Why standard linear interpolation (Lerp) gets flagged by behavioral analysis:

Linear interpolation produces constant velocity with sharp angular inflection points on direction changes. Natural human hand movements follow smooth bell-curve acceleration profiles.

Catmull-Rom Spline Formula:

Vector2 CatmullRom(Vector2 p0, Vector2 p1, Vector2 p2, Vector2 p3, float t) {
    float t2 = t * t;
    float t3 = t2 * t;
    return 0.5f * ( (2.0f * p1) +
                    (-p0 + p2) * t +
                    (2.0f * p0 - 5.0f * p1 + 4.0f * p2 - p3) * t2 +
                    (-p0 + 3.0f * p1 - 3.0f * p2 + p3) * t3 );
}

Generates organic, curved aim paths that perfectly mimic professional FPS players.

Adding randomized micro-overshoot at t = 0.9 and correcting back to center at t = 1.0 makes it indistinguishable from human hand aim.

Great math breakdown. Essential for modern aimbot smoothing engines.