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Quaternion Methods

The Quaternion type exposes the following members.

Methods
  NameDescription
Public methodStatic memberCrossProduct
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.

Public methodStatic memberDistance
Returns the distance or norm of the difference between two quaternions.
Public methodDistanceTo
Computes the distance or norm of the difference between this and another quaternion.
Public methodEpsilonEquals
Check that all values in other are within epsilon of the values in this
Public methodEquals(Object)
Determines whether an object is a quaternion and has the same value of this quaternion.
(Overrides ValueTypeEquals(Object).)
Public methodEquals(Quaternion)
Determines whether this quaternion has the same value of another quaternion.
Public methodGetHashCode
Gets a non-unique but repeatable hashing code for this quaternion.
(Overrides ValueTypeGetHashCode.)
Public methodGetRotation(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).
Public methodGetRotation(Double, Vector3d)
Returns the rotation defined by the quaternion.
Public methodGetType
Gets the Type of the current instance.
(Inherited from Object.)
Public methodInvert
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).

Public methodMatrixForm
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.
Public methodStatic memberProduct
The quaternion product of p and q. This is the same value as p*q.
Public methodRotate
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.
Public methodStatic memberRotation(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.
Public methodStatic memberRotation(Plane, Plane)
Returns the unit quaternion that represents the the rotation that maps plane0.xaxis to plane1.xaxis, plane0.yaxis to plane1.yaxis, and plane0.zaxis to plane1.zaxis.
Public methodSet
Sets all coefficients of the quaternion.
Public methodSetRotation(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.
Public methodSetRotation(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.
Public methodToString
Returns the fully qualified type name of this instance.
(Inherited from ValueType.)
Public methodUnitize
Scales the quaternion's coordinates so that a*a + b*b + c*c + d*d = 1.
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