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Uniform random point in a circle

Naively picking r = R·random() bunches points near the centre, because the disc's area grows with r. The fix is r = R·√random() — sampling r² uniformly cancels the radial area-weighting. Toggle between the two methods to see the difference.

See also: Uniform random point in an annulus — the same idea applied to a ring.

Pseudocode

// Correct: sample r² uniformly
angle = 2π · random()
r     = R · sqrt(random())
x     = cx + r · cos(angle)
y     = cy + r · sin(angle)

Source

function uniformInCircle(cx, cy, R) {
    const angle = 2 * Math.PI * Math.random()
    const r = R * Math.sqrt(Math.random())     // sqrt is the key
    return { x: cx + r * Math.cos(angle), y: cy + r * Math.sin(angle) }
}

// Biased version (don't use): r = R * Math.random() bunches points near centre