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

Lobe — where it appears

One piece of an interrupted map: a strip of the sphere drawn about its own central meridian and separated from its neighbours by a cut. Every point in a lobe is measured from that meridian rather than from the sheet's, which is the whole of what interruption changes.

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

Sinusoidal, cut into 6 lobes. six lobes, cut through the oceans so each continent stays whole. Each lobe is the same projection about its own central meridian, so each point is near a line where the shape distortion vanishes: the mean angular deformation over the mapped world falls from 38.6° uninterrupted to 17.8° here. What is given up is that the map is no longer one surface — the graticule stops at every cut because there is nothing on the other side of it.

Giving up continuity

Cutting a map into lobes really does reduce the distortion, by a factor that can be measured. What is paid is that the map stops being one surface — and the size of the tear is the number that pictures of interrupted maps never carry.

choosing · Choosing Cut into Goode's lobes, the ranking of uncut sheets turns over. Mean angular deformation over the sphere for eight equal-area pseudocylindricals, each read two ways: as one uncut sheet, and cut into Goode's lobes with every point measured from its own lobe's central meridian. Uncut, Eckert IV is the best named map at 27.70° and the one-term curve fitted to the uncut sheet beats Goode's composite by 6.83°. Cut, Eckert IV falls to 21.34°, second from last, the curve fitted uncut reads 20.77° against the composite's 18.48, and the plain sinusoidal beats the composite at 17.88°. A curve refitted for the cut sheet reaches 17.01°.

Scored lobe by lobe, the homolosine loses to its own lower half

Read as one uncut sheet, a single smooth curve beats Goode's composite by 9.6 degrees. But the homolosine is used cut into six lobes, so here it is scored cut, with each point measured from its own lobe's meridian, and the ranking turns over. Eckert IV, the best named map uncut, falls to second from last. The curve that beat the composite is now 2.3° worse than it. The plain sinusoidal, the composite's own lower half, wins at 17.88° against 18.48. The best smooth curve for a cut map is the sinusoidal with a few per cent of correction.

families · Families

Named alongside it

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

Angular deformationGoode homolosineTrade-offDiscontinuityEqual-areaInterrupted projectionInterruptionOptimisationPseudocylindricalPurposeSinusoidal

All concepts