A mathematical construct representing a rotation in 3D space. More...

#include <Quaternion.h>

Public Member Functions
	Quaternion ()
	Default constructor. Initializes the quaternion to identity (1,0,0,0).

	Quaternion (const Quaternion &quaternion)
	Copy constructor. Clones the values of another quaternion.

	Quaternion (const Vector3D &vector)
	Constructs a quaternion purely from a 3D vector (0, X, Y, Z).

	Quaternion (const float &w, const float &x, const float &y, const float &z)
	Constructs a quaternion with individual scalar and vector components.

Vector2D	RotateVector (const Vector2D &v) const
	Rotates a 2D vector by this quaternion, projecting it in 2D.

Vector2D	RotateVectorUnit (const Vector2D &v, const Quaternion &q) const
	Rotates a 2D vector by a unit quaternion (assumes normalized), allowing a different quaternion to be used if desired.

Vector2D	UnrotateVector (const Vector2D &coordinate) const
	Applies the inverse of this quaternion's rotation to a 2D vector.

Vector3D	RotateVector (const Vector3D &v) const
	Rotates a 3D vector by this quaternion.

Vector3D	UnrotateVector (const Vector3D &coordinate) const
	Applies the inverse of this quaternion's rotation to a 3D vector.

Vector3D	GetBiVector () const
	Retrieves the bi-vector (X, Y, Z) portion of the quaternion (with W=0).

Vector3D	GetNormal () const
	Retrieves the normal vector part of the quaternion, typically its axis of rotation.

Quaternion	DeltaRotation (const Vector3D &angularVelocity, const float &timeDelta) const
	Computes a small rotation quaternion given an angular velocity and time delta.

Quaternion	Add (const Quaternion &quaternion) const
	Adds two quaternions component-wise.

Quaternion	Subtract (const Quaternion &quaternion) const
	Subtracts a quaternion from this quaternion component-wise.

Quaternion	Multiply (const Quaternion &quaternion) const
	Multiplies (composes) this quaternion with another (order matters).

Quaternion	Multiply (const float &scalar) const
	Scales this quaternion by a scalar factor.

Quaternion	Divide (const Quaternion &quaternion) const
	Divides this quaternion by another quaternion component-wise (not a typical quaternion operation).

Quaternion	Divide (const float &scalar) const
	Divides this quaternion by a scalar.

Quaternion	Power (const Quaternion &exponent) const
	Raises this quaternion to the power of another quaternion (component-wise).

Quaternion	Power (const float &exponent) const
	Raises this quaternion to a scalar power.

Quaternion	Permutate (const Vector3D &permutation) const
	Performs a permutation operation using a 3D vector (custom transform).

Quaternion	Absolute () const
	Returns a quaternion where each component is the absolute value of the original.

Quaternion	AdditiveInverse () const
	Negates each component (an additive inverse).

Quaternion	MultiplicativeInverse () const
	Returns the multiplicative inverse of this quaternion, such that q * q^-1 = identity.

Quaternion	Conjugate () const
	Returns the conjugate of this quaternion (W stays the same, X/Y/Z get negated).

Quaternion	UnitQuaternion () const
	Returns a unit quaternion (normalized) version of this quaternion.

float	Magnitude () const
	Computes the magnitude (length) of this quaternion.

float	DotProduct (const Quaternion &q) const
	Computes the dot product between this quaternion and another.

float	Normal () const
	Computes the quaternion's norm (equivalent to squared magnitude).

bool	IsNaN () const
	Checks if any component of this quaternion is NaN.

bool	IsFinite () const
	Checks if all components are finite.

bool	IsInfinite () const
	Checks if any component is infinite.

bool	IsNonZero () const
	Checks if the quaternion is non-zero (i.e., any component != 0).

bool	IsEqual (const Quaternion &quaternion) const
	Checks if two quaternions are exactly equal (component-wise).

bool	IsClose (const Quaternion &quaternion, const float &epsilon) const
	Checks if two quaternions are nearly equal within a tolerance.

String	ToString () const
	Converts this quaternion to a string representation (e.g. "(W, X, Y, Z)").

bool	operator== (const Quaternion &quaternion) const
	Equality operator. Checks if two quaternions match exactly (component-wise).

bool	operator!= (const Quaternion &quaternion) const
	Inequality operator. Checks if two quaternions differ in any component.

