Naive uniform r in [0, R] and uniform θ in [0, 2π) clusters points near center — area grows as r², so small radii get overrepresented.

Use inverse transform sampling: r = R × √(rand(0,1)) yields uniform area distribution. Or rejection-sample in bounding square [-R,R]² and reject points where x² + y² > R².

Rejection sampling expected ~π/4 acceptance rate (~78.5%). Polar sqrt method guarantees exactly 1 point per call but requires sin/cos. Both need floating-point precision.