FA-69928 / Map projection transforms / Member archive

Geographic bounds of a map tile: edge latitude factor · case 03

All tile edges crowd toward the north, the south half of the world disappears.

Member previewVariant 3 · 3 implementations · 8 checks per implementation

Case contract

Input [z, col, row, scheme] where scheme is "xyz" (row 0 at north) or "tms" (row 0 at south). Return [west, south, east, north] in degrees rounded to 6 decimals, using lon = col/n*360-180 and lat = degrees(atan(sinh(pi*(1-2*r/n)))) for an xyz row edge r, n = 2**z. A tms row t is the xyz row n-1-t.

Why this case matters

Tile footprints drive cache invalidation, label placement and raster reprojection; wrong edges misalign tiles.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
control #2	`[90.0, 79.171335, 180.0, 85.051129]`	`[90.0, 66.51326, 180.0, 85.051129]`	Failed

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