[mdsumner]

Requested by Michael · project thread

New page peel.html, after Globals and interrupteds in the nav. It treats globe gores and peeling an orange as one topic, and asks whether orange peel can be a sinusoidal map.

Gores. You choose n gores from pole to pole. Each is flattened on its own central meridian as sinu, cass or tmerc on the sphere. They are laid out either as a flower joined at the south pole (the way an orange is peeled) or as a row joined at the equator (with sinu, this is the interrupted sinusoidal). The 3D view opens the flower: each gore is wrapped on a sphere of radius 1/(1 - p) that touches the orange at its south pole. A table compares the three flattenings for the current n by worst area, angle and stretch error, and by how much longer the flat edge is than the meridian it came from.

Spiral. One strip of constant width is wound from pole to pole. Its flat centre line turns at tan(latitude). The flat strip is drawn against the Euler spiral it tends to (Bartholdi and Henriques 2012, Orange peels and Fresnel integrals). The readout says how much of the strip stays within half a width of that spiral. In 3D, the peeled part lies in the plane that touches the orange where the peel comes away.

The answer the page gives. A gore whose parallels keep their length is a sinusoidal gore. Peel, though, can hardly stretch at all. The sinusoidal keeps area but shears near the poles: for 12 gores, angles are off by up to 15 degrees. That shear only halves when the gore width halves. Cassini and transverse Mercator stretch by at most 3.5%, and their error falls with the square of the width. So a real segment of peel is nearer a Cassini or transverse Mercator gore.

Files

• src/core/peel.js: the geometry (pure core, exported from src/core/index.js)
• js/peel.js, peel.html, plus a few lines in css/app.css
• test/check-peel.mjs (added to npm test): checks the gores against PROJ 9.8 (fixture from test/make-peel-fixture.py), their inverses, what each keeps, the w and w^2 rates, both ends of the peel, and the spiral's curvature, length and limit
• Nav link added on every page; the guide (chapter 8), the globals page's gores paragraph and the README all link to the new page

Checks

• npm test passes.
• Page loaded in headless Chromium with no page errors. Screenshots are in the project's playproj-shots/peel-*.png.

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