THE FOLD / BOSS / THE GATEKEEPER / THE SEPARATING AXIS
THE SEPARATING AXIS
convex collision by looking for one separating line
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
The separating axis theorem decides whether two convex shapes overlap: they are disjoint if and only if there exists a line (an axis) onto which their projections do not overlap. And you only need to test each shape’s own edge normals as candidate axes — if the projections overlap on all of them, the shapes collide.
It is the standard fast collision test in 2D game physics.
LIT verified live: over 500 random convex-polygon pairs SAT’s verdict matches an independent overlap oracle (a vertex inside the other, or crossing edges) every time (window.__sat). FIG no framing; exact for convex shapes.
It is the standard fast collision test in 2D game physics.
LIT verified live: over 500 random convex-polygon pairs SAT’s verdict matches an independent overlap oracle (a vertex inside the other, or crossing edges) every time (window.__sat). FIG no framing; exact for convex shapes.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at the-gatekeeper — the hitbox check that decides whether two things have made contact, the gate between touching and not. SAT is that gatekeeper. AVAN (AI) built the instrument: the edge-normal axes, the interval projections, the separation test, the independent overlap oracle.
Credit as content: the separating hyperplane theorem (Minkowski; the game-physics SAT formulation). The weave: David names the gatekeeper; I look for one axis that separates the shapes, and confirm the collision verdict against a direct overlap check.
Credit as content: the separating hyperplane theorem (Minkowski; the game-physics SAT formulation). The weave: David names the gatekeeper; I look for one axis that separates the shapes, and confirm the collision verdict against a direct overlap check.
3 ONE DIMENSION
Project both shapes onto a candidate axis (an edge normal). If the two intervals leave a gap, that axis separates them — no collision. Only if every axis’s intervals overlap do they touch.
4 TWO DIMENSIONS · INTERACTIVE
Two convex polygons; SAT’s collide/separate verdict is shown and checked against a direct overlap oracle.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: a single separating axis (or its absence, meaning collision).
AVAN’s addition (the inverse-companion): two convex shapes are disjoint iff there exists a separating line — and you only need to test the shapes’ own edge directions as candidate axes; if every projection overlaps, they collide. The inverse of ‘compute the intersection region’ is ‘look for a single axis that separates them — a line, not a region.’ Magenta is the overlap region you never compute; green is the one separating axis (or its absence). A collision is simply the failure to find a gap.
LIT Genuine separating axis theorem (separating hyperplane; the game-physics SAT). Verified live: SAT's collide/separate verdict (testing edge-normal axes) matches an independent overlap oracle (vertex-in-polygon or crossing-edges) for 500 random convex-polygon pairs (window.__sat.matchesOracle).
FIG No framing: the edge-normal axes, the interval projections, the separation test, and the independent overlap oracle run in-browser and agree exactly for convex shapes. The AVAN inverse is honest — two convex shapes are disjoint iff a separating line exists, found among their own edge directions, so a collision is the failure to find a gap; magenta is the overlap region never computed, green the separating axis (or its absence).
FIG No framing: the edge-normal axes, the interval projections, the separation test, and the independent overlap oracle run in-browser and agree exactly for convex shapes. The AVAN inverse is honest — two convex shapes are disjoint iff a separating line exists, found among their own edge directions, so a collision is the failure to find a gap; magenta is the overlap region never computed, green the separating axis (or its absence).
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE GATEKEEPER · David Lee Wise (ROOT0), with AVAN