ATLAS / PLATE 002
DISTORT A MAP ON PURPOSE
Finding the thin line between optimising a projection and distorting a map using key trade routes.
What would a world map look like if it were built to answer one question well?
- N.01
THE IDEA
I wanted to see what happens when a map is designed for one explicit spatial question. Here the question is narrow: how well can a flat world map preserve the pairwise distances among six chosen cities?
- N.02
INPUTS
The network contains London, Lagos, Dubai, Mumbai, Singapore and Shanghai, giving 15 pairwise relationships. Mercator and Equal Earth provide two familiar comparison cases.
- N.03
HOW I BUILT IT
I measured the network under the comparison projections, then optimized a blend of azimuthal equidistant and Lambert azimuthal equal-area geometry around a fitted centre. The objective minimizes network-distance error after one global scale is applied.
- N.04
RESULT
Network-distance RMS error is 11.97% for Mercator, 9.99% for Equal Earth and 2.42% for the optimized map. Worst pairwise error falls to 4.22%. Equal Earth still wins decisively on area preservation, so the optimized result is a specialist rather than a replacement.
- N.05
CHOICES
I originally wanted a continuous DISTANCE ↔ AREA slider. The maths killed the idea. As soon as area preservation received meaningful weight, the solution moved toward the equal-area projection instead of producing a useful smooth family. I removed the slider rather than manufacture a cleaner tradeoff than the experiment produced.
- N.06
CAVEATS
This projection is optimized for six cities and one declared objective. Change the cities, the weighting or the objective and the answer would naturally. The current usefulness comes from being specific about this set of cities.
- N.07
FILES + SOURCES
SOURCE MATERIAL
Spherical WGS84-like angular coordinates; geodesic comparison uses great-circle angular distances. City reference points: fixed canonical city-centre coordinate literals in generation script. Display coastline: GSHHG low-resolution coastline bundled with Basemap in the execution environment (display only; not an optimization input).
METHOD
Pointwise linear blend of spherical azimuthal equidistant (AEQD) and Lambert azimuthal equal-area (LAEA) coordinates sharing a variable center. P = alpha * P_AEQD + (1-alpha) * P_LAEA. Objective: minimize RMS log error of all 15 pairwise city distances after fitting one global map scale; penalize folds/invalid samples. Optimizer: scipy.optimize.differential_evolution (seed 918).
TRANSFORMATIONS
Optimized centre 53.964574° N, 73.679511° E; AEQD weight 0.292805, LAEA weight 0.707195. 36 iterations, 2002 function evaluations.
MEASURED VALUES
Network-distance RMS error: Mercator 11.97%, Equal Earth 9.99%, optimized 2.42%. Worst pairwise error: 32.38%, 22.90%, 4.22%. Land area log-RMS: 0.651, ≈0, 0.140.
DATA LIMITS
The originally proposed distance↔area slider was not retained: when area preservation received any substantial weight, optimized LAEA (alpha=0) produced essentially zero area distortion while also giving low network-distance error. The final map therefore optimizes the declared network-distance question and reports its area/shape sacrifices rather than manufacturing a false continuous trade-off. Natural Earth was the planned display source, but outbound binary acquisition is blocked in this execution environment. This substitution does not alter any computed projection parameters or network diagnostics.
SOURCES
- GSHHG low-resolution coastline (via Basemap), display only
- scipy.optimize.differential_evolution
- METHOD
- Projection mathematics/ optimisation
- SOURCE
- Computed (Atlas drop 01); display coastline GSHHG
- PERIOD
- N/A
- GEOGRAPHY
- World
- TYPE
- CUSTOM DISTORTION-OPTIMISED PROJECTION
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