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 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 directionspreserving shape (conformality) preserving area (equivalence)general distortion pattern (Tissot indicatrices)the angular deformation pattern Mathematics of Cartography How projections are created, including equations for: 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 Some unusual applications of map projections (in construction) Conclusion Summary and table of depicted projections Resources and links Quick answers and personal rants

 www.progonos.com/furuti    October 30, 2014