public static Quaternion Slerp(double t, Quaternion p, Quaternion q)
{
var cos = p.Dot(q);
var angle = System.Math.Acos(cos);
if (System.Math.Abs(angle) > 0)
{
var sin = System.Math.Sin(angle);
var invSin = 1 / sin;
var coeff0 = System.Math.Sin((1 - t) * angle) * invSin;
var coeff1 = System.Math.Sin(t * angle) * invSin;
return p.Mult(coeff0).Add(q.Mult(coeff1));
}
return p;
}
public static Quaternion SlerpExtraSpins(double t, Quaternion p, Quaternion q, int extraSpins)
{
var cos = p.Dot(q);
var angle = System.Math.Acos(cos);
if (System.Math.Abs(angle) > 0)
{
var sin = System.Math.Sin(angle);
var phase = System.Math.PI * extraSpins * t;
var invSin = 1 / sin;
var coeff0 = System.Math.Sin((1 - t) * angle - phase) * invSin;
var coeff1 = System.Math.Sin(t * angle + phase) * invSin;
return p.Mult(coeff0).Add(q.Mult(coeff1));
}
return p;
}
public static Quaternion Immediate(Quaternion q0, Quaternion q1, Quaternion q2)
{
// assert: Q0, Q1, Q2 all unit-length
var q1inv = q1.Conjugate();
var p0 = q1inv.Mult(q0);
var p2 = q1inv.Mult(q2);
var arg = (p0.Log().Add(p2.Log())).Mult(-0.25);
return q1.Mult(arg.Exp());
}
