| Cell ID | {{ state.cellId }} |
|---|---|
| DGGRID claimed area | {{ state.cellAreaKm.toFixed(4) }} km² |
| Area (geodetic vertices, Girard) | +{{ state.geoArea.toFixed(4) }} km² | +
| Area (authalic vertices, Girard) | +{{ state.authArea.toFixed(4) }} km² | +
| Geo / authalic ratio | +{{ (state.geoArea / state.authArea).toFixed(6) }} | +
+ DGGRID emits cells that are equal-area on the authalic + sphere. Computing area from the raw lat/lng vertices on a + uniform-radius sphere gives a slightly different number; the + authalic-shifted version recovers the equal-area property. +
+| i | lng | geo lat | authalic lat | Δ |
|---|---|---|---|---|
| {{ i }} | +{{ v[0].toFixed(2) }} |
+ {{ v[1].toFixed(4) }} |
+ {{ state.vertsAuth[i][1].toFixed(4) }} |
+ + {{ state.shift[i].toFixed(4) }}° + | +
+ Max |Δ| at this cell: {{ maxShift.toFixed(4) }}°. + The shift peaks near ±45° and is zero at the equator and poles. +
+
+ geodetic
+ authalic
+ (vertices marked). At 1× the rings essentially
+ coincide — the conversion is a near-pure latitude translation
+ for any cell that doesn't span much latitude. With "subtract
+ bulk shift" on and amplification ≥100, what's left is the *shape
+ distortion* — the part where vertices at different lats shift by
+ slightly different amounts because dξ/dφ is non-
+ constant. It's small, but it's not zero.
+
| edge | geo | authalic | Δ% |
|---|---|---|---|
| {{ i }} | +{{ g.toFixed(3) }} |
+ {{ state.edgesAuth[i].toFixed(3) }} |
+ + {{ ((state.edgesAuth[i] - g) / g * 100).toFixed(4) }}% + | +
+ If the conversion were a pure rigid translation, every edge would + change length identically. The non-uniform Δ% is direct evidence + of shape distortion (north–south edges shrink/stretch differently + from east–west edges). +
+