Physics for Game Developers, 2nd Edition

Appendix C. Quaternion Operations

This appendix implements a class called Quaternion that encapsulates all of the operations you need to handle quaternions when writing 3D rigid-body simulations.

Quaternion Class

The Quaternion class is defined with a scalar component, n, and vector component, v, where v is the vector, × i + y j + z k. The class has two constructors, one of which initializes the quaternion to 0, and the other of which initializes the elements to those passed to the constructor:

class Quaternion {
public:
     float      n;     // number (scalar) part
     Vector     v;     // vector part: v.x, v.y, v.z

     Quaternion(void);
     Quaternion(float e0, float e1, float e2, float e3);

     float      Magnitude(void);
     Vector     GetVector(void);
     float      GetScalar(void);
     Quaternion operator+=(Quaternion q);
     Quaternion operator-=(Quaternion q);
     Quaternion operator*=(float s);
     Quaternion operator/=(float s);
     Quaternion operator~(void) const { return Quaternion( n,
                                                           -v.x,
                                                           -v.y,
                                                           -v.z);}
};

// Constructor
inline     Quaternion::Quaternion(void)
{
     n   = 0;
     v.x = 0;
     v.y = 0;
     v.z = 0;
}

// Constructor
inline     Quaternion::Quaternion(float e0, float e1, float e2, float e3)
{
     n   = e0;
     v.x = e1;
     v.y = e2;
     v.z = e3;
}

Magnitude

The method Magnitude returns the magnitude of the quaternion according to the following formula:

|q| =

This is similar to calculating the magnitude of a vector except that for quaternions you have to take the fourth term, the ...