A curved modification of the Mercator projection that is neither equal-area nor conformal. Although it is usually classed with the various pseudocylindrical projections it is not really a pseudocylindrical projection.
Only the Equator is true to scale.
The central meridian and Equator are straight lines. All other meridians and parallels are arcs of circles. Great distortion in polar regions. Most maps using this projection do not extend past Greenland and the outer rim of Antarctica.
Used for world maps.
Presented in 1904 by Alphons J. van der Grinten of Chicago writing in a German geographical journal and patented in the United States in 1904. Van der Grinten originally invented two projections, the first of which is known as the " Van der Grinten I" or simply the "Van der Grinten" and the second of which is (confusingly) known as the "Van der Grinten IV." See the Van der Grinten topic for the Manifold implementation of the first projection.
Van der Grinten's second projection is known as "IV" because after van der Grinten's original publication Alois Bludau in 1912 presented a variation of the first van der Grinten projection that became known as the "Van der Grinten II," as well as a second variation in 1912 based upon the second of van der Grinten's original projections and given the name of "Van der Grinten III."
Thus the original two projections are known as Van der Grinten I and IV, while Bludau's two variations are known as II (based upon the first original) and III (based upon the second original).
Used only in the spherical form.