class Quaternion

Defined in: C4Quaternion.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::SetRotationAboutX`	Sets a quaternion to represent a rotation about the x axis.
`Quaternion::SetRotationAboutY`	Sets a quaternion to represent a rotation about the y axis.
`Quaternion::SetRotationAboutZ`	Sets a quaternion to represent a rotation about the z axis.
`Quaternion::SetRotationAboutAxis`	Sets a quaternion to represent a rotation about a given axis.
`Quaternion::GetRotationMatrix`	Converts a quaternion to a 3 × 3 matrix.
`Quaternion::GetRotationScaleMatrix`	Converts a quaternion to a 3 × 3 matrix with scale information.
`Quaternion::SetRotationMatrix`	Converts a 3 × 3 matrix to a quaternion.

Data Members

`float x;`	The x coordinate.
`float y;`	The y coordinate.
`float z;`	The z coordinate.
`float w;`	The w coordinate.

Constructor

Quaternion();

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

explicit Quaternion(const Vector3D& v);

Quaternion(const Vector3D& v, float s);

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 components of the quaternion, respectively. The scalar s is always assigned to the real component w, and the components of v are assigned to the imaginary components x, y, and z of the quaternion. If a quaternion is constructed with only the Vector3D object v, then the real component 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

`float& operator [](long k);`	Returns a reference to the `k`-th component of a quaternion. The value of `k` must be 0, 1, 2, or 3.
`const float& operator [](long k) const;`	Returns a constant reference to the `k`-th component of a quaternion. The value of `k` must be 0, 1, 2, or 3.
`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.