Quaternion	operator= (const Quaternion &quaternion)
	Assignment operator. Copies another quaternion's components to this one.

Quaternion	operator+ (const Quaternion &quaternion) const
	Adds two quaternions (component-wise).

Quaternion	operator- (const Quaternion &quaternion) const
	Subtracts one quaternion from another (component-wise).

Quaternion	operator* (const Quaternion &quaternion) const
	Multiplies (composes) two quaternions.

Quaternion	operator/ (const Quaternion &quaternion) const
	Divides this quaternion by another quaternion, component-wise.

Quaternion	operator/ (const float &value) const
	Divides this quaternion by a scalar.

Static Public Member Functions
static Quaternion	SphericalInterpolation (const Quaternion &q1, const Quaternion &q2, const float &ratio)
	Performs spherical linear interpolation (slerp) between two quaternions.

static Quaternion	Add (const Quaternion &q1, const Quaternion &q2)
	Static convenience function: Adds two quaternions.

static Quaternion	Subtract (const Quaternion &q1, const Quaternion &q2)
	Static convenience function: Subtracts one quaternion from another.

static Quaternion	Multiply (const Quaternion &q1, const Quaternion &q2)
	Static convenience function: Multiplies (composes) two quaternions.

static Quaternion	Divide (const Quaternion &q1, const Quaternion &q2)
	Static convenience function: Divides one quaternion by another (component-wise).

static Quaternion	Power (const Quaternion &q1, const Quaternion &q2)
	Static convenience function: Raises one quaternion to the power of another (component-wise).

static float	DotProduct (const Quaternion &q1, const Quaternion &q2)
	Static convenience function: Computes the dot product of two quaternions.

static Quaternion	Power (const Quaternion &quaternion, const float &exponent)
	Static convenience function: Raises a quaternion to a scalar power.

static Quaternion	Permutate (const Quaternion &quaternion, const Vector3D &vector)
	Static convenience function: Permutates a quaternion with a 3D vector input.

static Quaternion	Absolute (const Quaternion &quaternion)
	Static convenience function: Returns a quaternion with absolute values of its components.

static Quaternion	AdditiveInverse (const Quaternion &quaternion)
	Static convenience function: Returns the additive inverse of a quaternion.

static Quaternion	MultiplicativeInverse (const Quaternion &quaternion)
	Static convenience function: Returns the multiplicative inverse of a quaternion.

static Quaternion	Conjugate (const Quaternion &quaternion)
	Static convenience function: Returns the conjugate of a quaternion.

static Quaternion	UnitQuaternion (const Quaternion &quaternion)
	Static convenience function: Normalizes a quaternion, returning a unit quaternion.

static float	Magnitude (const Quaternion &quaternion)
	Static convenience function: Computes the magnitude of a quaternion.

static float	Normal (const Quaternion &quaternion)
	Static convenience function: Computes the norm (squared magnitude) of a quaternion.

Public Attributes
float	W
	Scalar part of the quaternion.

float	X
	X component of the quaternion's vector part.

float	Y
	Y component of the quaternion's vector part.

float	Z
	Z component of the quaternion's vector part.

Friends
Quaternion	operator* (const float &scalar, const Quaternion &q)
	Scalar multiplication operator (on the left).

Quaternion	operator* (const Quaternion &q, const float &scalar)
	Scalar multiplication operator (on the right).

Detailed Description

A mathematical construct representing a rotation in 3D space.

Quaternions consist of a scalar part (W) and a vector part (X, Y, Z). They allow smooth interpolation (slerp), concatenation of rotations, and are often used to avoid gimbal lock problems that can occur when using Euler angles.

Definition at line 30 of file Quaternion.h.

Constructor & Destructor Documentation

◆ Quaternion() [1/4]

Quaternion ( )

Default constructor. Initializes the quaternion to identity (1,0,0,0).

Definition at line 4 of file Quaternion.cpp.

Referenced by DeltaRotation(), Divide(), Divide(), MultiplicativeInverse(), Multiply(), Multiply(), Permutate(), RotateVector(), RotateVector(), RotateVectorUnit(), UnrotateVector(), and UnrotateVector().

◆ Quaternion() [2/4]

Quaternion ( const Quaternion & quaternion )

Copy constructor. Clones the values of another quaternion.

Parameters

quaternion The quaternion to copy from.

