class Quaternion

The Quaternion class encapsulates a quaternion.

class Quaternion

Quaternion::Set	Sets all four components of a quaternion.
Quaternion::Normalize	Normalizes a quaternion.
Quaternion::MakeRotationX	Returns a quaternion that represents a rotation about the x axis.
Quaternion::MakeRotationY	Returns a quaternion that represents a rotation about the y axis.
Quaternion::MakeRotationZ	Returns a quaternion that represents a rotation about the z axis.
Quaternion::MakeRotation	Returns a quaternion that represents a rotation about a given axis.
Quaternion::GetRotationMatrix	Converts a quaternion to a 3 × 3 matrix.
Quaternion::SetRotationMatrix	Converts a 3 × 3 matrix to a quaternion.

Component<TypeQuaternion, 4, 0>                 x;	The x coordinate of the bivector part.
Component<TypeQuaternion, 4, 1>                 y;	The y coordinate of the bivector part.
Component<TypeQuaternion, 4, 2>                 z;	The z coordinate of the bivector part.
Component<TypeQuaternion, 4, 3>                 w;	The w coordinate, which is the scalar part.
Subvec3D<TypeQuaternion, true, 4, 0, 1, 2>      xyz;	The x, y, and z coordinates together as a single bivector.

Quaternion();

Quaternion(float a, float b, float c, float s);

Quaternion(const Vector3D& v, float s);

explicit Quaternion(const Vector3D& v);

explicit Quaternion(float s);

The Quaternion class encapsulates a Hamiltonian quaternion having the form xi + yj + zk + w.

The default constructor leaves the components of the quaternion undefined. If the values a, b, c, and s are supplied, then they are assigned to the x, y, z, and w coordinates of the quaternion, respectively. The components of v are assigned to the imaginary components x, y, and z of the quaternion, and the scalar s is assigned to the real component w. If a quaternion is constructed with only the Vector3D object v, then the real coordinate w is set to 0. If a quaternion is constructed with only the scalar s, then the imaginary components x, y, and z are set to 0.

When performing arithmetic with quaternions, 3D vectors are always treated as quaternions with w = 0, and scalars are always treated as quaternions with x,y,z = 0.

Quaternion& operator =(const Vector3D& v);	Assigns the of v to the imaginary components x, y, and z of the quaternion. The real component w is set to 0.
Quaternion& operator =(float s);	Sets the real component w of the quaternion to s, and sets the imaginary components x, y, and z to 0.
Quaternion& operator +=(const Quaternion& q);	Adds the quaternion q.
Quaternion& operator +=(const Vector3D& v);	Adds the vector v.
Quaternion& operator +=(float s);	Adds the scalar s.
Quaternion& operator -=(const Quaternion& q);	Subtracts the quaternion q.
Quaternion& operator -=(const Vector3D& v);	Subtracts the vector v.
Quaternion& operator -=(float s);	Subtracts the scalar s.
Quaternion& operator *=(const Quaternion& q);	Multiplies by the quaternion q.
Quaternion& operator *=(const Vector3D& v);	Multiplies by the vector v.
Quaternion& operator *=(float s);	Multiplies by the scalar s.
Quaternion& operator /=(const Quaternion& q);	Multiplies by the inverse of the quaternion q.
Quaternion& operator /=(const Vector3D& v);	Multiplies by the inverse of the vector v.
Quaternion& operator /=(float s);	Multiplies by the inverse of the scalar s.

bool operator ==(const Quaternion& q1, const Quaternion& q2);	Returns a boolean value indicating whether the two quaternions q1 and q2 are equal.
bool operator ==(const Quaternion& q, const Vector3D& v);	Returns a boolean value indicating whether the quaternion q and the vector v are equal.
bool operator ==(const Vector3D& v, const Quaternion& q);	Returns a boolean value indicating whether the vector v and the quaternion q are equal.
bool operator ==(const Quaternion& q, float s);	Returns a boolean value indicating whether the quaternion q and the scalar s are equal.
bool operator ==(float s, const Quaternion& q);	Returns a boolean value indicating whether the scalar a and the quaternion q are equal.
bool operator !=(const Quaternion& q1, const Quaternion& q2);	Returns a boolean value indicating whether the two quaternions q1 and q2 are not equal.
bool operator !=(const Quaternion& q, const Vector3D& v);	Returns a boolean value indicating whether the quaternion q and the vector v are not equal.
bool operator !=(const Vector3D& v, const Quaternion& q);	Returns a boolean value indicating whether the vector v and the quaternion q are not equal.
bool operator !=(const Quaternion& q, float s);	Returns a boolean value indicating whether the quaternion q and the scalar s are not equal.
bool operator !=(float s, const Quaternion& q);	Returns a boolean value indicating whether the scalar s and the quaternion q are not equal.
Quaternion operator -(const Quaternion& q);	Returns the negation of the quaternion q.
Quaternion operator +(const Quaternion& q1, const Quaternion& q2);	Returns the sum of the quaternions q1 and q2.
Quaternion operator +(const Quaternion& q, const Vector3D& v);	Returns the sum of the quaternion q and the vector v.
Quaternion operator +(const Vector3D& v, const Quaternion& q);	Returns the sum of the vector v and the quaternion q.
Quaternion operator +(const Quaternion& q, float s);	Returns the sum of the quaternion q and the scalar s.
Quaternion operator +(float s, const Quaternion& q);	Returns the sum of the scalar s and the quaternion q.
Quaternion operator -(const Quaternion& q1, const Quaternion& q2);	Returns the difference of the quaternions q1 and q2.
Quaternion operator -(const Quaternion& q, const Vector3D& v);	Returns the difference of the quaternion q and the vector v.
Quaternion operator -(const Vector3D& v, const Quaternion& q);	Returns the difference of the vector v and the quaternion q.
Quaternion operator -(const Quaternion& q, float s);	Returns the difference of the quaternion q and the scalar s.
Quaternion operator -(float s, const Quaternion& q);	Returns the difference of the scalar s and the quaternion q.
Quaternion operator *(const Quaternion& q1, const Quaternion& q2);	Returns the product of the quaternions q1 and q2.
Quaternion operator *(const Quaternion& q, const Vector3D& v);	Returns the product of the quaternion q and the vector v.
Quaternion operator *(const Vector3D& v, const Quaternion& q);	Returns the product of the vector v and the quaternion q.
Quaternion operator *(const Quaternion& q, float s);	Returns the product of the quaternion q and the scalar s.
Quaternion operator *(float s, const Quaternion& q);	Returns the product of the scalar s and the quaternion q.
Quaternion operator /(const Quaternion& q1, const Quaternion& q2);	Returns the quotient of the quaternions q1 and q2.
Quaternion operator /(const Quaternion& q, const Vector3D& v);	Returns the quotient of the quaternion q and of the vector v.
Quaternion operator /(const Vector3D& v, const Quaternion& q);	Returns the quotient of the vector v and the quaternion q.
Quaternion operator /(const Quaternion& q, float s);	Returns the quotient of the quaternion q and the scalar s.
Quaternion operator /(float s, const Quaternion& q);	Returns the quotient of the scalar s and the quaternion q.
float Magnitude(const Quaternion& q);	Returns the magnitude of a quaternion.
float SquaredMag(const Quaternion& q);	Returns the squared magnitude of a quaternion.
Quaternion Reverse(const Quaternion& q);	Returns the reverse of a quaternion.
Quaternion Inverse(const Quaternion& q);	Returns the inverse of a quaternion.
Vector3D Transform(const Vector3D& v, const Quaternion& q);	Transforms the vector v with the quaternion q.

Vector3D

Matrix3D

Motor3D