Map Projections Theory and Applications 1st edition by Frederick Pearson 1351433693 9781351433693

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ISBN-10 :  1351433693 

ISBN-13 :  9781351433693

Author:   Frederick Pearson 

About the Author: Frederick Pearson has extensive experience in teaching map projection at the Air Force Cartography School and Virginia Polytechnic Institute. He developed star charts, satellite trajectory programs, and a celestial navigation device for the Aeronautical Chart and Information Center. He is an expert in orbital analysis of satellites, and control and guidance systems. At McDonnell-Douglas, he worked on the guidance system for the space shuttle.This text develops the plotting equations for the major map projections. The emphasis is on obtaining usable algorithms for computed aided plotting and CRT display. The problem of map projection is stated, and the basic terminology is introduced. The required fundamental mathematics is reviewed, and transformation theory is developed. Theories from differential geometry are particularized for the transformation from a sphere or spheroid as the model of the earth onto a selected plotting surface. The most current parameters to describe the figure of the earth are given. Formulas are included to calculate meridian length, parallel length, geodetic and geocentric latitude, azimuth, and distances on the sphere or spheroid. Equal area, conformal, and conventional projection transformations are derived. All result in direct transformation from geographic to cartesian coordinates. For selected projections, inverse transformations from cartesian to geographic coordinates are given. Since the avoidance of distortion is important, the theory of distortion is explored. Formulas are developed to give a quantitative estimate of linear, area, and angular distortions. Extended examples are given for several mapping problems of interest. Computer applications, and efficient algorithms are presented. This book is an appropriate text for a course in the mathematical aspects of mapping and cartography. Map projections are of interest to workers in many fields. Some of these are mathematicians, engineers, surveyors, geodi

Map Projections: Theory and Applications 1st Table of contents:

1. Introduction
I. Introduction to the Problem
II. Basic Geometric Shapes
III. Distortion
IV. Scale
A. Example 1
B. Example 2
V. Feature Preserved in Projection
VI. Projection Surface
VII. Orientation of the Azimuthal Plane
VIII. Orientation of a Cone or Cylinder
IX. Tangency and Secancy
X. Projection Techniques
XI. Plotting Equations
XII. Plotting Tables
References
2. Mathematical Fundamentals
I. Introduction
II. Coordinate Systems and Azimuth
III. Grid Systems
IV. Differential Geometry of Space Curves
A. Example 1
B. Example 2
V. Differential Geometry of a General Surface
VI. First Fundamental Form
A. Example 3
B. Example 4
C. Example 5
D. Example 6
E. Example 7
VII. Second Fundamental Form
VIII. Surfaces of Revolution
IX. Developable Surfaces
X. Transformation Matrices
A. Example 8
XI. Mathematical Definition of Equality of Area and Conformality
XII. Rotation of Coordinate System
XIII. Convergency of the Meridians
A. Example 9
XIV. Constant of the Cone and Slant Height
A. Example 10
B. Example 11
References
3. Figure of the Earth
I. Introduction
II. Geodetic Considerations
A. Example 1
III. Geometry of the Ellipse
A. Example 2
IV. The Spheroid as a Model of the Earth
A. Example 3
B. Example 4
C. Example 5
V. The Spherical Model of the Earth
A. Example 6
B. Example 7
C. Example 8
D. Example 9
E. Example 10
F. Example 11
VI. The Triaxial Ellipsoid
References
4. Equal Area Projections
I. Introduction
II. General Procedure
III. The Authalic Sphere
A. Example 1
B. Example 2
IV. Albers, One Standard Parallel
A. Example 3
B. Example 4
V. Albers, Two Standard Parallels
A. Example 5
VI. Bonne
A. Example 6
VII. Azimuthal
A. Example 7
VIII. Cylindrical
A. Example 8
B. Example 9
IX. Sinusoidal
A. Example 10
B. Example 11
X. Mollweide
A. Example 12
B. Example 13
XI. Parabolic
A. Example 14
B. Example 15
XII. Hammer-Aitoff
A. Example 16
XIII. Boggs Eumorphic
XIV. Eckert IV
XV. Interrupted Projections
A. Example 17
References
5. Conformal Projections
I. Introduction
II. General Procedures
III. Conformal Sphere
A. Example 1
IV. Lambert Conformal, One Standard Parallel
A. Example 2
V. Lambert Conformal, Two Standard Parallels
VI. Stereographic
A. Example 3
B. Example 4
VII. Mercator
A. Example 5
B. Example 6
C. Example 7
D. Example 8
E. Example 9
VIII. State Plane Coordinates
IX. Military Grid Systems
A. Example 10
References
6. Conventional Projections
I. Introduction
II. Summary of Procedures
III. Gnomonic
A. Example 1
B. Example 2
C. Example 3
IV. Azimuthal Equidistant
A. Example 4
B. Example 5
V. Orthographic
A. Example 6
B. Example 7
C. Example 8
VI. Simple Conic, One Standard Parallel
VII. Simple Conical, Two Standard Parallels
VIII. Conical Perspective
IX. Polyconic
A. Example 9
X. Perspective Cylindrical
A. Example 10
XI. Plate Carree
A. Example 11
XII. Carte Parallelogrammatique
A. Example 12
XIII. Miller
A. Example 13
XIV. Globular
XV. Aerial Perspective
A. Example 14
XVI. Van der Grinten
XVII. Cassini
A. Example 15
XVIII. Robinson
A. Example 16
References
7. Theory of Distortions
I. Introduction
II. Qualitative View of Distortion
III. Quantization of Distortions
IV. Distortions from Euclidian Geometry
V. Distortions from Differential Geometry
VI. Distortions in Equal Area Projections
A. Distortions in Length in the Albers Projection with One Standard Parallel
B. Distortions in Length in the Albers Projection with Two Standard Parallels
C. Distortion in Length in the Azimuthal Projection
D. Distortion in Length in the Cylindrical Projection
E. Distortion in Angle in Equal Area Projections
F. Example 1
G. Example 2
H. Example 3
VII. Distortion in Conformal Projections
A. Distortion in Length for the Lambert Conformal Projection, One Standard Parallel
B. Distortion in Length for the Lambert Conformal Projection, Two Standard Parallels
C. Distortion in Length for the Polar Stereographic Projections
D. Distortion in Length for the Regular Mercator Projection
E. Distortions in Area and Angle
F. Example 4
G. Example 5
H. Example 6
VIII. Distortion in Conventional Projections
A. Distortions in Length for the Polar Gnomonic Projection
B. Distortion in Length for the Polar Azimuthal Equidistant Projection
C. Distortion in Length for the Polyconic Projection
D. Distortions in Angle and Area
E. Example 7
F. Example 8
References
8. Mapping Applications
I. Introduction
II. Map Projections in the Southern Hemisphere
A. Example 1
B. Example 2
C. Example 3
III. Distortion in the Transformation from the Spheroid to the Authalic Sphere
IV. Distances on the Loxodrome
V. Tracking System Displays
VI. Differential Distances from a Position
References
9. Computer Applications
I. Introduction
II. Direct Transformation Subroutines
III. Inverse Transformation Subroutines
IV. Calling Program for Subroutines
V. State Plane Coordinates
VI. UTM Grids
VII. Computer Graphics
References
10. Uses of Map Projections
I. Introduction
II. Fidelity to Features on the Earth
III. Characteristics of Parallels and Meridians
IV. Considerations in the Choice of a Projection
V. Recommended Areas of Coverage
VI. Recommended Set of Map Projections
VII. Conclusion

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