# Map Projections #

The subject of map projections is fascinating. It is one of the first cases where high level mathematics had a profound impact on day to day life and, to this day, very few look at a map and fully understand the complexity hidden behind a deceptively simple object.

For anyone who gains some interest in the subject, a reference point is the publication of John P. Snyder, Map Projections - A Working Manual. To this day (it was published in 1987), it remains *the* reference when searching for a map projection.

John Parr Snyder (1926-1997) was a chemical engineer working for CIBA-Geigy with a lifelong interest in maps and map projections. At the age of 50, in 1976, he attended a cartography conference and learned about the need for a new projection to be used with Landsat satellites data. He designed what become known as the Space Oblique Mercator and offered it free to US Geological Survey (USGS). Two years later he was working in USGS and, in 1987, he published this compendium of map projections.

_{E}X and rendered using MathJax. The numerical examples are implemented using JavaScript. The default values can be changed and all affected formulas will be recalculated.

**I am not claiming any intellectual rights: this is a transcription in a new form of the original publication and it is done only as a tribute to a truly valuable work. All rights remain with the original copyright holders.** I am inclined to believe that, as a U.S. government work, the original publication is in public domain (see this reference). As such, this online manual would also be in public domain. However, I am no lawyer and may want to verify this information.

## Contents #

General Concepts

1. Characteristics of Map Projections

2. Latitude and Longitude

3. The Datum and the Earth as an Ellipsoid

4. Scale Variation and Angular Distortion

5. Transformation of Map Graticules

6. Classification and Selection of Map ProjectionsCylindrical Map Projections

7. Mercator Projection

8. Transverse Mercator Projection

9. Oblique Mercator Projection

10. Cylindrical Equal-Area Projection

11. Miller Cylindrical Projection

12. Equidistant Cylindrical Projection

13. Cassini ProjectionConic Map Projections

14. Albers Equal-Area Conic Projection

15. Lambert Conformal Conic Projection

16. Equidistant Conic Projection

17. Bipolar Oblique Conic Conformal Projection

18. Polyconic Projection

19. Bonne projectionAzimuthal and Related Map Projections

20. Orthographic Projection

21. Stereographic Projection

22. Gnomonic Projection

23. General Perspective Projection

24. Lambert Azimuthal Equal-Area Projection

25. Azimuthal Equidistant Projection

26. Modified-Stereographic Conformal ProjectionsSpace Map Projections

27. Space Oblique Mercator Projection

28. Satellite-Tracking projectionsPseudocylindrical and Miscellaneous Map Projections

29. Van der Grinten Projection

30. Sinusoidal Projection

31. Mollweide Projection

32. Eckert IV and VI projections

## Further References #

- NASA Landsat Science - John Parr Snyder’s Space Oblique Mercator Projection
- Library of Congress Blogs - From Childhood Fancy to Space Age Discovery