Definition at line 7 of file Quaternion.cpp.

References W, X, Y, and Z.

◆ Quaternion() [3/4]

Quaternion ( const Vector3D & vector )

Constructs a quaternion purely from a 3D vector (0, X, Y, Z).

Parameters

vector The vector that forms the (X, Y, Z) part of the quaternion.

The W component is initialized to 0.0f.

Definition at line 15 of file Quaternion.cpp.

References W, X, Vector3D::X, Y, Vector3D::Y, Z, and Vector3D::Z.

◆ Quaternion() [4/4]

Quaternion	(	const float &	w,
		const float &	x,
		const float &	y,
		const float &	z
	)

Constructs a quaternion with individual scalar and vector components.

Parameters

w	Scalar (real) component.
x	X component of the vector part.
y	Y component of the vector part.
z	Z component of the vector part.

Definition at line 23 of file Quaternion.cpp.

References W, X, Y, and Z.

Member Function Documentation

◆ Absolute() [1/2]

Quaternion Absolute ( ) const

Returns a quaternion where each component is the absolute value of the original.

Returns: A quaternion with absolute-valued components.

Definition at line 292 of file Quaternion.cpp.

References W, X, Y, and Z.

◆ Absolute() [2/2]

Quaternion Absolute ( const Quaternion & quaternion )

static

Static convenience function: Returns a quaternion with absolute values of its components.

Parameters

quaternion The input quaternion.

Returns: A quaternion whose components are the absolute values of quaternion's components.

Definition at line 487 of file Quaternion.cpp.

◆ Add() [1/2]

Quaternion Add	(	const Quaternion &	q1,
		const Quaternion &	q2
	)

static

Static convenience function: Adds two quaternions.

Parameters

q1	The first quaternion.
q2	The second quaternion.

Returns: A new quaternion representing the sum.

Definition at line 455 of file Quaternion.cpp.

◆ Add() [2/2]

Quaternion Add ( const Quaternion & quaternion ) const

Adds two quaternions component-wise.

Parameters

quaternion The quaternion to add to the current one.

Returns: A new quaternion representing the sum.

Definition at line 152 of file Quaternion.cpp.

References W, X, Y, and Z.

Referenced by QuaternionKalmanFilter::Filter(), and operator+().

◆ AdditiveInverse() [1/2]

Quaternion AdditiveInverse ( ) const

Negates each component (an additive inverse).

Returns: A quaternion representing -this.

Definition at line 302 of file Quaternion.cpp.

References W, X, Y, and Z.

◆ AdditiveInverse() [2/2]

Quaternion AdditiveInverse ( const Quaternion & quaternion )

static

Static convenience function: Returns the additive inverse of a quaternion.

Parameters

quaternion The input quaternion.

Returns: A quaternion representing -q.

Definition at line 491 of file Quaternion.cpp.

◆ Conjugate() [1/2]

Quaternion Conjugate ( ) const

Returns the conjugate of this quaternion (W stays the same, X/Y/Z get negated).

Returns: The conjugated quaternion.

Definition at line 322 of file Quaternion.cpp.

References W, X, Y, and Z.

Referenced by SerialInterpreter::GetOrientation(), ObjectAlign::GetTransform(), MultiplicativeInverse(), UnrotateVector(), and UnrotateVector().

◆ Conjugate() [2/2]

Quaternion Conjugate ( const Quaternion & quaternion )

static

Static convenience function: Returns the conjugate of a quaternion.

Parameters

quaternion The input quaternion.

Returns: A quaternion with (W, -X, -Y, -Z).

Definition at line 499 of file Quaternion.cpp.

◆ DeltaRotation()

Quaternion DeltaRotation	(	const Vector3D &	angularVelocity,
		const float &	timeDelta
	)		const

Computes a small rotation quaternion given an angular velocity and time delta.

Parameters

angularVelocity	A 3D vector representing the angular velocity (e.g., degrees/sec or radians/sec).
timeDelta	The time step.

Returns: A new quaternion representing the rotation over the given time delta.

Definition at line 136 of file Quaternion.cpp.

References Mathematics::EPSILON, Quaternion(), UnitQuaternion(), W, X, Y, and Z.

Referenced by BNO055::Update().

◆ Divide() [1/3]

Quaternion Divide ( const float & scalar ) const

Divides this quaternion by a scalar.

