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Showing papers on "Bicubic interpolation published in 1984"



Journal ArticleDOI
TL;DR: In this article, the stability and accuracy of multiply-upstream, semi-Lagrangian method of integrating the advective equation in two dimensions is examined for four different interpolation schemes; namely, bilinear, biquadratic, bicubic and biquartic.
Abstract: The stability and accuracy of the multiply-upstream, semi-Lagrangian method of integrating the advective equation in two dimensions is examined for four different interpolation schemes; namely, bilinear, biquadratic, bicubic and biquartic. All are shown to be consistent and unconditionally stable for constant advecting velocity. Their respective amplitude and phase errors are discussed. They are then used to integrate the test problem of a cone being advected about the plane at constant angular velocity. The merits of the schemes relative to each other and relative to a well tried Eulerian scheme am examined with particular regard to accuracy and computation time.

112 citations


Journal ArticleDOI
TL;DR: In this article, an algorithm is described for constructing a smooth computable function, f, defined over the surface of a sphere and interpolating a set of n data values, u sub i, associated with n locations, P sub i. The locations are not required to lie on any type of regular grid.
Abstract: An algorithm is described for constructing a smooth computable function, f, defined over the surface of a sphere and interpolating a set of n data values, u sub i, associated with n locations, P sub i, on the surface of the sphere. The interpolation function, f, will be continuous and have continuous first partial derivatives. The locations, p sub i, are not required to lie on any type of regular grid.

89 citations



Journal ArticleDOI
TL;DR: In this paper, the representation and approximation of 3D and 4D surfaces is accomplished by means of local, piecewise defined, smooth interpolation methods on geometric domains of triangles or tetrahedra.
Abstract: The representation and approximation of three- and four-dimensional surfaces is accomplished by means of local, piecewise defined, smooth interpolation methods. In order to interpolate to arbitrarily located data, the schemes are defined on geometric domains of triangles or tetrahedra, respectively.

47 citations


Journal ArticleDOI
01 Sep 1984-Calcolo
TL;DR: In this article, a necessary and sufficient condition for the existence of cubic differentiable interpolating splines which are monotone and convex is presented, and their approximation properties when applied to the interpolation of functions having a preassigned degree of smoothness.
Abstract: Given a set of monotone and convex data, we present a necessary and sufficient condition for the existence of cubic differentiable interpolating splines which are monotone and convex. Further, we discuss their approximation properties when applied to the interpolation of functions having preassigned degree of smoothness.

40 citations


Journal ArticleDOI
TL;DR: This paper presents computational techniques using which subdivision algorithms may be devised for the processing (rendering, intersection detection, silhouette detection) of parametrically defined surfaces by subd dividing surface patches until they are simple enough for direct handling.
Abstract: This paper presents computational techniques using which subdivision algorithms may be devised for the processing (rendering, intersection detection, silhouette detection) of parametrically defined surfaces. These algorithms work by subdividing surface patches until they are simple enough for direct handling. For example, planar surface patches can be handled analytically. For interference it is necessary to box the surface as well. The computational techniques presented are essentially for efficient computation of surface properties needed by the processing tasks. The three properties considered are: (1) Euclidean bounds: this is done by working in extrema in x, y, and z over the patch; (2) planarity estimate: this test is defined in terms of the linearity of constituent curves; (3) Local visibility: which says whether a patch is totally visible, invisible, or partially visible from a given viewpoint. Rendering algorithms make use of this information. This too is done by working in extrema of the visibility function. All the techniques are based on the parametric form of the surface representation. The class of surfaces that can be handled by these techniques is very large, basically C2 continuous surfaces. A class of surfaces known as product surfaces is specially introduced as the above methods are extremely efficient for this class. Application of these methods to bicubic surfaces is also discussed.

29 citations


Journal ArticleDOI
01 Dec 1984-Calcolo
TL;DR: An algorithm for the construction of shape-preserving cubic splines interpolating a set of data point based upon some existence properties recently developed is presented.
Abstract: We present an algorithm for the construction of shape-preserving cubic splines interpolating a set of data point. The method is based upon some existence properties recently developed. Graphical examples are given.

