A mathematical introduction to the fundamental
techniques behind projections in use today.

Benjamin Høyer


1. Introduction
2. Mathematical foreword
Assumptions, simplifications and conventions
The Problem of Map Projection
Preserved Quantities
3. Azimuthal Projections
Gnomonic Projection
Stereographic Projection
Orthographic Projection
Comments on other Azimuthal Projections
4. Cylindrical Projections
Equirectangular Projection or Plate Carrée
Lambert's or Cylindrical Equal-Area Projection
Mercator's or Cylindrical Orthomorphic Projection
Comments on other Cylindrical Projections
5. Conical Projections
Conical Projection with One Standard Parallel
Conic Projection with Two Standard Parallels
Bonne's Projection
6. Closing Comments
Interrupted Projections
Haversine Formula
Craig Retroazimuthal or Mecca Projection
7. Conclusion
Diagrams and calculations
Further Reading

Benjamin Høyer June 2009

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School of Mathematics and Statistics
University of St Andrews, Scotland