Dual-Quaternion-Library-C++

This library was build for Quaternion & Dual Quaternion Calculation Tutorial.

Quaternion::

Name	Type	Description
Create	std::array	Create Quaternion Rotation, Angle in Degree
Conjugate	std::array	Quaternion Conjugate
Normalize	double	Normalize Quaternion , Unit Quaternion = 1
Add	std::array	Add Two Quaternions
Subtract	std::array	Subtract Two Quaternions
Multiply	std::array	Multiply Two Quaternions
MultiplyScalar	std::array	Multiply Quaternion with scalar value

DualQuaternion::

Name	Type	Description
Create	std::array	Create Dual Quaternion Rotation and Translation, Angle in Degree
Rotation	std::array	Return Dual Quaternion Pure Rotation
Translation	std::array	Return Vector Quaternion Translation
Conjugate	std::array	Dual Quaternion Conjugate
Add	std::array	Add Two Dual Quaternions
Subtract	std::array	Subtract Two Dual Quaternions
Multiply	std::array	Multiply Two Dual Quaternions

Quaternion::Create

Create a quaternion rotation based on the equation below :

$q= [cos( \theta /2), d*sin( \theta /2)]$

where :

$q_{s} = cos( \theta /2)$

$q_{v} = d*sin( \theta /2)$

Example :

double Angle = 90; //in Degrees

std::array DirectionOfRotation = {0,1,0};

std::array Quaternion1;

Quaternion1 = Quaternion::Create(Angle,DirectionOfRotation);

Quaternion::Conjugate

Return Quaternion Conjugate based on the equation below :

$q = [cos( \theta /2), -d*sin( \theta /2)]$

Example :

Quaternion::Conjugate(Quaternion1);

Quaternion::Normalize

Return Quaternion Normalize based on the equation below :

$||q|| = \sqrt{q0^{2} + q1^{2} + q2^{2} + q3^{2}}$

Note : Normalize Unit Quaternion will return 1

Example :

Quaternion::Normalize(Quaternion1);

Quaternion::Add

Add two Quaternions (P + Q) based on the equation below :

$p + q = [p_{s} + q_{s},p_{v} + q_{v}]$

Example :

Quaternion::Add(Quaternion1,Quaternion2);

Note :

This library used std::array<>

Any improvment are appreciated