Mathematical Techniques in GIS: 2nd Edition (Hardback) book cover

Mathematical Techniques in GIS

2nd Edition

By Peter Dale

CRC Press

359 pages | 142 B/W Illus.

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pub: 2014-05-15
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Description

The second edition of a bestseller, Mathematical Techniques in GIS demystifies the mathematics used in the manipulation of spatially related data. The author takes a step-by-step approach through the basics of arithmetic, algebra, geometry, trigonometry and calculus that underpin the management of such data. He then explores the use of matrices, determinants and vectors in the handling of geographic information so that the data may be analyzed and displayed in two-dimensional form either in the visualization of the terrain or as map projections.

See What’s New in the Second Edition:

  • Summaries at the end of each chapter
  • Worked examples of techniques described
  • Additional material on matrices and vectors
  • Further material on map projections
  • New material on spatial correlation
  • A new section on global positioning systems

Written for those who need to make use geographic information systems but have a limited mathematical background, this book introduces the basic statistical techniques commonly used in geographic information systems and explains best-fit solutions and the mathematics behind satellite positioning. By understanding the mathematics behind the gathering, processing, and display of information, you can better advise others on the integrity of results, the quality of the information, and the safety of using it.

Reviews

"The insight provided by this book is extremely valuable. It represents a significant effort to explain - in an interesting and pedagogical way - the basic mathematical techniques and principles underpinning the manipulation of geographical data. Modern technologies have made the "where" highly important, and computers and mobile devices provide all kind of sophisticated solutions to dealing with this issue. However, it is worth remembering that eventually only good data and good processing will provide reliable information. The mathematics behind this processing thereby becomes essential. This book enables an easy access to the rules and manipulations applied behind the scene. This book is needed."

––Stig Enemark, professor of land management, Department of Development and Planning, Aalborg University, Denmark

"… an excellent introduction to the mathematics behind these complexities. By having some understanding of the technology behind GIS users are better able to ensure the data and results from GIS are "fit for purpose" and can be safely used. … I enthusiastically encourage GIS users to read this book."

—Ian P. Williamson, Emeritus Professor, The University of Melbourne

"Professor Peter Dale is one of the great pioneers of the GIS and geomatics fields, having made seminal contributions to the development and application of the technology in support of natural resource management and land administration. His writing is richly informed by both a deep intellect and a wealth of experience."

—John McLaughlin, President Emeritus, University of New Brunswick

"…this text is an effective tool for teaching fundamental quantitative methods to its intended audience." —Photogrammetric Engineering & Remote Sensing, November 2016

Table of Contents

Characteristics of Geographic Information

Geographic Information and Data

Categories of Data

Summary

Numbers and Numerical Analysis

The Rules of Arithmetic

The Binary System

Square Roots

Indices and Logarithms

Summary

Algebra: Treating Numbers as Symbols

The Theorem of Pythagoras

The Equations for Intersecting Lines

Points in Polygons

The Equation for a Plane

Further Algebraic Equations

Functions and Graphs

Interpolating Intermediate Values

Summary

The Geometry of Common Shapes

Triangles and Circles

Areas of Triangles

Centers of a Triangle

Polygons

The Sphere and the Ellipse

Sections of a Cone

Summary

Plane and Spherical Trigonometry

Basic Trigonometric Functions

Obtuse Angles

Combined Angles

Bearings and Distances

Angles on a Sphere

Summary

Differential and Integral Calculus

Differentiation

Differentiating Trigonometric Functions

Polynomial Functions

Linearization

Basic Integration

Areas and Volumes

Summary

Matrices and Determinants

Basic Matrix Operations

Determinants

Related Matrices

Applying Matrices

Rotations and Translations

Simplifying Matrices

Summary

Vectors

The Nature of Vectors

Dot and Cross Products

Vectors and Planes

Angles of Incidence

Vectors and Rotations

Summary

Curves and Surfaces

Parametric Forms

The Ellipse

The Radius of Curvature

Fitting Curves to Points

The Bezier Curve

B-Splines

Summary

2D/3D Transformations

Homogeneous Coordinates

Rotating an Object

Hidden Lines and Surfaces

Photogrammetric Measurements

Summary

Map Projections

Map Projections

Cylindrical Projections

Azimuthal Projections

Conical Projections

Summary

Basic Statistics

Probabilities

Measures of Central Tendency

The Normal Distribution

Levels of Significance

The T-Test

Analysis of Variance

The Chi-Squared Test

The Poisson Distribution

Summary

Correlation and Regression

Correlation

Regression

Weights

Spatial Autocorrelation

Summary

Best-Fit Solutions

Least Square Solutions

Survey Adjustments

Satellite Position Fixing

Summary

Further Reading

Index

About the Author

Peter Dale is a professor in land information management at the University College London.

Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
TEC010000
TECHNOLOGY & ENGINEERING / Environmental / General
TEC036000
TECHNOLOGY & ENGINEERING / Remote Sensing & Geographic Information Systems