Cartographic Projection
every map is wrong, and by exactly how much
Concept

Corridor — where it appears

The set of places within a stated distance of a route, which is what a buffer operation returns. Its area is a band plus two end caps that together make one disc, and the closed form for it stops being the area once the two sides meet round the far side of the body.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

The scale along the Madrid–Tokyo corridor. The scale factor of four projections along the great circle from Madrid to Tokyo, each normalised to its own average over the route so the comparison is of variation rather than of size. The oblique Mercator whose own equator is laid along the corridor holds the scale to 0 parts per million; Mercator varies by 118.7% over the same line. A corridor is a curve, not a region, and the projection an area criterion picks is not the one a curve wants.

Choosing for a line, not a region

Every criterion in this subject integrates over an area. A pipeline, a railway or a coastal survey is a curve, and the projection an area criterion picks for it is not the one it should have — measurably, by a factor of five thousand.

choosing · Choosing Everywhere within 200 km of the route from London to Tokyo. The shortest route between the two places, and the set of places within 200 kilometres of it, with both edges computed on the sphere and then projected. On the ground the set holds 3.949 million square kilometres — the band 3.823 and the two end caps 0.126, which between them make one disc of the corridor's own width. Drawn in Mollweide the corridor is visibly wider at one end than the other, and the ground it stands for is not.

A corridor has a width the page cannot keep

Buffering a line is the most-run operation in spatial analysis and the corridor it produces is a reach set with two failures nobody separates: stroked on the page, one width covers 190 to 471 kilometres of ground along a single route; computed in closed form, the formula stops being the area at a width the route's own length fixes, and eventually claims more ground than the sphere has.

paths · Reach

Named alongside it

The objects these essays reach for when they reach for this one.

Great circleAreaAspectBoundaryBufferClosed formCut locusGeneralisationLaborde's projectionLine scale factorMercatorObjective function

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