Showing papers on "Bicubic interpolation published in 1980"
TL;DR: In this article, a monotone piecewise bicubic interpolation algorithm was proposed for data on a rectangular mesh, where the first partial derivatives and first mixed partial derivatives are determined by the mesh points.
Abstract: In a 1980 paper [SIAM J. Numer. Anal., 17 (1980), pp. 238–246] the authors developed a univariate piecewise cubic interpolation algorithm which produces a monotone interpolant to monotone data. This paper is an extension of those results to monotone $\mathcal{C}^1 $ piecewise bicubic interpolation to data on a rectangular mesh. Such an interpolant is determined by the first partial derivatives and first mixed partial (twist) at the mesh points. Necessary and sufficient conditions on these derivatives are derived such that the resulting bicubic polynomial is monotone on a single rectangular element. These conditions are then simplified to a set of sufficient conditions for monotonicity. The latter are translated to a system of linear inequalities, which form the basis for a monotone piecewise bicubic interpolation algorithm.
2,174 citations
TL;DR: In this article, a computational scheme for determining global geometric properties of solid object models is presented, which operates directly on the boundary representation of the model and is tested on a number of models produced by an experimental modelling system.
Abstract: A computational scheme for determining global geometric properties of solid object models is presented. The method operates directly on the boundary representation of the model. The scheme is tested on a number of models produced by an experimental modelling system. Primitive objects combined for the tests are all represented in terms of parametric bicubic patches.
54 citations
TL;DR: The theoretical basis for constructing the map is shown to be mathematically sound and the resulting programs modules have proved highly successful in constructing thousands of maps rapidly, reliably, and accurately.
27 citations
TL;DR: Methods for preparation of three dimensional information for isoline mapping are described based on Fourier, Chebyshev, and cubic interpolation from regularly spaced arrays of spatial data.
17 citations
TL;DR: In this article, an algorithm which combines the accuracy of linear interpolation and the speed of nearest neighbour interpolation is developed and applied to computed axial tomography by way of illustration.
Abstract: Simple linear interpolation requires numerical multiplication which is time-consuming when a large number of interpolated data points is required. In practice, nearest neighbour interpolation is often employed, even though it is appreciably less accurate. An algorithm which combines the accuracy of linear interpolation and the speed of nearest neighbour interpolation is developed and applied to computed axial tomography by way of illustration.
13 citations
TL;DR: In this paper, a class of end conditions for cubic spline interpolation at unequally spaced knots is derived, which lead to 0 (h 4 ) convergence uniformly on the interval of interpolation.
11 citations
TL;DR: In this paper, a uniform, space-filling array of tetrahedra whose vertices form a body-centered cubic grid is described, and an economical scheme is described for using FFT's to link discrete spectra with records over a tetrahedral mesh.
Abstract: A uniform, space-filling array of tetrahedra is described whose vertices form a body-centered cubic grid. The symmetries of this system make it, in a sense, more isotropic than alternatives. Linear finite elements over this array result in a 9-point Laplace operator. Their use for interpolation of spectral data is studied, and the best mean-square fit to any harmonic is obtained; RMS errors are calculated. Aliassing limits are determined: this occurs outside a rhombic dodecahedron in wave-number space. An economical scheme is described for using FFT's to link discrete spectra with records over a tetrahedral mesh. Finally, the logic of tetrahedral indexing and the evaluation of the weights for interpolation are merged into one compact algorithm.
6 citations
TL;DR: A simple method of circumventing the problem of acute problem of computer storage space by optimizing the use of computer central memory and disk space is presented.
5 citations
2 citations
01 Jan 1980
TL;DR: A recursive two-dimensional vector processor is introduced as an approximation to the nonrecursive constrained least-squares estimation of smoothed estimates of function values, particularly their derivatives, from a finite set of inaccurate measurements.
Abstract: The problem of obtaining smoothed estimates of function values, particularly their derivatives, from a finite set of inaccurate measurements is considered. A recursive two-dimensional vector processor is introduced as an approximation to the nonrecursive constrained least-squares estimation. Here, piecewise bicubic Hermite polynomials are extensively used as approximating functions, and the smoothing integral is converted to a discrete quadratic form. This makes it possible to convert the problem of fitting an approximating function to one of estimating the function values and derivatives at the nodes.