In short: the science of mapmaking (map projection theory).
In cartography projections of the Earth onto a plane (map projections) are constructed. As a mathematical model of the Earth either the sphere or the rotation ellipsoid is used.
The parameter representation of the unit sphere reads for - / 2 ≤ v ≤
/ 2 and -
≤ u ≤
as follows
x = cos(u) * cos(v) ,
y = sin(u) * cos(v) ,
z = sin(v)
and of the plane
=
* cos(
) ,
=
* sin(
) .
The task of cartography consists in finding suitable projection functions
=
(u,v) and
=
(u,v)
which project the surface of the sphere onto the plane while considering certain side conditions as
(illustration from [3] under literature).
Note:
In consequence of the THEOREMA EGREGIUM by C.F. Gauss it is impossible to construct maps which are an accurate image of the Earth's surface. Single curves however can be projected while preserving length.
What we want is to keep distortion in tolerable limits.
See also | |
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About Mapmaking |