Parameters

scalar The scalar divisor.

Returns: A new quaternion scaled by the reciprocal of scalar.

Definition at line 240 of file Quaternion.cpp.

References Mathematics::EPSILON, Mathematics::IsClose(), Quaternion(), W, X, Y, and Z.

◆ Divide() [2/3]

Quaternion Divide	(	const Quaternion &	q1,
		const Quaternion &	q2
	)

static

Static convenience function: Divides one quaternion by another (component-wise).

Parameters

q1	The first quaternion.
q2	The second quaternion (divisor).

Returns: A new quaternion representing the division result.

Definition at line 467 of file Quaternion.cpp.

◆ Divide() [3/3]

Quaternion Divide ( const Quaternion & quaternion ) const

Divides this quaternion by another quaternion component-wise (not a typical quaternion operation).

Parameters

quaternion The quaternion to divide by.

Returns: A new quaternion representing the component-wise result.

Definition at line 228 of file Quaternion.cpp.

References Mathematics::EPSILON, Quaternion(), W, X, Y, and Z.

Referenced by operator/(), and operator/().

◆ DotProduct() [1/2]

float DotProduct ( const Quaternion & q ) const

Computes the dot product between this quaternion and another.

Parameters

q	Another quaternion.

Returns: The dot product (W*W' + X*X' + Y*Y' + Z*Z').

Definition at line 349 of file Quaternion.cpp.

References W, X, Y, and Z.

◆ DotProduct() [2/2]

float DotProduct	(	const Quaternion &	q1,
		const Quaternion &	q2
	)

static

Static convenience function: Computes the dot product of two quaternions.

Parameters

q1	The first quaternion.
q2	The second quaternion.

Returns: The scalar dot product.

Definition at line 475 of file Quaternion.cpp.

◆ GetBiVector()

Vector3D GetBiVector ( ) const

Retrieves the bi-vector (X, Y, Z) portion of the quaternion (with W=0).

Returns: A 3D vector representing the (X, Y, Z) parts of this quaternion.

Definition at line 87 of file Quaternion.cpp.

References X, Y, and Z.

◆ GetNormal()

Vector3D GetNormal ( ) const

Retrieves the normal vector part of the quaternion, typically its axis of rotation.

Returns: A 3D vector representing the axis (X, Y, Z).

Definition at line 95 of file Quaternion.cpp.

References RotateVector().

◆ IsClose()

bool IsClose	(	const Quaternion &	quaternion,
		const float &	epsilon
	)		const

Checks if two quaternions are nearly equal within a tolerance.

Parameters

quaternion	The quaternion to compare to.
epsilon	The tolerance for comparison.

Returns: true if each component differs by less than epsilon.

Definition at line 388 of file Quaternion.cpp.

References W, X, Y, and Z.

Referenced by RotateVector(), RotateVector(), RotateVectorUnit(), UnrotateVector(), and UnrotateVector().

◆ IsEqual()

bool IsEqual ( const Quaternion & quaternion ) const

Checks if two quaternions are exactly equal (component-wise).

Parameters

quaternion The quaternion to compare to.

Returns: true if all components match exactly.

Definition at line 379 of file Quaternion.cpp.

References IsNaN(), W, X, Y, and Z.

Referenced by operator!=(), and operator==().

◆ IsFinite()

bool IsFinite ( ) const

Checks if all components are finite.

Returns: true if finite, otherwise false.

Definition at line 364 of file Quaternion.cpp.

References Mathematics::IsInfinite(), W, X, Y, and Z.

◆ IsInfinite()

bool IsInfinite ( ) const

Checks if any component is infinite.

Returns: true if infinite, otherwise false.

Definition at line 369 of file Quaternion.cpp.

References Mathematics::IsFinite(), W, X, Y, and Z.

◆ IsNaN()

bool IsNaN ( ) const

Checks if any component of this quaternion is NaN.

Returns: true if any component is NaN, otherwise false.

Definition at line 359 of file Quaternion.cpp.

References Mathematics::IsNaN(), W, X, Y, and Z.

Referenced by IsEqual().

◆ IsNonZero()

bool IsNonZero ( ) const

Checks if the quaternion is non-zero (i.e., any component != 0).

Returns: true if non-zero, otherwise false.

Definition at line 374 of file Quaternion.cpp.

