAT image data are identified, using the nearest neighbor, bilinear interpolation and bicubic interpolation techniques. Potential impacts of registration on image compression and classification are explored.
Jayroe, R. R., Jr.↗
Minimal norm constrained interpolation
In computational fluid dynamics and in CAD/CAM, a physical boundary is usually known only discreetly and most often must be approximated. An acceptable approximation preserves the salient features of the data such as convexity and concavity. In this dissertation, a smooth interpolant which is locally concave where the data are concave and is locally convex where the data are convex is described. The interpolant is found by posing and solving a minimization problem whose solution is a piecewise cubic polynomial. The problem is solved indirectly by using the Peano Kernal theorem to recast it into an equivalent minimization problem having the second derivative of the interpolant as the solution. This approach leads to the solution of a nonlinear system of equations. It is shown that Newton's method is an exceptionally attractive and efficient method for solving the nonlinear system of equations. Examples of shape-preserving interpolants, as well as convergence results obtained by using Newton's method are also shown. A FORTRAN program to compute these interpolants is listed. The problem of computing the interpolant of minimal norm from a convex cone in a normal dual space is also discussed. An extension of de Boor's work on minimal norm unconstrained interpolation is presented.
Irvine, L. D.↗
Supersonic inlet contour interpolation
A method for designing supersonic inlet contours is described which consists in the interpolation of the contours of two known inlets designed for different Mach numbers, thereby determining the contours for a third inlet at an intermediate design Mach number. Several similar axisymmetric inlet contours were interpolated from known inlets with design Mach numbers ranging from 2.16 to 4.0 and with design Mach numbers differing by as much as 1.0. The flowfields were calculated according to Sorensen's (1965) computer program. Shockwave structure and pressure distribution characteristics are shown for the interpolated inlets. The validity of the interpolation is demonstrated by comparing the plots of the flowfield properties across the throat station of the interpolated inlet with the known inlets which were designed iteratively. It seems possible to write a computer program so that a matrix of known inlet contours can be interpolated.
Sorensen, N. E.↗
Interpolation of a surface from sets of discrete height data of different statistical characteristics
This paper presents and analyzes a method for the interpolation of a unique surface from two sets of independent digital height data of differing statistical characteristics. This method is based on linear prediction and thus relies on the concepts of auto- and cross-covariance functions. The linear prediction algorithm for two sets of digital height measurements is first derived and then evaluated using the method of moving averages and bilinear interpolation for comparison. It is found that the overall root mean square interpolation errors of linear prediction are similar to those from moving averages and bilinear interpolation. This accuracy performance, together with the well known potential for controlled filtering of measuring errors and good-behavior in areas of poor control, makes linear prediction a versatile and general method for interpolating a unique surface from two sets of digital height data, with applications in photogrammetric mapping, remote sensing, and other fields.
Leberl, F.↗
Modal interpolation program, L215 (INTERP). Volume 1: Engineering and usage
The usage of the Modal Interpolation Program L215 (INTERP) is described. The program uses modal data to form sets of arrays containing interpolation coefficients. The interpolation arrays can then be used to determine displacements at various aerodynamic surface and surface slopes that are parallel and perpendicular to the freestream direction. Five different interpolation methods are available. A description of the data manipulation and the interpolation methods is presented.
Kroll, R. I.↗
Use of shape-preserving interpolation methods in surface modeling
In many large-scale scientific computations, it is necessary to use surface models based on information provided at only a finite number of points (rather than determined everywhere via an analytic formula). As an example, an equation of state (EOS) table may provide values of pressure as a function of temperature and density for a particular material. These values, while known quite accurately, are typically known only on a rectangular (but generally quite nonuniform) mesh in (T,d)-space. Thus interpolation methods are necessary to completely determine the EOS surface. The most primitive EOS interpolation scheme is bilinear interpolation. This has the advantages of depending only on local information, so that changes in data remote from a mesh element have no effect on the surface over the element, and of preserving shape information, such as monotonicity. Most scientific calculations, however, require greater smoothness. Standard higher-order interpolation schemes, such as Coons patches or bicubic splines, while providing the requisite smoothness, tend to produce surfaces that are not physically reasonable. This means that the interpolant may have bumps or wiggles that are not supported by the data. The mathematical quantification of ideas such as physically reasonable and visually pleasing is examined.
Ftitsch, F. N.↗
Spectral analysis of linear, shift-invariant interpolants
The use of a spectral analysis technique to evaluate the reconstruction/interpolation performance of linear, shift-invariant interpolants is examined. The technique was utilized to measure the performance of cubic hermite, quintic hermite, exponential, cubic, spline, Nu, PCC, Keys cubic, and BAWA cubic interpolants. The performance criterion is based upon the mean square error of the difference between the sampled and reconstructed functions. The reconstruction properties, interpolation functions, and reconstruction filters for the interpolants are studied and compared. It is noted that the spectral analysis technique is applicable to reconstruction algorithms used in signal and image processes, and interpolants used in numerical analysis, computer-aided design, and computer graphics.
Lansing, Donald L.↗
INPUTB: A thermal/structural data interface program for 2-dimensional and 3-dimensional interpolation
A computer program (INPUTB) for interpolation in both space and time, and based on a linear interpolation scheme using simplex spatial regions is described. The program was developed to provide data interfacing between the output from thermal analyzers and the input to the BOPACE 3-D program. The INPUTB interpolator is of a general nature and could be used for other tasks. The INPUTB program utilizes temperature values which are given at some sequence of time for a list of strategically located thermal nodes. It operates on these values by performing a double interpolation to provide temperature values at another desired sequence of times for a list of structural nodes.
