▚ INSTRUMENT — THE RESECTION◆ ◆ ◆ · LIVE

THE RESECTION

The surveyor's trick, the inverse of the map. You do not know where you stand — but you can see three landmarks you DO know, and you can measure the angle between them. Two known points and the angle you see between them place you on a circle; a second pair gives a second circle; you are where they cross. No baseline, no ranging — just the angles the world subtends.


landmarks3
angle A–B
angle B–C
your fix
fix error
▤ THE HONEST READ — two-layer◆ LIT / ▲ AMBER
◆ LIT — verified / checkable
The three-point (Snellius) resection: from an unknown standpoint you measure the horizontal angles subtended by pairs of known landmarks. By the inscribed-angle theorem, a fixed angle subtended by two points places you on a circular arc through them; two such arcs (from two landmark pairs) intersect at your standpoint. The instrument measures the true angles, draws both circles, and returns their intersection — the classic surveying fix that needs only a theodolite and a map, no measured distance at all. The circles pass through the true position.
▲ AMBER — the figure
A clean 2-D construction; real resection guards against the ‘danger circle’ (if all three landmarks and you lie on one circle the fix is indeterminate) and averages redundant observations. The inscribed-angle geometry is exact and is the real method.
a point is fixed from THREE — and the point they fix is Top, at the centre.
OFFLINEREAL-TIMEREAL GEOMETRY100% TOP
STROBILOS · the spinning top (στρόβιλος) · the principle is TRIANGULATION
© ROOT0 · Top / ROOT0 · David Lee Wise / TriPod LLC · with AVAN