References W, X, Y, and Z.

◆ Magnitude() [1/2]

float Magnitude ( ) const

Computes the magnitude (length) of this quaternion.

Returns: The magnitude (sqrt(W^2 + X^2 + Y^2 + Z^2)).

Definition at line 344 of file Quaternion.cpp.

References Normal(), and Mathematics::Sqrt().

◆ Magnitude() [2/2]

float Magnitude ( const Quaternion & quaternion )

static

Static convenience function: Computes the magnitude of a quaternion.

Parameters

quaternion The input quaternion.

Returns: The magnitude (length) of quaternion.

Definition at line 507 of file Quaternion.cpp.

◆ MultiplicativeInverse() [1/2]

Quaternion MultiplicativeInverse ( ) const

Returns the multiplicative inverse of this quaternion, such that q * q^-1 = identity.

Returns: The multiplicative inverse.

Definition at line 312 of file Quaternion.cpp.

References Conjugate(), Mathematics::EPSILON, Mathematics::IsClose(), Multiply(), Normal(), and Quaternion().

Referenced by BoundaryCube::Update(), and BoundarySphere::Update().

◆ MultiplicativeInverse() [2/2]

Quaternion MultiplicativeInverse ( const Quaternion & quaternion )

static

Static convenience function: Returns the multiplicative inverse of a quaternion.

Parameters

quaternion The input quaternion.

Returns: A quaternion such that q * q^-1 = identity.

Definition at line 495 of file Quaternion.cpp.

◆ Multiply() [1/3]

Quaternion Multiply ( const float & scalar ) const

Scales this quaternion by a scalar factor.

Parameters

scalar The scalar to multiply.

Returns: A new quaternion scaled by scalar.

Definition at line 215 of file Quaternion.cpp.

References Mathematics::EPSILON, Mathematics::IsClose(), Quaternion(), W, X, Y, and Z.

◆ Multiply() [2/3]

Quaternion Multiply	(	const Quaternion &	q1,
		const Quaternion &	q2
	)

static

Static convenience function: Multiplies (composes) two quaternions.

Parameters

q1	The first quaternion.
q2	The second quaternion.

Returns: The resulting quaternion composition.

Definition at line 463 of file Quaternion.cpp.

◆ Multiply() [3/3]

Quaternion Multiply ( const Quaternion & quaternion ) const

Multiplies (composes) this quaternion with another (order matters).

Parameters

quaternion The right-hand side quaternion.

Returns: The resulting quaternion from the multiplication.

Definition at line 172 of file Quaternion.cpp.

References Mathematics::EPSILON, Quaternion(), W, X, Y, and Z.

Referenced by SerialInterpreter::GetOrientation(), ObjectAlign::GetTransform(), MultiplicativeInverse(), operator*(), Rasterizer::Rasterize(), Triangle2D::Triangle2D(), BoundaryCube::Update(), and BoundarySphere::Update().

◆ Normal() [1/2]

float Normal ( ) const

Computes the quaternion's norm (equivalent to squared magnitude).

Returns: (W^2 + X^2 + Y^2 + Z^2).

Definition at line 354 of file Quaternion.cpp.

References Mathematics::Sqrt(), W, X, Y, and Z.

Referenced by Magnitude(), MultiplicativeInverse(), and UnitQuaternion().

◆ Normal() [2/2]

float Normal ( const Quaternion & quaternion )

static

Static convenience function: Computes the norm (squared magnitude) of a quaternion.

Parameters

quaternion The input quaternion.

Returns: The squared length of quaternion.

Definition at line 511 of file Quaternion.cpp.

◆ operator!=()

bool operator!= ( const Quaternion & quaternion ) const

Inequality operator. Checks if two quaternions differ in any component.

Parameters

quaternion The quaternion to compare.

Returns: true if not equal, otherwise false.

Definition at line 410 of file Quaternion.cpp.

References IsEqual().

◆ operator*()

Quaternion operator* ( const Quaternion & quaternion ) const

Multiplies (composes) two quaternions.

Parameters

quaternion The right-hand side quaternion.

Returns: A new quaternion representing the multiplication result.

Definition at line 431 of file Quaternion.cpp.

References Multiply().

◆ operator+()

Quaternion operator+ ( const Quaternion & quaternion ) const

Adds two quaternions (component-wise).

