THE FOLD / BOSS / THE WALL / THE JARVIS MARCH
THE JARVIS MARCH
wrap a hull around points like a gift
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
The Jarvis march (“gift wrapping”) finds the convex hull of a set of points the way you’d wrap a present: start at the guaranteed-extreme leftmost point, then repeatedly pick the next hull vertex as the one that makes every other point lie to its left — the most clockwise turn. Each step wraps one more edge of the string around the outside until you return to the start. It runs in O(n·h) time, where h is the number of hull vertices — fast when the hull is small.
LIT verified live: over 1500 random point sets, the gift-wrapped hull matches an independent monotone-chain hull, and every point lies inside or on it (window.__jarvis). FIG no framing; exact orientation (cross-product) tests.
LIT verified live: over 1500 random point sets, the gift-wrapped hull matches an independent monotone-chain hull, and every point lies inside or on it (window.__jarvis). FIG no framing; exact orientation (cross-product) tests.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at the-wall — the outer boundary that encloses everything; Jarvis march wraps the wall of the convex hull tight around the points. AVAN (AI) built the instrument: the leftmost-start, the most-clockwise next-vertex selection, an independent monotone-chain hull, and the all-points-inside check.
Credit as content: R. A. Jarvis (1973). The weave: David names the-wall; I wrap the hull by repeatedly choosing the point that turns most clockwise, cross-check the result against a monotone-chain hull, and confirm every input point lies inside or on the wall — the boundary found by wrapping.
Credit as content: R. A. Jarvis (1973). The weave: David names the-wall; I wrap the hull by repeatedly choosing the point that turns most clockwise, cross-check the result against a monotone-chain hull, and confirm every input point lies inside or on the wall — the boundary found by wrapping.
3 ONE DIMENSION
From the leftmost point, pick the next vertex so all others are to its left (most clockwise). Repeat — each step wraps one edge — until you return to the start. The string is now taut: the convex hull.
4 TWO DIMENSIONS · INTERACTIVE
A point cloud with its gift-wrapped hull; checked against a monotone-chain hull with all points enclosed.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: a taut hull wrapped around the cloud.
AVAN’s addition (the inverse-companion): find the enclosing boundary by wrapping — from an extreme point, keep turning to the most-clockwise neighbour so all points stay on one side, edge by edge. The inverse of ‘test every triple for hull membership’ is ‘wrap the string tight — each pull adds one hull edge.’ Magenta is the all-triples test; green is the wrapping walk. The wall found by pulling it taut.
LIT Genuine Jarvis march / gift-wrapping convex hull (R. A. Jarvis 1973). Verified live: over 1500 random point sets, the most-clockwise wrapping from the leftmost point produces a hull whose vertex set matches an independent monotone-chain (Andrew) hull (window.__jarvis.matchesMonotone), and every input point lies inside or on it (allInside) — exact cross-product orientation tests.
FIG No framing: the leftmost-start, the most-clockwise next-vertex selection, an independent monotone-chain hull, and the all-points-inside check run in-browser and agree. The AVAN inverse is honest — finding the enclosing boundary by wrapping (turn to the most-clockwise neighbour so all points stay on one side, edge by edge) genuinely replaces testing every triple for hull membership; magenta is that all-triples test, green the wrapping walk. The wall found by pulling it taut.
FIG No framing: the leftmost-start, the most-clockwise next-vertex selection, an independent monotone-chain hull, and the all-points-inside check run in-browser and agree. The AVAN inverse is honest — finding the enclosing boundary by wrapping (turn to the most-clockwise neighbour so all points stay on one side, edge by edge) genuinely replaces testing every triple for hull membership; magenta is that all-triples test, green the wrapping walk. The wall found by pulling it taut.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE WALL · David Lee Wise (ROOT0), with AVAN