Map Projections: Contents

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Map Projections

Cartographical Map Projections

Cartography is the science of map-making. It comprises many problems and techniques, including:

South America in selected projections at identical scale. Which projection is best? Which is right? The short answer is none, at least not all the time. Even if a single projection is used, just switching the aspect can also radically reshape the continents.

measuring the Earth's shape and features
collecting and storing information about terrain, places and people
representing the three-dimensional planet as flat maps (my main concern)
devising and designing conventions for graphical representation of data
printing and publishing information.

There is an endless variety of geographic maps for every kind of purpose. When looking at two different world maps one can wonder why the differences: do we draw the world as a rectangle, or an oval? Shouldn't it be a circle? Must coordinate grid lines be parallel? Straight or curved? Does South America's "tail" bend eastwards or westwards? What's the "right" way (or, more properly, is there one?) to draw our unique planet?

One important concern of cartography is solving how to project, i.e. transfer points from an almost spherical lump of rock (our Earth) onto flat surfaces, either paper pages or computer screens.

Here are informally described important cartographic concepts, how maps are drawn and why there are so many different kinds of projections for world maps. You may start reading here and follow the buttons, or use this table of contents:

Introduction		A gentle introduction to tinkering with maps
Introduction		Basic definitions and concepts about the Earth, maps and the mapmaker's choices
Fitting Map to Purpose		Useful map properties: preserving distances (equidistance, isometry) geodesics (great circles) preserving directions preserving shape (conformality) preserving area (equivalence) general distortion pattern (Tissot indicatrices) the angular deformation pattern
Mathematics of Cartography		How projections are created, including equations for: azimuthal orthographic central and stereographic cylindrical (Braun, Gall, and others) Kavrayskiy VII sinusoidal (Sanson-Flamsteed) Craster's parabolic Mollweide polar/equatorial azimuthal equidistant/equal-area equidistant cylindrical/Winkel I and II Aitoff, Hammer and Winkel Tripel
Main Projection Groups		Azimuthal projections, perspective or not
		Cylindrical projections, arbitrary or perspective
		Pseudocylindrical projections, pure, continued or crossbred
		Conic projections, non-perspective and polyconic
		Pseudoconic projections
		Modified azimuthal projections
		Conformal projections
		Other interesting projections
Coping with Distortion		Tilted and crooked projections: oblique maps
		Tearing Earth's skin: interrupted maps introduction star projections interrupted and compound conic maps classic interrupted maps arbitrary interrupted maps interruption techniques
		Rebuilding the Earth into an exotic planet: polyhedral maps introduction and tetrahedral maps cubic and octahedral maps icosahedral, dodecahedral and other maps fold-outs for printing and assembling pseudoglobes
Pieces of History		Projections developed before the Modern Age
Projections at Work		Projections which helped making the world smaller: the Mercator and azimuthal equidistant
Projections at Work		Some unusual applications of map projections (in construction)
Conclusion		Summary and table of depicted projections
		Resources and links
		Quick answers and personal rants

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