Parameters

quaternion The right-hand side quaternion to add.

Returns: A new quaternion representing the sum.

Definition at line 423 of file Quaternion.cpp.

References Add().

◆ operator-()

Quaternion operator- ( const Quaternion & quaternion ) const

Subtracts one quaternion from another (component-wise).

Parameters

quaternion The right-hand side quaternion to subtract.

Returns: A new quaternion representing the difference.

Definition at line 427 of file Quaternion.cpp.

References Subtract().

◆ operator/() [1/2]

Quaternion operator/ ( const float & value ) const

Divides this quaternion by a scalar.

Parameters

value The scalar divisor.

Returns: A new quaternion scaled by 1.0 / value.

Definition at line 439 of file Quaternion.cpp.

References Divide().

◆ operator/() [2/2]

Quaternion operator/ ( const Quaternion & quaternion ) const

Divides this quaternion by another quaternion, component-wise.

Parameters

quaternion The right-hand side quaternion divisor.

Returns: A new quaternion after division.

Definition at line 435 of file Quaternion.cpp.

References Divide().

◆ operator=()

Quaternion operator= ( const Quaternion & quaternion )

Assignment operator. Copies another quaternion's components to this one.

Parameters

quaternion The quaternion to copy.

Returns: A reference to this quaternion.

Definition at line 414 of file Quaternion.cpp.

References W, X, Y, and Z.

◆ operator==()

bool operator== ( const Quaternion & quaternion ) const

Equality operator. Checks if two quaternions match exactly (component-wise).

Parameters

quaternion The quaternion to compare.

Returns: true if equal, otherwise false.

Definition at line 406 of file Quaternion.cpp.

References IsEqual().

◆ Permutate() [1/2]

Quaternion Permutate	(	const Quaternion &	quaternion,
		const Vector3D &	vector
	)

static

Static convenience function: Permutates a quaternion with a 3D vector input.

Parameters

quaternion	The base quaternion.
vector	A 3D vector used for permutation.

Returns: The permuted quaternion.

Definition at line 483 of file Quaternion.cpp.

◆ Permutate() [2/2]

Quaternion Permutate ( const Vector3D & permutation ) const

Performs a permutation operation using a 3D vector (custom transform).

Parameters

permutation A vector used for permuting the quaternion's components.

Returns: The permuted quaternion.

Definition at line 276 of file Quaternion.cpp.

References Quaternion(), W, X, Y, and Z.

◆ Power() [1/4]

Quaternion Power ( const float & exponent ) const

Raises this quaternion to a scalar power.

Parameters

exponent The exponent (e.g., 2.0f).

Returns: A new quaternion representing this^exponent.

Definition at line 266 of file Quaternion.cpp.

References Mathematics::Pow(), W, X, Y, and Z.

◆ Power() [2/4]

Quaternion Power ( const Quaternion & exponent ) const

Raises this quaternion to the power of another quaternion (component-wise).

Parameters

exponent The quaternion exponent.

Returns: A new quaternion representing the powered result.

Definition at line 256 of file Quaternion.cpp.

References Mathematics::Pow(), W, X, Y, and Z.

◆ Power() [3/4]

Quaternion Power	(	const Quaternion &	q1,
		const Quaternion &	q2
	)

static

Static convenience function: Raises one quaternion to the power of another (component-wise).

Parameters

q1	The base quaternion.
q2	The exponent quaternion.

Returns: A new quaternion representing the power result.

Definition at line 471 of file Quaternion.cpp.

◆ Power() [4/4]

Quaternion Power	(	const Quaternion &	quaternion,
		const float &	exponent
	)

static

Static convenience function: Raises a quaternion to a scalar power.

Parameters

quaternion	The base quaternion.
exponent	The scalar exponent.

Returns: A new quaternion representing the power result.

Definition at line 479 of file Quaternion.cpp.

◆ RotateVector() [1/2]

Vector2D RotateVector ( const Vector2D & v ) const

Rotates a 2D vector by this quaternion, projecting it in 2D.

This method uses quaternion-based rotation to transform a 2D vector.

