Implementing dual quaternions
In this section, you will implement dual quaternions in code. By the end of this section, you will have implemented a dual quaternion struct, along with all the mathematical functions needed for using dual quaternions to skin a mesh.
Dual quaternions need to be implemented as structures, similar to transforms or matrices. Create two new files, DualQuaternion.h and DualQuaternion.cpp. You will implement the math relevant to dual quaternions in these files.
Start by declaring a DualQuaternion structure. This structure will allow you to access the data in the dual quaternion struct as two quaternions or a floating-point array of eight numbers. The constructor should set the dual quaternion to identity. The identity dual quaternion has an identity quaternion in its real part and a zero quaternion in its dual part, as illustrated in the following code block:
struct DualQuaternion {
    union {
      ...
