bfc99ff827
Every reference to the Driver in library/ is reworded: the engineering reason stays, the speaker and the quote go, and a decision still open reads "provisional, pending a product decision". Comments only: each changed file is identical after stripping comments (JavaScript, template and CSS, including CSS comments inside the style strings shadow-DOM components inject). Those style-string comments do ship, so several bundles change by exactly those comment bytes.
57 lines
2.8 KiB
JavaScript
57 lines
2.8 KiB
JavaScript
/**
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* mercator-slice.js — cut a map's bounds into EQUAL-HEIGHT rows, which is not the same as equal degrees.
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*
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* ★ THE DEFECT THIS EXISTS FOR (Simple Research's poster export): the poster showed too much of
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* Antarctica and came out at the wrong, vertical aspect.
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*
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* The big-poster renderer stitches a grid of tiles, each rendered into an EQUAL-HEIGHT slot in the
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* output image. It chose each tile's latitude band by dividing the degree span evenly:
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*
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* latStep = (ne.lat - sw.lat) / rows
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*
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* Web Mercator is not linear in latitude — screen y is proportional to ln(tan(pi/4 + lat/2)) — so equal
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* DEGREE bands are not equal SCREEN bands. MEASURED on a -60..75 view in 4 rows: the top band is 37.0%
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* of the true screen height and is drawn into 25% of the poster; the next is 19.7% drawn into 25%. Every
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* row is squeezed or stretched, which is the wrong aspect, and the high-latitude bands — where a degree
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* is worth the most pixels — are the most over-represented, which is where the excess Antarctica came from.
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*
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* Slicing in MERCATOR Y instead gives 25.0% per row exactly, because that IS the screen coordinate.
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*
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* ★ SAME MISTAKE, THIRD PLACE TODAY. A whiteboard chart nearly shipped with a linear scale into degrees,
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* and a measurement harness nearly reported a false threshold by correcting the wrong axis. Anything
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* that treats latitude as a screen coordinate is wrong; the conversion is one line and it belongs
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* somewhere shared rather than being rediscovered.
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*/
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/** Web Mercator's y for a latitude, in the same units the projection's x uses (radians of longitude). */
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export const mercatorY = (lat) => Math.log(Math.tan(Math.PI / 4 + (lat * Math.PI / 180) / 2))
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/** The inverse: the latitude at a Mercator y. */
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export const latAtMercatorY = (y) => (Math.atan(Math.sinh(y)) * 180) / Math.PI
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/** Web Mercator is undefined at the poles; the engines clamp here, so clamp before projecting. */
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export const MERCATOR_MAX_LAT = 85.051129
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const clampLat = (lat) => Math.max(-MERCATOR_MAX_LAT, Math.min(MERCATOR_MAX_LAT, lat))
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/**
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* Latitude bands of EQUAL RENDERED HEIGHT, north to south.
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* @param {number} southLat
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* @param {number} northLat
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* @param {number} rows
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* @returns {Array<[number, number]>} [southLat, northLat] per row, ordered north-first to match a
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* top-to-bottom tile grid
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*/
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export function equalHeightLatBands(southLat, northLat, rows) {
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const n = Math.max(1, Math.floor(rows) || 1)
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const yN = mercatorY(clampLat(Math.max(southLat, northLat)))
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const yS = mercatorY(clampLat(Math.min(southLat, northLat)))
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const step = (yN - yS) / n
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const out = []
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for (let r = 0; r < n; r++) {
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const top = yN - r * step
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const bottom = yN - (r + 1) * step
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out.push([latAtMercatorY(bottom), latAtMercatorY(top)])
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}
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return out
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}
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