Mathematical formulation:

\[ s_2 = 2 \cdot w \]

\[ d_{PUV} = 2 \cdot (x \cdot v_x + y \cdot v_y) \]

\[ d_{PUU} = w^2 - (x^2 + y^2 + z^2) \]

The rotated vector is computed as:

\[ v'_x = x \cdot d_{PUV} + v_x \cdot d_{PUU} + (-z \cdot v_y) \cdot s_2 \]

\[ v'_y = y \cdot d_{PUV} + v_y \cdot d_{PUU} + (z \cdot v_x) \cdot s_2 \]

Resulting in:

\[ \vec{v'} = (v'_x, v'_y) \]

Parameters

v	The 2D vector to rotate.

Returns: A new 2D vector that has been rotated.

Note: If the quaternion is close to zero (no rotation), the input vector is returned unchanged.

Definition at line 31 of file Quaternion.cpp.

References Mathematics::EPSILON, IsClose(), Quaternion(), UnitQuaternion(), X, and Y.

Referenced by ObjectAlign::AlignObjects(), ObjectAlign::AlignObjectsNoScale(), GetNormal(), ObjectAlign::GetObjectPlanarityRatio(), SpiralMaterial::GetRGB(), Rotation::GetRotationMatrix(), ObjectAlign::GetTransform(), UnrotateVector(), UnrotateVector(), BoundaryCube::Update(), BoundarySphere::Update(), and Object3D::UpdateTransform().

◆ RotateVector() [2/2]

Vector3D RotateVector ( const Vector3D & v ) const

Rotates a 3D vector by this quaternion.

Parameters

v	The 3D vector to rotate.

Returns: A new 3D vector that has been rotated.

Definition at line 68 of file Quaternion.cpp.

References Mathematics::EPSILON, IsClose(), Quaternion(), and UnitQuaternion().

◆ RotateVectorUnit()

Vector2D RotateVectorUnit	(	const Vector2D &	v,
		const Quaternion &	q
	)		const

Rotates a 2D vector by a unit quaternion (assumes normalized), allowing a different quaternion to be used if desired.

Parameters

v	The 2D vector to rotate.
q	The (unit) quaternion to apply for the rotation.

Returns: A new 2D vector that has been rotated using q.

Definition at line 47 of file Quaternion.cpp.

References Mathematics::EPSILON, IsClose(), Quaternion(), X, and Y.

◆ SphericalInterpolation()

Quaternion SphericalInterpolation	(	const Quaternion &	q1,
		const Quaternion &	q2,
		const float &	ratio
	)

static

Performs spherical linear interpolation (slerp) between two quaternions.

Parameters

q1	The start quaternion.
q2	The end quaternion.
ratio	A normalized value (0 to 1) indicating how far to interpolate from `q1` to `q2`.

Returns: A new quaternion representing the slerped result.

Definition at line 100 of file Quaternion.cpp.

References Mathematics::EPSILON.

Referenced by QuaternionKalmanFilter::Filter(), and BNO055::Update().

◆ Subtract() [1/2]

Quaternion Subtract	(	const Quaternion &	q1,
		const Quaternion &	q2
	)

static

Static convenience function: Subtracts one quaternion from another.

Parameters

q1	The first quaternion.
q2	The second quaternion to subtract from `q1`.

Returns: A new quaternion representing the difference.

Definition at line 459 of file Quaternion.cpp.

◆ Subtract() [2/2]

Quaternion Subtract ( const Quaternion & quaternion ) const

Subtracts a quaternion from this quaternion component-wise.

Parameters

quaternion The quaternion to subtract.

Returns: A new quaternion representing the difference.

Definition at line 162 of file Quaternion.cpp.

References W, X, Y, and Z.

Referenced by operator-().

◆ ToString()

String ToString ( ) const

Converts this quaternion to a string representation (e.g. "(W, X, Y, Z)").

Returns: A String displaying the quaternion's components.

Definition at line 396 of file Quaternion.cpp.

References Mathematics::DoubleToCleanString(), W, X, Y, and Z.

◆ UnitQuaternion() [1/2]

Quaternion UnitQuaternion ( ) const

Returns a unit quaternion (normalized) version of this quaternion.

Returns: A normalized quaternion.

Definition at line 332 of file Quaternion.cpp.

References Normal(), W, X, Y, and Z.

Referenced by CameraLayout::CalculateTransform(), DeltaRotation(), Rotation::DirectionAngleToQuaternion(), QuaternionKalmanFilter::Filter(), Rotation::GetDirectionAngle(), RotateVector(), RotateVector(), UnrotateVector(), and BNO055::Update().

