Cartographic Science: A Compendium of Map Projections, with Derivations, 1st Edition (Hardback) book cover

Cartographic Science

A Compendium of Map Projections, with Derivations, 1st Edition

By Donald Fenna

CRC Press

504 pages | 167 B/W Illus.

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Hardback: 9780849381690
pub: 2006-10-25
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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.


". . . 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

Table of Contents


The Task: Curved Earth to flat map

The Task in Hand: A globe as model and intermediary


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


Squeezing the Circle: Ellipses and ellipsoids

Pinpointing the Place: UTM & UPS


Reality Check: The geoid and geodesy


Greek letters and words

Glossary of symbols

Glossary of terms

Index to projections

Historical bibliography


Subject Categories

BISAC Subject Codes/Headings:
TECHNOLOGY & ENGINEERING / Remote Sensing & Geographic Information Systems