Showing papers on "Bicubic interpolation published in 1976"

General Properties of Interpolation Spaces

Abstract: In this chapter we introduce some basic notation and definitions. We discuss a few general results on interpolation spaces. The most important one is the Aronszajn-Gagliardo theorem.

Bicubic spline smoothing of two-dimensional geophysical data

Abstract: A computational method for fitting smoothed bicubic splines to data given in a regular rectangular grid is suggested. The one-dimensional spline fit has well defined smoothness properties. These are duplicated for a two-dimensional approximation by solving the corresponding variational problem. The complete algorithm for computing the functional values and its derivatives at arbitrary points is presented. The posibilities of the method are demonstrated on an example from geomagnetic surveys.

Cubic splines with infinite derivatives at some knots

Abstract: A generalization of cubic spline interpolation with vertical slopes at some knots is proposed An existence theorem including an algorithm for constructing such generalized splines is proved The resulting splines are obtained in closed form and they are partition invariant

Modifications and alternatives to the cubic interpolation process for one-dimensional search

Abstract: : In this paper, the numerical solution of the problem of minimizing a unimodal function f(alpha) is considered, where alpha is a scalar. Two modifications of the cubic interpolation process are presented, so as to improve the robustness of the method and force the process to converge in a reasonable number of iterations. An alternative to the cubic interpolation process is also presented. This is a Lagrange interpolation scheme in which the quadratic approximation to the derivative of the function is considered. The coefficients of the quadratic are determined from the values of the slope at three points: alpha sub 1, alpha sub 2, and alpha sub 3 = (alpha sub 1 + alpha sub 2)/2, where alpha sub 1 and alpha sub 2 are the endpoints of the interval of interpolation.

Nearest neighbor, bilinear interpolation and bicubic interpolation geographic correction effects on LANDSAT imagery

Abstract: 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.

Piecewise Cubic Hermite Interpolation at the Gaussian Points

Abstract: An interpolation scheme based on piecewise cubic polynomials with the Gaussian points as interpolation points is analyzed. Optimal order a priori estimates are obtained for the interpolation error in the maximum norm.

Bicubic patch surfaces for high-speed numerical control processing

Abstract: Parametric bicubic patch surfaces have been used for some time in manufacture and design. It is convenient to have such surfaces available as standard numerical control surfaces using the APT programming language. A major drawback is that they are costly to use for data processing of numerical control programs. If, however, nonparametric bicubics are used, computer time, and hence cost, can be reduced dramatically. This paper details a strategy and algorithms for this purpose. Experimental data suggest that computer costs are comparable to, or somewhat lower than, the costs for processing tabulated cylinder surfaces.