Introduction to Mathematical Techniques Used in GIS / Edition 1

by Peter Dale

Overview

To understand the output from a geographic information system, one must understand the quality of the data that is entered into the system, the algorithms driving the data processing, and the limitations of the graphic displays.

Introduction to Mathematical Techniques Used in GIS explains to nonmathematicians the fundamentals that support the manipulation and display of geographic information. It focuses on basic mathematical techniques, building upon a series of steps that enable a deeper understanding of the complex forms of manipulation that arise in the handling of spatially related data.

The book moves rapidly through a wide range of data transformations, outlining the techniques involved. Many are precise, building logically on underlying assumptions. Others are based upon statistical analysis and the pursuit of the optimum rather than the perfect and definite solution.

By understanding the mathematics behind the gathering, processing, and display of information, GIS professionals can advise others on the integrity of results, the quality of the information, and the safety of using it.

Product Details

ISBN-13:	9780415334143
Publisher:	Taylor & Francis
Publication date:	10/28/2004
Edition description:	Older Edition
Pages:	220
Product dimensions:	6.12(w) x 9.25(h) x 0.70(d)

Table of Contents

CHARACTERISTICS OF GEOGRAPHIC INFORMATION
Geographic Information and Data
Categories of Data
Spatial Referencing
Lines and Shapes

NUMBERS AND NUMERICAL ANALYSIS
The Rules of Arithmetic
The Binary System
Square Roots
Indices and Logarithms

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

THE GEOMETRY OF COMMON SHAPES
Triangles and Circles
Areas of Triangles
Centres of a Triangle
Polygons
The Sphere and the Ellipse
Sections of a Cone

PLANE AND SPHERICAL TRIGONOMETRY
Basic Trigonometric Functions
Obtuse Angles
Combined Angles
Bearings and Distances
Angles on a Sphere

DIFFERENTIAL AND INTEGRAL CALCULUS
The Basis of Differentiation
Differentiating Trigonometric Functions
Polynomial Functions
Basic Integration
Areas and Volumes

MATRICES, DETERMINANTS AND VECTORS
Basic Matrix Operations
Determinants
Related Matrices
Applying Matrices
Rotations and Translations
Simplifying Matrices
Vectors

CURVES AND SURFACES
Parametric Forms
The Ellipse
The Radius of Curvature
Fitting Curves to Points
The Bezier Curve

TRANSFORMATIONS
Homogeneous Coordinates
Rotating an Object
Hidden Lines and Surfaces
Map Projections
Cylindrical Projections
Azimuthal Projections
Conical Projections

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

BEST-FIT SOLUTIONS
Correlation
Regression
Weights
Linearization
Least Square Solutions