Cheap way of calculating cubic bezier length

Question

An analytical solution for cubic bezier length seems not to exist, but it does not mean that coding a cheap solution does not exist. By cheap I mean something like in the rang

Answer 1

public float FastArcLength()
{
    float arcLength = 0.0f;
    ArcLengthUtil(cp0.position, cp1.position, cp2.position, cp3.position, 5, ref arcLength);
    return arcLength;
}

private void ArcLengthUtil(Vector3 A, Vector3 B, Vector3 C, Vector3 D, uint subdiv, ref float L)
{
    if (subdiv > 0)
    {
        Vector3 a = A + (B - A) * 0.5f;
        Vector3 b = B + (C - B) * 0.5f;
        Vector3 c = C + (D - C) * 0.5f;
        Vector3 d = a + (b - a) * 0.5f;
        Vector3 e = b + (c - b) * 0.5f;
        Vector3 f = d + (e - d) * 0.5f;

        // left branch
        ArcLengthUtil(A, a, d, f, subdiv - 1, ref L);
        // right branch
        ArcLengthUtil(f, e, c, D, subdiv - 1, ref L);
    }
    else
    {
        float controlNetLength = (B-A).magnitude + (C - B).magnitude + (D - C).magnitude;
        float chordLength = (D - A).magnitude;
        L += (chordLength + controlNetLength) / 2.0f;
    }
}