public static bool SolveCubic(float e, float f, float g, out float t, out float u, out float v)
{
float p, q, h, rc, d, theta, costh3, sinth3;
p = f - (e * e / 3.0f);
q = g - (e * f / 3.0f) + (e * e * e * 2.0f / 27.0f);
h = (q * q / 4.0f) + (p * p * p / 27.0f);
if (h > 0.0f)
{
t = u = v = 0.0f;
return(false); // only one real root
}
// all the same root
if ((h == 0.0f) && (q == 0.0f))
{
t = -e / 3;
u = -e / 3;
v = -e / 3;
return(true);
}
d = (float)Math.Sqrt((q * q / 4.0f) - h);
if (d < 0)
{
rc = (float)-Math.Pow(-d, 1.0f / 3.0f);
}
else
{
rc = (float)Math.Pow(d, 1.0f / 3.0f);
}
theta = XMScalar.ACos(-q / (2.0f * d));
costh3 = XMScalar.Cos(theta / 3.0f);
sinth3 = (float)Math.Sqrt(3.0f) * XMScalar.Sin(theta / 3.0f);
t = (2.0f * rc * costh3) - (e / 3.0f);
u = (-rc * (costh3 + sinth3)) - (e / 3.0f);
v = (-rc * (costh3 - sinth3)) - (e / 3.0f);
return(true);
}