Data and Accuracy

Two axes of distortion

Phase two added a second reading: shape distortion. It comes from Tissot's indicatrix - project an infinitesimal circle on the ground and it lands as an ellipse. The ratio of its axes is shape distortion; their product is area distortion.

Both axes have to be there, because one of them is always dead. Under any equal-area projection the area reading is 1.00x at every latitude by definition, so dragging moves nothing; under any conformal projection the shape reading is 1.00 everywhere, for the mirror reason. No axis is alive on all five projections, but every projection has one that is.

The distortion-ellipse grid uses the same function, evaluated on a lattice of about 15 by 8. It is the only view that can show what a projection gets right: on Mercator every ellipse is a circle, on Equal Earth every ellipse holds the same area.

What the area multiplier is measured against

The area reading treats each projection's own measured area scale at the equator as 1. V1 divided by projection.scale() squared instead; for Mercator those are the same number, so no v1 reading moved. For a compromise projection they are not: Natural Earth squeezes low latitudes to fit its canvas and sits at 0.877 of its nominal scale on the equator, which would print as 0.88x. Measuring the baseline instead of assuming it makes "compared with the equator" true for all five at once.

The equator cannot hold the continents

"Distribute along equator" lays the visible layers side by side at the true width each one occupies on the equator. The six continents need 428 degrees of longitude and all fourteen objects need 783, out of the 360 a full turn provides. That is not a failure of the command. It is the most direct statement of scale the tool can make: Earth's own equator is not long enough to stand its continents side by side.

Where the data comes from

Boundaries are Natural Earth 110m Admin 0 countries, which is in the public domain. The source file is committed to the repository and the build never touches the network, so CI and deploys cannot fail because an upstream host had a bad day.

110m is a scale prepared for world-scale display and is already generalised. Coastlines are therefore coarse, and very small islands may be missing.

How the shapes move

Dragging an object rotates it rigidly across the globe. It does not add an offset to each longitude and latitude. That distinction is the whole project.

Mercator maps longitude linearly onto the horizontal axis, so a pure coordinate translation never changes a shape's on-screen width; only its height moves. Greenland dragged to the equator that way would still occupy 62 degrees of longitude, about 6,900 km, against a true east-west width of roughly 2,100 km. The readout would say no distortion while the picture showed a Greenland stretched 3.2 times too wide.

Rigid rotation preserves every ground distance inside the shape, so the shrinking you see at the equator is real rather than drawn.

Spinning the active layer about its own anchor uses the third angle of that same spherical rotation. It is equally rigid: true area does not budge, but apparent area does, because a turned shape covers different latitudes. This is a fresh rotation on the globe followed by a fresh projection, not the old picture turned on its side.

One honest side effect: dragging diagonally also turns the shape slightly. A rigid body moved across a sphere cannot hold a fixed compass bearing. This is geometry, not a rendering fault. Dragging straight north or south along the anchor's own meridian produces no such turn.

How the multiplier is computed

The headline number is measured from the geometry actually drawn: projected area divided by true spherical area, normalised so the equator reads 1. It is exact for the whole polygon, holes and multi-part shapes included, and equals the area-weighted mean of sec-squared across the shape.

The sec-squared value at the anchor is shown only as supporting detail. For objects spanning many latitudes the two part company: Greenland's true multiplier is about 16.4 while the anchor estimate is 11.9, a 27 percent gap. Sec-squared is convex, and Greenland's northern tip sits at 84 degrees north where the local inflation is already about 92 times.

How far an object can be dragged is limited by keeping all of it inside Mercator's practical limit of 85.05 degrees. The larger the object, the narrower the band its anchor can reach. That is a real constraint: something wide enough genuinely cannot approach a pole without wrapping over it.

How continents are defined

Continents here are political groupings taken from country metadata, not geological landmasses. Each country belongs to exactly one.

There is one deliberate departure. Russia is grouped under Asia, where the source files it under Europe. Taken literally, Europe would be 74 percent Russia by area, would reach Kamchatka, and would have its anchor in Siberia, which leaves nothing useful to compare against Africa. Russia is still selectable on its own.

There is a second. The source models France as one feature that includes French Guiana; the Europe object leaves that part out. It is only 1.4 percent of Europe's area but sits 74 degrees from the anchor, which would squeeze the object's draggable range from about plus or minus 56 degrees down to 11. The base map still draws France whole.

Known limits

Computed areas against published figures: Canada, Brazil, Australia, Russia and Greenland land within about 1 percent; India is about 4 percent low, where simplification and disputed boundaries both bite.

Earth is treated as a sphere rather than an ellipsoid. That is a fraction of a percent, far below the error from simplified boundaries.

Continents keep their internal national borders rather than being dissolved.

The upshot: good for teaching and visual comparison, not for legal, navigation, surveying, or GIS analysis.