Using IDL: Map Projections

## Pseudocylindrical Projections

Pseudocylindrical projections are distinguished by the fact that in their simplest form, lines of latitude are parallel straight lines and meridians are curved lines.

### Robinson Cylindrical

This pseudocylindrical projection was designed by Arthur Robinson in 1963 for Rand McNally. It is suitable for World maps and is a compromise to best fulfill a number of conflicting requirements, including an uninterrupted format, minimal shearing, minimal apparent area-scale distortion for major continents, and simplicity. It was designed to make the world look right. Since its introduction, it has been adopted by the National Geographic Society for many of their world maps.

Each individual parallel is equally divided by the meridians. The poles are represented by lines rather than points to avoid compressing the northern land masses. The central meridian should always be 0 degrees longitude to retain the correct balance of shapes, sizes, and relative positions.

The following figure shows a Robinson projection.

Figure 9-13: Robinson Projection

### Sinusoidal Projection

With the sinusoidal projection, the central meridian is a straight line and all other meridians are equally spaced sinusoidal curves. The scaling is true along the central meridian as well as along all parallels.

The sinusoidal projection is one of the easiest projections to construct. The formulas below from Snyder (1987) give the relationship between the latitude f and longitude l of a point on the globe and its image on the UV plane.

 u = lcosf v = f

The following shows the sinusoidal map of the whole globe centered at longitude 0 degrees and latitude 0 degrees.

Figure 9-14: Sinusoidal Projection

### Mollweide Projection

With the Mollweide projection, the central meridian is a straight line, the meridians 90 degrees from the central meridian are circular arcs and all other meridians are elliptical arcs. The Mollweide projection maps the entire globe onto an ellipse in the UV plane. The circular arcs encompass a hemisphere and the rest of the globe is contained in the lunes on either side.

The following figure shows a Mollweide projection in oblique form.

Figure 9-15: Mollweide Projection

Since the center of the projection is not on the equator, parallels of latitude are not straight lines, just as they are not straight lines with an oblique Mercator or cylindrical equidistant projection.

### Goode's Homolosine Projection

The Goode interrupted Homolosine projection, developed by J. Paul Goode, in 1923, is designed for World maps to show the continents with minimal scale and shape distortion. This is accomplished by interrupting the projection and choosing several central meridians to coincide with large land masses. This projection is a fusion of the Sinusoidal projection between the latitudes of 44.7 degrees North and South, and the Mollweide projection between these parallels and the poles.

The following figure shows an example of Goode's Homolosine projection.

Figure 9-16: Goode's Homolosine Projection