Cartographic Science: A Compendium of Map Projections, with DerivationsGeographic books routinely introduce map projections without providing mathematical explanations of projections and few delve into complex mathematical development or cover the breadth of projections. From basic projecting to advanced transformations, Cartographic Science: A Compendium of Map Projections, with Derivations is a comprehensive reference that offers an explanation of the science of cartography. The book is a compilation of more than a hundred map projections, from classic conics to contemporary transformations using complex variables. Starting from widely described geometric projecting onto flat paper, cylinder, and cone and then progressing through several layers of mathematics to reach modern projections, the author maximizes the application of one layer of complex mathematics before continuing on to the next. He also supplies numerous one-page tutorials that review terms and methodologies, helping minimize the challenges of unfamiliar mathematical territory. Divided into four parts, the first section examines the shape and size of the Earth, then proceeds to investigate the means for relating the curved surface to a flat surface, and addresses scaling. It goes on to cover pertinent principles of projection including literal projecting, true but synthetic projections, secantal projections, pseudocylindrical projections, and pseudoconical projections, as well as the other variants of more serious projections. The book concludes by looking at factors influencing Mean Sea Level and notes the cartographic aspects of current developments. Cartographic Science: A Compendium of Map Projections, with Derivations explains the mathematical development for a large range of projections within a framework of the different cartographic methodologies. This carefully paced book covers more projections, with gentle and progressive immersion in the mathematics involved, than any other book of its kind. |
Contents
THE CURVED WORLD | 1 |
Tutorial number and title | 2 |
Curved Earth to flat map | 3 |
Vectors | 12 |
The transcendental number | 19 |
A globe as model and intermediary | 25 |
within Chapter 1 | 26 |
Sines cosines etc generalized | 36 |
Extension by arithmetic tricks | 239 |
Twopoint and nonazimuthal Azimuthals | 261 |
Partial differentiation | 276 |
Differential geometry | 277 |
Hyperbolic functions | 288 |
Of scales and distortion | 293 |
The ellipse and associated circles | 305 |
Functions of a complex variable | 322 |
A SPHERICAL WORLD | 37 |
Literal projections | 39 |
Mensuration formulae | 64 |
Equidistant and other algebraic variants | 65 |
Integration | 77 |
40 | 83 |
64 | 93 |
Circularcurve fitting | 100 |
Secantal projections | 101 |
Functions and their roots | 124 |
Pseudo projections | 125 |
Interrupted and composite maps | 167 |
Sphericaltriangle formulae | 186 |
At oblique aspect | 187 |
Matrix notation | 200 |
Computing surface distance 2 | 214 |
Globular projections | 221 |
Matrix multiplication | 238 |
Optimizing distortion | 323 |
More conformal projections | 347 |
Isometricgeodetic relationships | 352 |
Novelty projections | 363 |
Infinite series | 376 |
AN ELLIPSOIDAL WORLD | 377 |
Ellipses and ellipsoids | 379 |
UTM and UPS | 411 |
THE REAL WORLD | 431 |
The geoid and geodesy | 433 |
APPENDICES | 447 |
A Greek letters and words | 448 |
B Glossary of symbols | 450 |
Glossary of terms | 456 |
Index to projections | 460 |
E Historical bibliography | 469 |
| 487 | |
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Cartographic Science: A Compendium of Map Projections, with Derivations Donald Fenna No preview available - 2019 |
Common terms and phrases
3-dimensional angle applied authalic auxiliary axes axis Azimuthal Azimuthal projection cartographic central meridian centre Chapter circle circular arcs co-ordinates cone conformal map conformal projections Conical projection cos² curved Cylindrical projection defined derived developable surface developed differential distance distortion Earth ellipse ellipsoid Exhibit flat-polar formulae function geometry gives globe graticule Grinten hemisphere hence identical illustrated intermediate parameters intersection Lambert length linear longitude longitude and latitude loxodrome map projections mathematical Mercator Mollweide multiplier Obliq Oblique aspect orthogonal Orthographic P₁ plane Plate-Carrée plotting equations polar Polyconic Polyconic projection projection at Simple Pseudocylindricals Putnins radial radians radius Rcos relative secantal Simple aspect sin po sin² sino Sinusoidal Sinusoidal projection spacing of parallels sphere spherical standard parallels Stereographic Stereographic projection straight lines surface tangential transformation Transverse true scale Tutorial variable vector zero аф ба баг даг ду дх
Popular passages
Page 479 - Elements of Map Projection, with Applications to Map and Chart Con-struction.— Charles H. Deetz, Cartographer, and Oscar S.