Comparison operations

Comparing two quaternions can be done component-wise. Two quaternions can represent the same rotation even if they are not identical on a component level. This happens because a quaternion and its inverse rotate to the same spot but they take different routes:

1. Overload the == and != operators in quat.cpp. Add the declaration for these functions to quat.h:

   bool operator==(const quat& left, const quat& right) {

       return (fabsf(left.x - right.x) <= QUAT_EPSILON &&

               fabsf(left.y - right.y) <= QUAT_EPSILON &&

               fabsf(left.z - right.z) <= QUAT_EPSILON &&

               fabsf(left.w - right.w) <= QUAT_EPSILON);

   }

   bool operator!=(const quat& a, const quat& b) {

       return !(a == b);

   }

2. To test whether two quaternions represent the same rotation, the absolute difference between the two needs to be tested. Implement the sameOrientation function in quat.cpp. Add the function declaration to quat.h:

   bool sameOrientation(const quat&l, const quat&r) {

       return (fabsf(l.x - r.x) <= QUAT_EPSILON  &&

               fabsf(l.y - r.y) <= QUAT_EPSILON  &&

               fabsf(l.z - r.z) <= QUAT_EPSILON  &&

               fabsf(l.w - r.w) <= QUAT_EPSILON) ||

              (fabsf(l.x + r.x) <= QUAT_EPSILON  &&

               fabsf(l.y + r.y) <= QUAT_EPSILON  &&

               fabsf(l.z + r.z) <= QUAT_EPSILON  &&

               fabsf(l.w + r.w) <= QUAT_EPSILON);

   }

Most of the time, you will want to use the equality operator to compare quaternions. The sameOrientation function is not as useful because the rotation that a quaternion takes can be changed if the quaternion is inverted.

In the next section, you will learn how to implement a quaternion dot product.