Length and squared length

Like vectors, the squared length of a quaternion is the same as the dot product of the quaternion with itself. The length of a quaternion is the square root of the square length:

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

   float lenSq(const quat& q) {
     return q.x * q.x + q.y * q.y + q.z * q.z + q.w * q.w;
   }

2. Implement the len function in quat.cpp. Don't forget to add the function declaration to quat.h:

   float len(const 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 0.0f;
     }
     return sqrtf(lenSq);
   }

Quaternions that represent a rotation should always have a length of 1. In the next section, you will learn about unit quaternions, which always have a length of 1.