23 citations


Journal ArticleDOI
TL;DR: In this article, a mathematical analysis of image sampling and interpolative reconstruction is summarized and extended to two dimensions for application to data acquired from satellite sensors such as the Thematic mapper and SPOT.
Abstract: Mathematical analysis of image sampling and interpolative reconstruction is summarized and extended to two dimensions for application to data acquired from satellite sensors such as the Thematic mapper and SPOT. It is shown that sample-scene phase influences the reconstruction of sampled images, adds a considerable blur to the average system point spread function, and decreases the average system modulation transfer function. It is also determined that the parametric bicubic interpolator with alpha = -0.5 is more radiometrically accurate than the conventional bicubic interpolator with alpha = -1, and this at no additional cost. Finally, the parametric bicubic interpolator is found to be suitable for adaptive implementation by relating the alpha parameter to the local frequency content of an image.

19 citations


Journal ArticleDOI
TL;DR: This research aims to demonstrate the efforts towards in-situ applicability of EMMARM, which aims to provide real-time information about the response of the immune system to EMTs.
Abstract: Received July 1983; revised July 1984; accepted July 1984 Funding for this research was provided jointly by the National Science Foundation's Ecosystem Program under Interagency Agreement DEB-8115316 with the Ecological Science Division and the Mathematics Development Program in Techmcal Applications, Computer Sciences at Oak Ridge National Laboratory. Author's present address: Department of Computer Sciences, North Texas State University, P.O. Box 13886, Denton, TX 76203. Permission to copy without fee all or part of this material is granted provided that the copies are not made or &stributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission. © 1984 0098-3500/84/1200-0437 $00.75

19 citations


01 Mar 1984
TL;DR: The problem of the computation and display of all intersections of a given plane with a rational bicubic surface patch for use on an interactive CAD/CAM system is examined and an algorithm is presented which can produce all intersection curves.
Abstract: The problem of the computation and display of all intersections of a given plane with a rational bicubic surface patch for use on an interactive CAD/CAM system is examined. The general problem of calculating all intersections of a plane and a surface consisting of rational bicubic patches is reduced to the case of a single generic patch by applying a rejection algorithm which excludes all patches that do not intersect the plane. For each pertinent patch the algorithm presented computed the intersection curves by locating an initial point on each curve, and computes successive points on the curve using a tolerance step equation. A single cubic equation solver is used to compute the initial curve points lying on the boundary of a surface patch, and the method of resultants as applied to curve theory is used to determine critical points which, in turn, are used to locate initial points that lie on intersection curves which are in the interior of the patch. Examples are given to illustrate the ability of this algorithm to produce all intersection curves.

Book ChapterDOI
01 Jan 1984

Book ChapterDOI
01 Jan 1984
TL;DR: In this article, the authors extended the generalized trigonometric spline interpolation algorithm to generalized cubic splines and showed that the obtained tridiagonal linear system will be strictly diagonally dominant if the partition is sufficiently fine.
Abstract: The algorithm for solving interpolation problems with cubic splines is extended to fourth order generalized trigonometric splines. The attained tridiagonal linear system will be strictly diagonally dominant if the partition is sufficiently fine. If the function to be interpolated is in C2 then the order of the error between this interpolating generalized spline and the cubic spline will be 4. Hence the interpolation error is of fourth order when the given function is in C4. An upper bound for this error is found for a subclass of the generalized trigonometric splines.

01 Jun 1984
TL;DR: A specific approach to this problem is described that is modeled after univariate spline interpolation, which yields visually pleasing surfaces and is therefore suitable for design applications but is less suitable for the approximation of derivatives of a given function.
Abstract: : Many multivariate interpolation schemes require as data values of derivatives that are not available in a practical application, and that therefore have to be generated suitably. A specific approach to this problem is described that is modeled after univariate spline interpolation. Derivative values are defined by the requirement that a certain functional be minimized over a suitable space subject to interpolation of given positional data. In principle, the technique can be applied in arbitrarily many variables. The theory is described in general, and particular applications are given in one and two variables. A major tool in the implementation of the technique is the Bezier-Bernstein form of a multivariate polynomial. The technique yields visually pleasing surfaces and is therefore suitable for design applications. It is less suitable for the approximation of derivatives of a given function. (Author)

