Map Projection Transformation: Principles and Applications

by Snyder; John K.

• ISBN13: 9780748406685
• ISBN10: 0748406689
• Edition: 1st
• Format: Nonspecific Binding
• Copyright: 1999-12-16
• Publisher: CRC Press

Summary

With the advance of science and technology, there have been breakthroughs in the field of classical research and methods of map projection. Among these, computer science and space science have had the greater influence upon the field of research and the formation of a working body of map projection, developing them in breadth and depth. This book reflects several aspects of the development of modern mathematical cartography, especially the theory and methods of map projection transformation. Map projection transformation is an area of research in mathematical cartography newly developed over the last 25 years. It is widely used in surveying and computer-assisted cartography, data processing for information systems, and the transformation of data from space, remote sensing, and other space sciences. The development of map projection transformation not only expands new areas of research on mathematical cartography, but it also further develops the applied area with the creation and application of map projection transformation software and mapping mathematics bases on the computer.

Author Biography

Professor Oihe Yang is a doctoral tutor in the Department of Cartography of the Zhengzhou Institute of Surveying and Mapping. He is known for his great achievements in the fields of map projection, map projection transformation, spatial information positioning systems and map pattern recognition. He is the author of over 100 scientific papers and seven books. The late John P. Snyder retired from the U.S. Geological Survey, Reston, Virginia, and was a past president of the American Cartographic Association. He was the author of numerous papers and seven books about map projections Waldo R. Tobler is an emeritus professor at the University of California, Santa Barbara.

Table of Contents

Symbols	ix
Preface	xiii
Introduction	1	(4)
Fifty Years' Advancement of Map Projection Study in China	5	(8)
Basic mathematics for topographic maps and for atlases	5	(1)
General theory of map projection	6	(1)
Exploration of new types of map projection	7	(1)
Selection of map projection and its application	8	(1)
Theory and application of map projection transformation	9	(1)
Continuous development of new research and applications to the field of map projection	10	(3)
Map Projection Equations	13	(40)
Earth ellipsoid and sphere	13	(3)
Azimuthal projections	16	(5)
Cylindrical projections	21	(7)
Conic projections	28	(4)
Pseudoazimuthal projections	32	(1)
Pseudocylindrical projections	33	(3)
Pseudoconical projections	36	(1)
Polyconical projections	37	(4)
Other types of projections	41	(7)
Projection from the ellipsoid to the sphere	48	(1)
Space map projection	49	(1)
Chinese topographic maps	50	(3)
General Theory of Map Projection Transformation	53	(58)
Research objectives and basic methods	53	(3)
Equations for map projection transformation	56	(5)
Plane feature transformation	61	(10)
Coordinate systems on the surfaces of the ellipsoid and sphere	71	(8)
Three kinds of latitude functions q, S, F on the surface of the ellipsoid	79	(7)
Inverse transformation of q, S, F -- iteration method	86	(1)
Inverse transformation of q, S, F -- trigonometric series method with constant coefficients	87	(5)
Inverse transformation of q, S, F -- Taylor series method with varied coefficients	92	(7)
Inverse transformation of q, S, F -- numerical methods	99	(2)
Transformation formulae among six kinds of latitudes	101	(6)
Commonly used power series in map projection transformation	107	(4)
Analytical Transformation	111	(38)
Azimuthal projection	111	(7)
Cylindrical projection	118	(3)
Conic projection	121	(6)
Transformation among azimuthal, cylindrical and conic projections	127	(6)
Pseudoazimuthal, pseudocylindrical and pseudoconic projections	133	(4)
Polyconic projection	137	(7)
Double projection	144	(5)
Analytical Transformation for Conformal Projection	149	(32)
General model for conformal projection transformation	149	(8)
Direct transformation between two conformal projections	157	(15)
Direct transformation of conformal projections	172	(1)
Inverse transformation of conformal projections	173	(2)
Conformal oblique cylindrical and oblique conic projections	175	(6)
Numerical Transformation	181	(24)
General polynomial approximations	181	(6)
Refining parallels and meridians	187	(7)
Orthogonal polynomial approximation	194	(5)
Accuracy considerations in numerical transformation	199	(6)
Numerical Transformation for Conformal Projection	205	(24)
Conformal polynomial approximation	205	(6)
Interpolation	211	(3)
Difference method	214	(4)
Finite element method	218	(11)
The Third Type of Coordinate Transformation	229	(16)
Principle and applications	229	(6)
Transverse Mercator (or Gauss--Kruger) projection	235	(2)
Conformal projections	237	(3)
Linear interpolation	240	(1)
Spherical coordinates	241	(4)
Zone Transformation for the Transverse Mercator (Gauss--Kruger) Projection	245	(18)
The general method	245	(1)
Indirect transformation	246	(1)
Direct transformation	247	(7)
Plane coordinate network transformation between adjacent zones	254	(3)
Application of double projection	257	(6)
New Map Projections	263	(8)
Affine transformation of equal-area projections and seeking of modified equal-area projections (Yang 1992)	263	(4)
Linear transformation of the gnomonic projection and seeking the double-azimuthal projection (Yang 1990b)	267	(4)
Variable-scale Map Projections	271	(16)
Variable-scale projections	271	(7)
Composite projections	278	(9)
Position Lines	287	(22)
Types of position lines and their projection	287	(13)
Determining the position of a target	300	(9)
Spatial Information Positioning Systems	309	(54)
Introduction	309	(1)
Mapping and image positioning system	310	(1)
Registration model (map projection system)	311	(2)
Data processing of a digital map	313	(5)
Automatically setting up map mathematical foundation	318	(7)
Appendices
Appendix 1 Inverse Transformation of Algebraic Series	325	(4)
Appendix 2 Constant Coefficient Tables of Zone Transformation for the Gauss--Kruger Projection	329	(4)
Appendix 3 Examples of Numerical Transformation	333	(12)
Appendix 4 Transformation for the Mathematical Elements of Topographic Maps	345	(4)
Appendix 5 The Position Line and Position Navigation Software System	349	(4)
Appendix 6 Bibliography of Chinese Literature on Map Projections and Other References	353	(10)
Index	363