◆ UnitQuaternion() [2/2]

Quaternion UnitQuaternion ( const Quaternion & quaternion )

static

Static convenience function: Normalizes a quaternion, returning a unit quaternion.

Parameters

quaternion The input quaternion.

Returns: A normalized quaternion.

Definition at line 503 of file Quaternion.cpp.

◆ UnrotateVector() [1/2]

Vector2D UnrotateVector ( const Vector2D & coordinate ) const

Applies the inverse of this quaternion's rotation to a 2D vector.

Parameters

coordinate The 2D vector to transform.

Returns: The unrotated 2D vector.

Definition at line 61 of file Quaternion.cpp.

References Conjugate(), Mathematics::EPSILON, IsClose(), Quaternion(), and RotateVector().

Referenced by ObjectAlign::NormalizeObjectPlane(), and Triangle2D::Triangle2D().

◆ UnrotateVector() [2/2]

Vector3D UnrotateVector ( const Vector3D & coordinate ) const

Applies the inverse of this quaternion's rotation to a 3D vector.

Parameters

coordinate The 3D vector to transform.

Returns: The unrotated 3D vector.

Definition at line 80 of file Quaternion.cpp.

References Conjugate(), Mathematics::EPSILON, IsClose(), Quaternion(), RotateVector(), and UnitQuaternion().

Friends And Related Symbol Documentation

◆ operator* [1/2]

Quaternion operator*	(	const float &	scalar,
		const Quaternion &	q
	)

friend

Scalar multiplication operator (on the left).

Parameters

scalar	The scalar to multiply.
q	The quaternion to scale.

Returns: A new quaternion scaled by scalar.

Definition at line 444 of file Quaternion.cpp.

◆ operator* [2/2]

Quaternion operator*	(	const Quaternion &	q,
		const float &	scalar
	)

friend

Scalar multiplication operator (on the right).

Parameters

q	The quaternion to scale.
scalar	The scalar to multiply.

Returns: A new quaternion scaled by scalar.

Definition at line 448 of file Quaternion.cpp.

Member Data Documentation

◆ W

float W

Scalar part of the quaternion.

Definition at line 32 of file Quaternion.h.

Referenced by Absolute(), Add(), AdditiveInverse(), Conjugate(), DeltaRotation(), Divide(), Divide(), DotProduct(), IsClose(), IsEqual(), IsFinite(), IsInfinite(), IsNaN(), IsNonZero(), Multiply(), Multiply(), Normal(), operator=(), Permutate(), Power(), Power(), Quaternion(), Quaternion(), Quaternion(), Subtract(), ToString(), and UnitQuaternion().

◆ X

float X

X component of the quaternion's vector part.

Definition at line 33 of file Quaternion.h.

Referenced by Absolute(), Add(), AdditiveInverse(), Conjugate(), DeltaRotation(), Divide(), Divide(), DotProduct(), GetBiVector(), IsClose(), IsEqual(), IsFinite(), IsInfinite(), IsNaN(), IsNonZero(), Multiply(), Multiply(), Normal(), operator=(), Permutate(), Power(), Power(), Quaternion(), Quaternion(), Quaternion(), RotateVector(), RotateVectorUnit(), Subtract(), ToString(), and UnitQuaternion().

◆ Y

float Y

Y component of the quaternion's vector part.

Definition at line 34 of file Quaternion.h.

Referenced by Absolute(), Add(), AdditiveInverse(), Conjugate(), DeltaRotation(), Divide(), Divide(), DotProduct(), GetBiVector(), IsClose(), IsEqual(), IsFinite(), IsInfinite(), IsNaN(), IsNonZero(), Multiply(), Multiply(), Normal(), operator=(), Permutate(), Power(), Power(), Quaternion(), Quaternion(), Quaternion(), RotateVector(), RotateVectorUnit(), Subtract(), ToString(), and UnitQuaternion().

◆ Z

float Z

Z component of the quaternion's vector part.

Definition at line 35 of file Quaternion.h.

Referenced by Absolute(), Add(), AdditiveInverse(), Conjugate(), DeltaRotation(), Divide(), Divide(), DotProduct(), GetBiVector(), IsClose(), IsEqual(), IsFinite(), IsInfinite(), IsNaN(), IsNonZero(), Multiply(), Multiply(), