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class Quaternion

Defined in:  TSQuaternion.h
The Quaternion class encapsulates a quaternion.
Definition

class Quaternion

Member Functions
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 represent 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.
Data Members
float   x; The x coordinate of the vector part.
float   y; The y coordinate of the vector part.
float   z; The z coordinate of the vector part.
float   w; The w coordinate, which is the scalar part.
Constructor

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);

Description
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.
Overloaded Operators
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.
Nonmember Operations
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.
bool operator ==(const Quaternion& q1, const Quaternion& q2); Returns a boolean value indicating the equality of the two quaternions q1 and q2.
bool operator ==(const Quaternion& q, const Vector3D& v); Returns a boolean value indicating the equality of the quaternion q and the vector v.
bool operator ==(const Vector3D& v, const Quaternion& q); Returns a boolean value indicating the equality of the vector v and the quaternion q.
bool operator ==(const Quaternion& q, float s); Returns a boolean value indicating the equality of the quaternion q and the scalar s.
bool operator ==(float s, const Quaternion& q); Returns a boolean value indicating the equality of the scalar a and the quaternion q.
bool operator !=(const Quaternion& q1, const Quaternion& q2); Returns a boolean value indicating the inequality of the two quaternions q1 and q2.
bool operator !=(const Quaternion& q, const Vector3D& v); Returns a boolean value indicating the inequality of the quaternion q and the vector v.
bool operator !=(const Vector3D& v, const Quaternion& q); Returns a boolean value indicating the inequality of the vector v and the quaternion q.
bool operator !=(const Quaternion& q, float s); Returns a boolean value indicating the inequality of the quaternion q and the scalar s.
bool operator !=(float s, const Quaternion& q); Returns a boolean value indicating the inequality 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 Conjugate(const Quaternion& q); Returns the conjugate of a quaternion.
Quaternion Inverse(const Quaternion& q); Returns the inverse of a quaternion.
See Also

Vector3D

Matrix3D