Features
Builds a sufficient understanding of some of the main mathematical procedures encountered in GIS
Explains the most common symbols and operations for readers with no or very little knowledge of mathematics
Contains updated coverage of core concepts and new topics, like vectors
Presents the information in an updated format,with a page summary at the end of each chapter
Provides a foundation for a greater understanding of the mathematics that underpin spatial operations
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.
Author(s): Peter Dale
Edition: 2
Publisher: CRC Press
Year: 2014
Language: English
Pages: C,XXVII,317,B
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
