Selecting a model for a shape of the Earth involves choosing between the advantages and disadvantages of a sphere versus an ellipsoid.
The scale of orthographic projection is most accurate at the tangent area. The general pattern of distortion is radial. This is a good projection for uses like plotting airline connections from one airport to all others.
Print Latitude and longitude coordinates specify positions in a spherical grid called the graticule that approximates the more-or-less spherical Earth.
Depending on the map projection you choose, some projections may cause distance between features on a map to be preserved while distortion is introduced to shape. Suppose the same point, located at 60oN and oW, is projected on a map that uses the stereographic projection where the reference surface is a sphere with a radius of m.
The mapping of meridians to vertical lines can be visualized by imagining a cylinder whose axis coincides with the Earth's axis of rotation. The projection was originally designed to display accurate compass bearings for sea travel.
Transformation of geographic coordinates longitude and latitude to Cartesian x,y or polar plane coordinates. All great circles - the shortest routes between points on a sphere - are shown as straight lines on the gnomonic projection.
Whereas equal-area projections distort shapes while preserving fidelity of sizes, conformal projections distort sizes in the process of preserving shapes.