Hello, when using quaternions for rotations I faced a problem: when I interpolate between two quaternions with different axes the path of the rotated object is buckled. Example: when I have a rotation with axis = (0, 0, 1) and 90 degree and rotate to (1, 0, 0) and 180 degree I run through the inbetween states (1/3, 0, 2/3), 120 and (2/3, 0, 1/3), 150. Thus the path of the rotation is not straight.. I interpolate between the two quaternions by interpolating the angle and the axis independently and then creating a new quaternion from the result. I thought about the problem and came to the conclusion that this follows directly from the involved math. It seems to be a consequence of the interpolation between both axes. Has anyone an idea how to fix this? [Edited by - cmdkeen on May 19, 2008 8:32:08 PM]

Actually, you want to use Spherical Linear Interpolation (SLERP), which is (conveniently) exactly what interpolating the quaternion directly does.

There''s a great quaternion article on Gamasutra:

http://www.gamasutra.com/features/19980703/quaternions_01.htm

Good luck

Something like this:

inline void EQuat::SLerp(EQuat *out, EQuat *q2, float ratio){  float  omega, cosom, sinom, scale0, scale1;  // calc cosine  cosom = x * q2->x + y * q2->y + z * q2->z + w * q2->w;  // adjust signs (if necessary)  if ( cosom < 0.0 )  {    cosom = -cosom;    scale1 = -1.0f;  }  else  {    scale1 = 1.0f;  }  if ( (1.0 - cosom) > 0.0001f/*DELTA*/ )  {    // standard case (slerp)    omega = acosf(cosom);    sinom = sinf(omega);    scale0 = sinf((1.0f - ratio) * omega) / sinom;    scale1 *= sinf(ratio * omega) / sinom;  }  else  {            // "from" and "to" quaternions are very close     //  ... so we can do a linear interpolation    scale0 = 1.0f - ratio;    scale1 *= ratio;  }  // calculate final values  out->x = (EFloat) (scale0 * x + scale1 * q2->x);  out->y = (EFloat) (scale0 * y + scale1 * q2->y);  out->z = (EFloat) (scale0 * z + scale1 * q2->z);  out->w = (EFloat) (scale0 * w + scale1 * q2->w);}

Thanks for your replies, guys. I''ll try it this evening

[Edited by - cmdkeen on May 19, 2008 8:56:39 PM]

And if you use it only for animation you can try the linear interpolation (it is approximately like SLERP), it is a lot faster.

inline xxquaternion lerp_unit(const xxquaternion& q1, const xxquaternion& q2, float t ){
xxquaternion r;
float inner = q1.x*q2.x + q1.y*q2.y + q1.z*q2.z +q1.w*q2.w;
if(inner < 0 ){
r = q1 - (q2+q1)*t;
}else{
r = q1 + (q2-q1)*t;
}
r.normalize();
return r;
}