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extrinsics of map projections Map Projection
As already declared, a planar representation of the Earth has deformations compared to its shape on the Earth surface. These deformations depend on its position and the nature and specification of the map projection instance.
One way to minimise the deformation properties is to use an appropriate mapping surface like a cylinder, cone or horizontal plane and its aspect (alignment) as well as its coincidence with the Earth model. These characteristics are called the geometric extrinsics of the mapping surface:
mapping surfaces: their shape, aspects and coincidence [Voser 2003]
The nature of the mapping surface:
  • cylinder
  • cone
  • plane
  • polysuperficiality (a continuous system of mapping surfaces)
These mapping surfaces may be aligned in different ways. The name of its aspect is given based on the orientation of the axis of the mapping surface with the axis of the Earth. In literature, also other terms are used (see e.g. [Goussinsky 1951, Lee 1944, Richardus/Alder 1974, Snyder 1987]).
  • normal or direct aspect (axis parallel to the Earth axis)
  • transversal aspect (axis parallel to the equator plane)
  • oblique aspect (axis with any direction)
The third extrinsic category is the coincidence(the „contact“) of the mapping surface with the underlying Earth model:
  • tangency („touching“)
  • secancy („intersecting“)