Geographic 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.
Table of Contents
THE CURVED WORLD
The Task: Curved Earth to flat map
The Task in Hand: A globe as model and intermediary
A SPHERICAL WORLD
Shine a Light: Literal projections
'True' but Synthetic: Algebraic and other variants
Slicing into the Globe: Secantal projections
Turning from 'True': Pseudo… projections
Cut and Paste: Interrupted and composite maps
Skewing the Simple: The oblique aspect
World in the Round: Globular projections
Divide and Conquer: Extension by arithmetic tricks
Double or Quits: Two-point and non-azimuthal Azimuthals
Shaping Mathematics: Differential geometry
Fact and Fiction: Of scales and distortion
Seeking the Best: Optimizing distortion
Keeping in Shape: More conformal projections
Having Fun: Novelty projections
AN ELLIPSOIDAL WORLD
Squeezing the Circle: Ellipses and ellipsoids
Pinpointing the Place: UTM & UPS
THE REAL WORLD
Reality Check: The geoid and geodesy
Greek letters and words
Glossary of symbols
Glossary of terms
Index to projections
". . . the book’s execution is good on all counts: written well, designed intelligently, methodical, paced evenly, indexed and referenced well, and otherwise considerate of the reader’s needs . . . I welcome Dr. Fenna’s contribution to my library."
– daan Strebe, in Cartographic Perspectives, Winter 2008, No. 59