Quaternion Methods 
The Quaternion type exposes the following members.
Name  Description  

CrossProduct 
Computes the vector cross product of p and q = (0,x,y,z),
where (x,y,z) = CrossProduct(p.Vector,q.Vector). This is not the same as the quaternion product p*q.  
Distance 
Returns the distance or norm of the difference between two quaternions.
 
DistanceTo 
Computes the distance or norm of the difference between this and another quaternion.
 
EpsilonEquals 
Check that all values in other are within epsilon of the values in this
 
Equals(Object) 
Determines whether an object is a quaternion and has the same value of this quaternion.
(Overrides ValueTypeEquals(Object).)  
Equals(Quaternion) 
Determines whether this quaternion has the same value of another quaternion.
 
GetHashCode 
Gets a nonunique but repeatable hashing code for this quaternion.
(Overrides ValueTypeGetHashCode.)  
GetRotation(Plane) 
Returns the frame created by applying the quaternion's rotation
to the canonical world frame (1,0,0),(0,1,0),(0,0,1).
 
GetRotation(Transform) 
Returns a transformation matrix that performs the rotation defined by the quaternion.
The transformation returned by this method has the property that xform * V = q.Rotate(V).
If the quaternion is not unitized, the rotation of its unitized form is returned.
 
GetRotation(Double, Vector3d) 
Returns the rotation defined by the quaternion.
 
GetType  Gets the Type of the current instance. (Inherited from Object.)  
Invert 
Modifies this quaternion to become
(a/L2, b/L2, c/L2, d/L2), where L2 = length squared = (a*a + b*b + c*c + d*d). This is the multiplicative inverse, i.e., (a,b,c,d)*(a/L2, b/L2, c/L2, d/L2) = (1,0,0,0).  
MatrixForm 
Returns 4x4 real valued matrix form of the quaternion
a b c d
b a d c
c d a b
d c b a
which has the same arithmetic properties as the quaternion.
 
Product 
The quaternion product of p and q. This is the same value as p*q.
 
Rotate 
Rotates a 3d vector. This operation is also called conjugation,
because the result is the same as
(q.Conjugate()*(0,x,y,x)*q/q.LengthSquared).Vector.
 
Rotation(Double, Vector3d) 
Returns the unit quaternion
cos(angle/2), sin(angle/2)*x, sin(angle/2)*y, sin(angle/2)*z
where (x,y,z) is the unit vector parallel to axis. This is the
unit quaternion that represents the rotation of angle about axis.
 
Rotation(Plane, Plane) 
Returns the unit quaternion that represents the rotation that maps
plane0.xaxis to plane1.xaxis, plane0.yaxis to plane1.yaxis, and
plane0.zaxis to plane1.zaxis.
 
Set 
Sets all coefficients of the quaternion.
 
SetRotation(Double, Vector3d) 
Sets the quaternion to cos(angle/2), sin(angle/2)*x, sin(angle/2)*y, sin(angle/2)*z
where (x,y,z) is the unit vector parallel to axis. This is the unit quaternion
that represents the rotation of angle about axis.
 
SetRotation(Plane, Plane) 
Sets the quaternion to the unit quaternion which rotates
plane0.xaxis to plane1.xaxis, plane0.yaxis to plane1.yaxis,
and plane0.zaxis to plane1.zaxis.
 
ToString 
Returns a string representation of this Quaternion.
(Overrides ValueTypeToString.)  
Unitize 
Scales the quaternion's coordinates so that a*a + b*b + c*c + d*d = 1.
