Map Projections

## Quick Answers & Personal Rants

Are you a professional/academic mapmaker?
No, I have no formal training in cartography.
What is a map projection?
It is a rule defining how to convert between geographic coordinates (latitude and longitude) and location on a flat surface — in other words, where a point on Earth should be drawn on a map, and vice versa. Usually expressed as a set of mathematical equations, or a computer algorithm. Only a few projections can actually be expressed as a geometric perspective model.
Are maps and map projections the same?
No. In order to create a map, not only a projection must be chosen, but also the aspect, scaling factor, region to be mapped, datum, data set, and often projection-specific parameters like central meridian and standard latitudes. Therefore every map requires a projection (some maps are a patchwork of different projections) which is often the strongest factor affecting its purpose and usefulness, but a single projection can generate many different maps.
Who created the images in your site?
Except in three or four contributed and credited cases, myself, with custom software and publicly-available coordinate data sets.
Why did you fail to include projection X?
Most probably I lack the time/expertise/willpower to understand the projection's description well enough to express it in my software and write something interesting about it. Perhaps I can't afford the book/journal/paper describing it. Maybe it is not interesting and unique enough, or its creator has not disclosed mathematical details.
Why your maps have no scale indication?
Most of my maps are global or regional, covering large areas on Earth. Therefore, inevitably the scale varies widely depending on location, direction, or both, making any single scale indication misleading at best. In several projections, scale is constant or easily predictable, but only along certain lines. Notice also that numerical scales like “1 : 1000000” are seldom useful in Web images where screen resolution is unpredictable and users can zoom in and out at will.
Why your maps lack a north indicator?
See previous question about scales. Only in equatorial cylindrical maps the north-south direction is unique. Except in local, large-scale maps, the graticule is the best north-south indicator.
What do you think of the “Peters” projection?
An insufficient solution for the wrong problem.
Is the Mercator projection wrong/evil/racist/part of a capitalist conspiracy?
No. Mercator's design is a precise and very useful tool with well-defined properties which occasionally can, like knives, get stuck in wrong places such as maps which should preserve areas instead of angles and shapes. Although its distortions (like of several other projections) have in isolated cases been exploited for political propaganda, I am afraid most misconceptions involving its use simply result from mental inertia, careless publishing and uncritical reading. People who claim having been “deceived” by Africa's size in Mercator maps, or who believe some rectangular map can perfectly reproduce a spherical Earth, apparently had little exposure to globes, or never thought about wrapping a towel over a ball.
And yes, Google Maps had very good reasons to choose Mercator's.
Which is the best projection of all?
It depends on your map's purpose.
Will a perfect projection ever be created?
For presenting the whole Earth at once, no. There are several properties describing map fidelity, and it has been mathematically proved that no flat map can ever perfectly satisfy all of them simultaneously everywhere; any attempt to improve one of them will usually worsen the others. Or it can improve a property at some spots while worsening it elsewhere. Thus every projection is a trade-off, a balance of priorities (see e.g. a typical compromise of cylindrical projections).
Because a projection has “sweet spots” where properties are better matched to the map's intended purpose, mapmakers usually create local or regional maps by either selecting the projection or moving the place of interest to a sweet spot where errors are negligible in practice. Notice that this is not what happens when mapping services like Google Maps zoom in.
Have you seen the diagram with four heads in profile on different map projections?
Yes, it appears as early as the 1921 edition of Charles Deetz & Oscar Adams's Elements of Map Projection with Applications to Map and Chart Construction. Unfortunately, if taken out of context, it (yet another example endlessly copied and forwarded, seldom credited) suggests an unspecified globular projection is the best, while the azimuthal stereographic is barely acceptable and both the azimuthal orthographic and Mercator just awful. However, the head looks best on a globular simply because it was drawn there first (not on a sphere), then remapped (probably using the graticule as a guide) on the other three projections. As Deetz & Adams acknowledge, the experiment is not a quality test and could just as well start with any of the four, leading to diametrically opposite, equally faulty, conclusions; ironically, because the original profile is a flat representation of a head, the orthographic is arguably the best starting point, since it is the only one immediately related to an actual three-dimensional object.
Please do my homework
That is not a question.
May I include your images in my site?
At least include an easily visible reference to the original source.
May I use your text? May I use your images in my project?