Actually no projection can preserve linear scale/distance in general over a large extent and it's not just rectangular maps (Cylindrical Projections), any projection of the curved sphere onto a flat plane produces distortion. You can preserve Angles (Conformal), Areas (Equivalent/Equal Area), or distances along great circles through a particular pair of antipodal points (Equidistant). Only one projection preserves bearings, and that's Normal Mercator (Which requires that it be Conformal as well). A few other projections preserve other interesting properties (Gnomonic maps all great circles onto straight lines, Stereographic maps all circles onto circles).Originally Posted by RobA
The simple answer is "no"
Mapping from a sphere (planet) to a rectangular map will create distortion, for the same reason you can;t take an orange peel and flatten it out into a rectangle. Projection can preserver one or more (but not all) of:
* Area
* Shape
* Direction
* Bearing
* Distance
* Scale
http://en.wikipedia.org/wiki/Map_projection
For example, the equirectangular is great around the equator, but pinches the poles when used in the fashion you created your map, as distance is not preserved. (And to have a scale bar on such a projection makes no sense at all). here is your map:
-Rob A>
This projection is equidistant for distances along arcs of great circles through the poles, which is why it is also called Equidistant Cylindrical.
Over a small extent, as long as the projection is appropriate to the extent, linear scale, area, and bearing should all be pretty close to true. This is one of the reasons you can't just crop out sections and scale them up. Maps of smaller extents need projections appropriate to those extents. You can sort of do it with Mercator as it sort of preserves shapes, but it has problems at intermediate scales like continents (This is what most zoomable web maps do) and you need to use a special formula to figure out the effective scale at a particular latitude. It also falls apart at the poles.
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