SYSTEM NOTE
Rotate the loop. Read what remains.
A visual knot observation model. Not a formal topology proof tool.
OBSERVATION CHAMBER / MVP
Knot Invariant Chamber
A visual knot observation model for rotating closed loops and reading crossings, over-under relations, twist, and traces that resist untangling.
knot
Prototype
KNOT PROJECTION FIELD
Rotate a closed loop and observe crossings, over-under relations, twist, and traces that resist untangling.
First observation
Use SPIN to rotate the loop. CROSS reveals over/under points. UNKNOT is the comparison loop.
KNOT PROJECTION
crossings 0 / writhe 0
OBS-000 / TREFOIL / 00:00
OBSERVATION POINTS
Crossings, twist, and the unknot comparison.
- SURFACE emphasizes depth and the front/back relation of the closed curve.
- CROSSING marks OVER and UNDER points so the projection becomes readable.
- WRITHE colors twist direction, while UNKNOT shows a loop that returns toward simplicity.
OBSERVATION GUIDE
Touchpoints for Observation
Observe a closed loop rotating through projection, crossing marks, over-under relation, and twist direction.
- Use SPIN, CROSS, SURFACE, CROSSING, and WRITHE, then compare TREFOIL, CINQUEFOIL, and UNKNOT.
- OVER and UNDER markers make the projected crossings readable.
- UNKNOT provides a simple loop comparison against tangled traces.
This is a visual knot observation model, not a formal topology proof tool.
Runs inside the browser with no upload and no registration.
SYSTEM NOTE
Torus curve: x=(R+r cos(qt)) cos(pt), y=(R+r cos(qt)) sin(pt), z=r sin(qt). Crossings and writhe are visual projection estimates, not formal topology proof results.
OBSERVATION POLICY
This lab runs in your browser. No image, pointer trace, or input is uploaded by this prototype.
OBSERVATION LOG
Observation logging will be connected with moderation in a later build.