[Next] [Up] [Previous]

# The Van der Grinten Projection

This projection

is another conventional projection, neither conformal nor equal-area.

Like the globular projection, this projection is constructed by drawing circular arcs for both the meridians and the parallels. However, while the globular projection serves as a simpler-to-draw replacement for the equatorial case of the azimuthal equidistant, a compromise about midway between conformality and equivalence, this projection has an obvious strong resemblance to the Mercator. Thus, while it is intended to moderate, slightly, the exaggeration of areas of the Mercator, and to provide a pleasing appearance with curved meridians and parallels, it definitely favors shapes at the expense of areas. (Again, it is not strictly conformal, but the Lagrange projection, which is somewhat similar in appearance, is.)

In fact, to realize that it even moderates areas at all compared to the Mercator, one must make a direct comparison:

If anything, given that its curved parallels and meridians may give it the appearance of truth, this projection might be viewed as even more dangerously misleading than the Mercator.

The meridians are constructed exactly as in the globular projection, except that the equator is now divided into 360 degrees instead of 180.

For the parallels, a simple geometrical construction determines where each parallel cuts the surrounding circle and the central meridian.

Divide the height of the projection uniformly to indicate latitude, as shown by the blue lines. Then, where a line (shown as red in the diagram) drawn from the bounding circle at the height corresponding to a given latitude to the point where the other side of the bounding circle intersects the equator intersects the central meridian is where the parallel for that latitude crosses the central meridian.

The height at which the parallel for that latitude intersects the bounding circle is found in a similar fashion. Here, however, instead of the bounding circle, one uses a diagonal line (shown in green) between a pole of the projection and a point where the bounding circle crosses the equator. A line (shown as purple) is drawn from the point on this diagonal line at the height determined by the uniform division of the height of the projection and corresponding to the desired latitude, again to the point where the bounding circle crosses the equator at the other side. The height of the point where this line crosses the central meridian is the height at which the parallel, as drawn on the actual map, intersects the bounding circle.

[Next] [Up] [Previous]