Vos, R. G.↗
Interpolation schemes for orbit determination with the global positioning system
This paper demonstrates that the Global Positioning System (GPS) and simple interpolation schemes can be utilized to satisfy typical orbit determination demands of applications satellites. The complete GPS consists of 24 satellites and permits a position fix of a user satellite at any arbitrary instant. The interpolation formulae used in this report fit generalized Keplerian orbits through a number of position fixes. For a given accuracy level the telemetry requirements as measured by the time intervals between position fixes and the computational load of an interpolation as measured by the number of points through which a generalized Keplerian orbit is fitted vary inversely. A set of possible compromises between these two factors is presented. The Phase I GPS consists of 6 satellites and permits a position fix of a user satellite just 36% of the time. It is shown that with this system more sophisticated interpolation schemes which model atmospheric drag and higher degree terms of the earth's gravity field must be employed to obtain accurate orbits.
Argentiero, P.↗
Modal Interpolation Program, L 215 (INTERP): Supplemental System Design and Maintenance Document - Volume 2
The design, structure, and usage of the modal interpolation program L215 are presented. The program uses modal data sets of arrays containing interpolation coefficients. The interpolation arrays are used to determine displacements at various aerodynamic control points. The displacements consist of translations normal to the aerodynamic surface and surface slopes that are parallel and perpendicular to the free stream direction. Five different interpolation methods are available.
Hirayama, M. Y.↗
Quantitative analysis of the reconstruction performance of interpolants
The analysis presented provides a quantitative measure of the reconstruction or interpolation performance of linear, shift-invariant interpolants. The performance criterion is the mean square error of the difference between the sampled and reconstructed functions. The analysis is applicable to reconstruction algorithms used in image processing and to many types of splines used in numerical analysis and computer graphics. When formulated in the frequency domain, the mean square error clearly separates the contribution of the interpolation method from the contribution of the sampled data. The equations provide a rational basis for selecting an optimal interpolant; that is, one which minimizes the mean square error. The analysis has been applied to a selection of frequently used data splines and reconstruction algorithms: parametric cubic and quintic Hermite splines, exponential and nu splines (including the special case of the cubic spline), parametric cubic convolution, Keys' fourth-order cubic, and a cubic with a discontinuous first derivative. The emphasis in this paper is on the image-dependent case in which no a priori knowledge of the frequency spectrum of the sampled function is assumed.
Lansing, Donald L.↗
High degree interpolation polynomial in Newton form
Polynomial interpolation is an essential subject in numerical analysis. Dealing with a real interval, it is well known that even if f(x) is an analytic function, interpolating at equally spaced points can diverge. On the other hand, interpolating at the zeroes of the corresponding Chebyshev polynomial will converge. Using the Newton formula, this result of convergence is true only on the theoretical level. It is shown that the algorithm which computes the divided differences is numerically stable only if: (1) the interpolating points are arranged in a different order, and (2) the size of the interval is 4.
Tal-Ezer, Hillel↗
Interpolation methods for shaped reflector analysis
The diffraction analysis of reflector surfaces which are described only at a discrete set of locations usually leads to the requirement of an interpolation to determine the surface characteristics over a continuum of locations. Two methods of interpolation, the global and the local methods, are presented. The global interpolation representation is a closed-form or series expression valid over the entire surface. The coefficients of a series expression are found by an integration of all of the raw data. Since the number of coefficients used to describe the surface is much smaller than the number of raw data points, the integration effectively provides a smoothing of the raw data. The local interpolation provides a closed-form expression for only a small area of the reflector surface. The subreflector is divided into sectors each of which has constant discretized data. Each area segment is then locally described by a two-dimensional quadratic surface. The second derivative data give the desired smoothed values.
Galindo-Israel, Victor↗
Curvilinear bicubic spline fit interpolation scheme
Modification of the rectangular bicubic spline fit interpolation scheme so as to make it suitable for use with a polar grid pattern. In the proposed modified scheme the interpolation function is expressed in terms of the radial length and the arc length, and the shape of the patch, which is a wedge or a truncated wedge, is taken into account implicitly. Examples are presented in which the proposed interpolation scheme was used to reproduce the equations of a hemisphere.
Chi, C.↗
Error in interpolation and choice of the range of discreteness in measurements in a hydrophysical field
Errors in interpolation and the choosing of the range of discreteness when making measurements in a hydrophysical field are discussed. Equations for optimum interpolating based on the theory of linear interpolation of stationary random sequences are presented; analogous equations are derived for the case of data collected at stations located at the apices of a right triangle.
Zudin, O. F.↗
Spectral interpolation - Zero fill or convolution
Zero fill, or augmentation by zeros, is a method used in conjunction with fast Fourier transforms to obtain spectral spacing at intervals closer than obtainable from the original input data set. In the present paper, an interpolation technique (interpolation by repetitive convolution) is proposed which yields values accurate enough for plotting purposes and which lie within the limits of calibration accuracies. The technique is shown to operate faster than zero fill, since fewer operations are required. The major advantages of interpolation by repetitive convolution are that efficient use of memory is possible (thus avoiding the difficulties encountered in decimation in time FFTs) and that is is easy to implement.
Forman, M. L.↗
Interpolating for the location of remote sensor data
An interpolation algorithm is presented as a practical alternative to common interpolation and approximation methods when applied to the problem of determining the location of remote sensor data. This algorithm is based upon knowledge of the geometry of the problem and is shown to be inherently more accurate than common interpolation schemes which may be applied to all types of data. A practical location problem is used to demonstrate its accuracy and computational cost.
Puccinelli, E. F.↗