Can an involute gear profile be modeled with a Bézier curve? In the context of a game, I want to draw gears. The most common curves available on the platforms I'm using are third degree Bézier curves. Is there an exact representation of the involute gear using only Bézier curves ?

No. From this paper that discusses approximating an involute curve using a 4th degree Bezier:

> The circle involute curves are by definition transcendental and cannot be expressed by algebraic equations