Conjugate and inverse

Games mostly use normalized quaternions, which comes in handy when inverting quaternions. The inverse of a normalized quaternion is its conjugate. The conjugate

of a quaternion flips its axis of rotation:

1. Implement the conjugate function in quat.cpp and remember to declare the function in quat.h:

   quat conjugate(const quat& q) {

       return quat(

           -q.x,

           -q.y,

           -q.z,

            q.w

       );

   }

2. The proper inverse of a quaternion is the conjugate divided by the squared length of the quaternion. Implement the quaternion inverse function in quat.cpp. Add the function declaration to quat.h:

   quat inverse(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 quat();

      }

      float recip = 1.0f / lenSq;

      return quat(-q.x * recip,

                  -q.y * recip,

                  -q.z * recip,

                   q.w * recip

      );

   }

If you need to find out whether a quaternion is normalized or not, check the squared length. The squared length of a normalized quaternion is always 1. If a quaternion is normalized, its conjugate and inverse are the same. This means you can use the faster conjugate function, instead of the inverse function. In the next section, you will learn how to multiply two quaternions together.