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Geography and the Properties of Surfaces. A Two-Dimensional Interpolation Function for Computer Mapping of Irregularly Spaced Data

Geography and the Properties of Surfaces. A Two-Dimensional Interpolation Function for Computer Mapping of Irregularly Spaced Data
Author: Donald Shepard
Publisher:
Total Pages: 21
Release: 1968
Genre:
ISBN:

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Techniques of interpolating from irregularly spaced known function values in two dimensions are discussed. First, a function defined as a weighted average of the given function values, with the weighting based on the inverse distance from the corresponding points, is explored. To shorten computation and improve the quality of interpolation, additional terms based on distances, directions and slopes are added. An interpolation function everywhere continuously differentiable and fitting the data exactly is finally presented. A provision for barriers to interpolation is described for applications in geographical analysis. The interpolation function has been incorporated into a computer mapping program in FORTRAN called SYMAP (Versions IV and V). (Author).


NASA Reference Publication

NASA Reference Publication
Author:
Publisher:
Total Pages: 396
Release: 1978
Genre: Astronautics
ISBN:

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Analytic Mapping and Geographic Databases

Analytic Mapping and Geographic Databases
Author: G. David Garson
Publisher: SAGE
Total Pages: 100
Release: 1992-06-11
Genre: Reference
ISBN: 9780803947528

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The techniques of analytic mapping and of geographic information systems (GIS) have become increasingly important tools for analysing census, crime, environmental and consumer data. The authors discuss data access, transformation and preparation issues, and how to select the appropriate analytic graphics techniques.


Geometric Modelling

Geometric Modelling
Author: G. Brunnett
Publisher: Springer Science & Business Media
Total Pages: 357
Release: 2012-12-06
Genre: Computers
ISBN: 370916270X

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Geometric Modelling is concerned with the computer aided design, manipulation, storage and transmission of geometric shape. It provides fundamental techniques to different areas of application as CAD/CAM, computer graphics, scientific visualization, and virtual Reality. 20 papers presented by leading experts give a state-of-the-art survey of the following topics: surface design and fairing; multiresolution models; reverse engineering; solid modelling; constrained based modelling.


Approximation Theory, Wavelets and Applications

Approximation Theory, Wavelets and Applications
Author: S.P. Singh
Publisher: Springer Science & Business Media
Total Pages: 580
Release: 2013-03-09
Genre: Mathematics
ISBN: 9401585776

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Approximation Theory, Wavelets and Applications draws together the latest developments in the subject, provides directions for future research, and paves the way for collaborative research. The main topics covered include constructive multivariate approximation, theory of splines, spline wavelets, polynomial and trigonometric wavelets, interpolation theory, polynomial and rational approximation. Among the scientific applications were de-noising using wavelets, including the de-noising of speech and images, and signal and digital image processing. In the area of the approximation of functions the main topics include multivariate interpolation, quasi-interpolation, polynomial approximation with weights, knot removal for scattered data, convergence theorems in Padé theory, Lyapunov theory in approximation, Neville elimination as applied to shape preserving presentation of curves, interpolating positive linear operators, interpolation from a convex subset of Hilbert space, and interpolation on the triangle and simplex. Wavelet theory is growing extremely rapidly and has applications which will interest readers in the physical, medical, engineering and social sciences.


Spatial Statistics and Models

Spatial Statistics and Models
Author: G.L. Gaile
Publisher: Springer Science & Business Media
Total Pages: 480
Release: 2013-11-27
Genre: Social Science
ISBN: 9401730482

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The quantitative revolution in geography has passed. The spirited debates of the past decades have, in one sense, been resolved by the inclusion of quantitative techniques into the typical geographer's set of methodological tools. A new decade is upon us. Throughout the quantitative revolution, geographers ransacked related disciplines and mathematics in order to find tools which might be applicable to problems of a spatial nature. The early success of Berry and Marble's Spatial Analysis and Garrison and Marble's volumes on Quantitative Geog raphy is testimony to their accomplished search. New developments often depend heavily on borrowed ideas. It is only after these developments have been established that the necessary groundwork for true innovation ob tains. In the last decade, geographers significantly -augmented their methodologi cal base by developing quantitative techniques which are specifically directed towards analysis of explicitly spatial problems. It should be pointed out, however, that the explicit incorporation of space into quantitative techniques has not been the sole domain of geographers. Mathematicians, geologists, meteorologists, economists, and regional scientists have shared the geo grapher's interest in the spatial component of their analytical tools.