public static quaternion operator *(quaternion a, quaternion b)
{
quaternion r = new quaternion();
r.s = a.s * b.s - (a.v * b.v);
r.v = (a.s * b.v) + (a.v * b.s) + (a.v % b.v);
return r;
}
public vect3d transformPoint(ref vect3d p)
{
vect3d vecTemp = p;
double mag = -(vecTemp * v);
vecTemp = ((vecTemp * s) + ((v % vecTemp)));
quaternion temp = new quaternion(mag, vecTemp);
return (temp * conjugate()).v;
}
quaternion slerp(ref quaternion q1, ref quaternion q2, double t)
{
double[] temp = new double[4];
double omega, cosom, sinom, scale0, scale1;
quaternion rvalue;
// calc cosine
cosom = q1.s * q2.s + q1.v.x * q2.v.x + q1.v.y * q2.v.y + q1.v.z * q2.v.z;
// adjust signs (if necessary)
if (cosom < 0.0)
{
cosom = -1.0 * cosom;
temp[0] = -1.0 * q2.s;
temp[1] = -1.0 * q2.v.x;
temp[2] = -1.0 * q2.v.y;
temp[3] = -1.0 * q2.v.z;
}
else
{
temp[0] = q2.s;
temp[1] = q2.v.x;
temp[2] = q2.v.y;
temp[3] = q2.v.z;
}
// calculate coefficients
if ((1.0 - cosom) > 0.001)
{
// standard case (slerp)
omega = System.Math.Acos(cosom);
sinom = System.Math.Sin(omega);
scale0 = System.Math.Sin((1.0 - t) * omega) / sinom;
scale1 = System.Math.Sin(t * omega) / sinom;
}
else
{
// q1 and q2 are about 1 degree apart so use linear
// interpolation to avoid division by very small numbers
scale0 = 1.0 - t;
scale1 = t;
}
// do the interpolation
rvalue.s = scale0 * q1.s + scale1 * temp[0];
rvalue.v.x = scale0 * q1.v.x + scale1 * temp[1];
rvalue.v.y = scale0 * q1.v.y + scale1 * temp[2];
rvalue.v.z = scale0 * q1.v.z + scale1 * temp[3];
return rvalue;
}