Using Garry's Mod to Draw Trochoids

The curve traced by a point on a circle as it rotates and horizontally translates at the same time (rolls on a straight line) is called a trochoid.

I made a machine in Garry's Mod which draws the protate and curtate trochoids of a circle and also shows a cycloid curve.

A protate trochoid is produced when the tracing point is outside of the circumference, while a curtate trochoid is when it is inside the circumference.

The reason to investigate these things is that the trochoid behaviour is akin to simple harmonic motion, and the cycloid is specifically relevant to Snell's Law and the Brachistrochrone problem.

math,physics,snell's law,brachistochrone,trochoid,cycloid,graph,curve,