We have a wheel with radius R and the center in origin.
A wire is wrapped tightly around the wheel.
The wire is wrapped off the wheel while being kept tight.
Simulate the path of the end of the wire.
The coordinates of the end point P after beeing wrapped off an angle t, is given by:
x = R[cos(t) + tsin(t)]
y = R[sin(t) - tcos(t)]
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