nx_geo_area.nx

nx_geo_area.nx -- LIB: GEO-010 polygon AREA + ORIENTATION, INTEGER-EXACT (shoelace / Gauss). THE EXCEED ANGLE (measured, not asserted): the area is the shoelace sum of INTEGER cross products over microdegree coordinates -- ZERO floating point. So both the doubled-area magnitude AND the orientation (its sign) are EXACT and DETERMINISTIC, and collinear / degenerate vertices contribute EXACTLY 0. Those are precisely the cases where Turf.js / Shapely / PostGIS (all float) accumulate epsilon error or flip orientation. Resolution is 1 microdegree (~0.11 m); a 1-microdegree apex yields its exact area, not noise. Convention (matches nx_geo): poly = flat [lat0,lon0, lat1,lon1, ...], npts vertices, implicitly closed (last->first); lat = Y, lon = X. The result is the DOUBLED (un-halved) area in microdegree^2 (deg^2 * 1e12) so it stays a pure integer -- halving is the caller's choice and exact when the doubled value is even. Overflow-safe for Earth coords in i64 (|lon*lat| <= 1.8e8 * 9e7 = 1.6e16; the sum of hundreds of such terms fits in i64's 9.2e18). Foundation rung: the area-weighted CENTROID and polygon clipping/union compose THIS. license_tier: ORIGINAL