Unit quaternions

Quaternions can be normalized just like vectors. Normalized quaternions represent only a rotation and non-normalized quaternions introduce a skew. In the context of game animation, quaternions should be normalized to avoid adding a skew to the transform.

To normalize a quaternion, divide each component of the quaternion by its length. The resulting quaternion's length will be 1. This can be implemented as follows:

1. Implement the normalize function in quat.cpp and declare it in quat.h:

   void normalize(quat& q) {
      float lenSq = q.x*q.x + q.y*q.y + q.z*q.z + q.w*q.w;
      if (lenSq < QUAT_EPSILON) { 
         return; 
      }
      float i_len = 1.0f / sqrtf(lenSq);
      q.x *= i_len;
      q.y *= i_len;
      q.z *= i_len;
      q.w *= i_len;
   }

2. Implement the normalized function in quat.cpp, and declare it in quat.h:

   quat normalized(const quat& q) {
    ...