Proceedings ArticleDOI
03 Aug 1984
TL;DR: A generalized interactive modeling and graphical display system is being developed to treat 3-D random data and a display mode is being implemented that allows displaying the model using animation techniques to simulate a beating heart.
Abstract: A generalized interactive modeling and graphical display system is being developed to treat 3-D random data. The modeling system generates an estimated surface using either a weighted average of a family of nearest neighbors or a bicubic surface patching technique. From such a model geometric properties can be calculated. Preliminary tests of the method using canine left venticles suggest that volume and surface area can be estimated within 10% of the true values. The modeled surface can be displayed as a wire-frame or shaded solid. The system can interactively display the model frame by frame with or without the original data points. A display mode is being implemented that allows displaying the model using animation techniques to simulate a beating heart.

Journal ArticleDOI
TL;DR: In this paper, the tool path is calculated real-time, during the cutting process, using cubic interpolation of the input of a CNC, a sequence of data points, describing the tool motion necessary for machining free-form curves and surfaces.



Journal ArticleDOI
TL;DR: In this article, a test of the accuracy of the linear interpolation used in the analytical tetrahedron method has been carried out with two different dispersion relations, and it was found that although the interpolation is suitable for spectral functions, it is not reliable for quantitative study of the Fermi wavevectors and Fermian surface cross sections.


22 Oct 1984
TL;DR: BIMOND is a FORTRAN 77 subroutine for piecewise bicubic interpolation to data on a rectangular mesh, which reproduces the monotonicity of the data.
Abstract: BIMOND is a FORTRAN 77 subroutine for piecewise bicubic interpolation to data on a rectangular mesh, which reproduces the monotonicity of the data. A driver program, BIMOND1, is provided which reads data, computes the interpolating surface parameters, and evaluates the function on a mesh suitable for plotting.

01 Mar 1984
TL;DR: In this article, the mathematical quantification of ideas such as physically reasonable and visually pleasing interpolation methods for large-scale scientific computations is examined. And the most primitive EOS interpolation scheme is bilinear interpolation.
Abstract: 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.

Journal ArticleDOI
TL;DR: In this article, algebraic conditions for interpolating piecewise cubic splines over two triangular elements with a common edge are found, and two methods of extending such cubic spline interpolates to arbitrary triangulations are introduced.
Abstract: Algebraic conditions which permit one to interpolate twice continuously differentiable piecewise cubic splines over two triangular elements with a common edge are found. Two methods of extending such cubic spline interpolates to arbitrary triangulations are introduced. Such extensions cannot as we see take place in an arbitrary manner and depend on the particular triangulation under consideration. An advantage to such cubic splines is that one can minimize strain energy in certain controlled directions.


01 Jan 1984
TL;DR: In this paper, it was shown that the number of one-factors in a bicubic graph with 2n vertices is more than polynomial in the total number of vertices.
Abstract: The number of one-factors in a bicubic graph is shown to be more than polynomial in the number of vertices. Thus the permanent of a matrix of O's and l?s in which each row and column includes precisely three l Ts is more than polynomial. This improves the known lower bound of 3n. The form of the bound for a graph with 2n vertices is cn , where c is some constant and a < log2(9/4)=.85... . OTHER

Book ChapterDOI
01 Jan 1984
TL;DR: In this paper, the convergence property of cubic Bessel interpolation is investigated and an exact error evaluation for functions of continuous third derivative when the interpolation points are uniformly spaced is given.
Abstract: The convergence property of cubic Bessel interpolation is investigated and an exact error evaluation for functions of continuous third derivative when the interpolation points are uniformly spaced is given

Book ChapterDOI
01 Jan 1984
TL;DR: In this article, the Hardy spaces of the interpolation spaces for L1 and L∞ are characterized, and a description of constructive solutions of ∂ problems and of Brudnyǐ-Krugljak in the general theory of interpolation is provided.
Abstract: The interpolation spaces for H and H∞ are characterized as the Hardy spaces of the interpolation spaces for L1 and L∞. This description is provided by recent work of Peter Jones on constructive solutions of ∂ problems and of Brudnyǐ — Krugljak in the general theory of interpolation.