Map Projections

### Arbitrary Interrupted Maps

Some interrupted projections were designed using very specific or handcrafted principles; their detailed descriptions can be quite elaborate, making those projections generally difficult to be faithfully reproduced on a computer.

#### Interrupted Maps by Spilhaus

After using Hammer and August projections for designing maps emphasizing nearly-continuous seas, Atelsthan Spilhaus proposed more complicated approaches, like a modified (not equal-area) Hammer map interrupted in three lobes, or interrupting the map at shorelines instead of, as usual, graticule lines.

 Kent Halstead's Equidistant interrupted projection, with 10°-step graticule. In this hand-drawn map a few features were simplified, not exactly matching the original description: for instance, polar caps are bound by uninterrupted circles, and edge lengths of some cells split at lobe boundaries don't add up exactly. Copyright © 1952 Kent Halstead.

A very different design was the "Equidistant" published by Kent Halstead in 1953, featuring many asymmetric lobes. Unlike most projections, it is built on a specific graticule.

Edges of every graticule "cell" - i.e. 10°-wide quadrilaterals, which degenerate to triangles surrounding the poles - are mapped to straight segments of true length and constant scale. Starting from each pole, the cells are separately and sequentially projected (possibly in successive rings), with just enough shearing necessary to fit along cells previously laid. Shearing is minimized along certain privileged meridians (e.g., the Northern 100°W and 60°E meridians are mostly continuous and cross parallels at nearly right angles), but inevitably angles become more and more oblique farther from them. The juxtaposition is arbitrarily interrupted whenever accumulated shearing is excessive, all the while avoiding cuts in continents. After the graticule is laid out, every cell's interior may be projected by linear interpolation between opposite edges. Therefore, this projection is equidistant along all meridians and parallels, which are both broken at most intersections, but neither conformal nor equal-area.

The graticule spacing can of course be reduced, yielding a smoother, more curvaceous grid, with a correspondingly more complicated description. Even at 10° steps - and 648 cells - the result is a pleasant and balanced map.