Editing Mercator projection (section)

===Oblique Mercator===
{{Main|Oblique Mercator projection}}
An oblique Mercator projection tilts the cylinder axis away from Earth's axis to an angle of one's choosing, so that its tangent or secant lines of contact are circles that are also tilted relative to Earth's parallels of latitude.<ref>{{cite web | url=https://mathworld.wolfram.com/MercatorProjection.html | title=Mercator Projection }}</ref> Practical uses for the oblique projection, such as national grid systems, use [[Oblique Mercator projection|ellipsoidal developments of the oblique Mercator]] in order to keep scale variation low along the surface projection of the cylinder's axis.

The animation below shows a continuous transformation between the normal Mercator projection and the transverse projection, running through the intermediate oblique states.  A rhumb line (blue) and great circle (red) from Tokyo, Japan, to Callao, Peru, change according to the projection's aspect. The rhumb between them is straight only on the normal projection. On one of the intermediate oblique projections, the great-circle path between the two cities is straight. In this plot the y-axis is always the projected axis of the cylinder. The sphere is rotated inside the cylinder to change aspect. Initially the axis is normal to the equator (projected as the thick green line) but ends transverse to it, when the projected equator extends to infinity in the vertical direction.

[[File:Mercator Polar Transverse.gif|thumb|500px|center|Continuous transformation from a normal Mercator projection to a transverse Mercator, with a rhumb line (blue) and great-circle line (red) from Tokyo to Callao.]]