Journal ArticleDOI
Multiquadric equations of topography and other irregular surfaces
TLDR
In this paper, a method of representing irregular surfaces that involves the summation of equations of quadric surfaces having unknown coefficients is described, and procedures are given for solving multiquadric equations of topography that are based on coordinate data.Abstract:
A new analytical method of representing irregular surfaces that involves the summation of equations of quadric surfaces having unknown coefficients is described. The quadric surfaces are located at significant points throughout the region to be mapped. Procedures are given for solving multiquadric equations of topography that are based on coordinate data. Contoured multiquadric surfaces are compared with topography and other irregular surfaces from which the multiquadric equation was derived.read more
Citations
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Networks for approximation and learning
Tomaso Poggio,Federico Girosi +1 more
TL;DR: Regularization networks are mathematically related to the radial basis functions, mainly used for strict interpolation tasks as mentioned in this paper, and two extensions of the regularization approach are presented, along with the approach's corrections to splines, regularization, Bayes formulation, and clustering.
Journal ArticleDOI
Scattered data interpolation: tests of some methods
TL;DR: In this paper, the evaluation of methods for scattered data interpolation and some of the results of the tests when applied to a number of methods are presented. But the evaluation process involves evaluation of the methods in terms of timing, storage, accuracy, visual pleasantness of the surface, and ease of implementation.
Journal ArticleDOI
Multiquadrics--a scattered data approximation scheme with applications to computational fluid-dynamics-- ii solutions to parabolic, hyperbolic and elliptic partial differential equations
TL;DR: In this paper, the authors used MQ as the spatial approximation scheme for parabolic, hyperbolic and the elliptic Poisson's equation, and showed that MQ is not only exceptionally accurate, but is more efficient than finite difference schemes which require many more operations to achieve the same degree of accuracy.
Approximation scheme with applications to computational fluid-dynamics-- i surface approximations and partial derivative estimates
TL;DR: In this article, the authors presented an enhanced multiquadrics (MQ) scheme for spatial approximations, which is a true scattered data, grid free scheme for representing surfaces and bodies in an arbitrary number of dimensions.
Journal ArticleDOI
Multiquadrics—A scattered data approximation scheme with applications to computational fluid-dynamics—I surface approximations and partial derivative estimates
TL;DR: In this article, the authors presented a powerful, enhanced multiquadrics (MQ) scheme developed for spatial approximations, which is a true scattered data, grid free scheme for representing surfaces and bodies in an arbitrary number of dimensions.
References
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Journal ArticleDOI
A spherical harmonic analysis of the Earth's topography
TL;DR: In this paper, the percentage of land, average land elevation, and average ocean depth in each 1° × 1° square and of percentages of lake and ice and average lake depth and ice thickness in each 5° × 5° square were estimated.
Journal ArticleDOI
Quantitative comparison of contour maps
Daniel F. Merriam,P.H.A. Sneath +1 more
TL;DR: Maps can be quantitatively compared by using trend-surface analysis to simplify complex situations and then studying the components by using equation coefficients of well-fitted first, second, and third-degree trend surfaces to determine similarity between any pair of maps.
Journal ArticleDOI
Statistical and geological implications of trend mapping with nonorthogonal polynomials
TL;DR: In this article, a polynomial function of order p is used to approximate a trend surface of a variable y in an area with coordinates u, v. The determination of the coefficients of the approximating poynomial requires the solution of p simultaneous "normal" equations.