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.
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.
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.
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.
See previous question about scales. Only in
equatorialcylindrical
maps the north-south direction is unique. Except in local, large-scale
maps, the graticule is the best north-south indicator.
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.
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.
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.