Unfold before measuring
A route that crosses a glued edge becomes an ordinary straight line when enough copies are laid out. Comparing image distances replaces seam bookkeeping with Euclidean geometry.
An atlas of ways out that return
Seam Compass
Drag A or B in the outlined tile. Every pale B is the same destination seen through a different seam; the gold line chooses the nearest lifted copy.
start A
images of B
shortest lift
images of B
shortest lift
Cylinderdistance 0.160winding −1
drag pins · keyboard: A/B then arrows
The destination one tile left is nearer than the destination in the central copy.
Keyboard: focus the map, press A or B to select a pin, then use arrow keys to move it. Hold Shift for fine steps.
Three gluing rules
Cylinder (0,y) ~ (1,y)
Torus also (x,0) ~ (x,1)
Möbius (0,y) ~ (1,1−y)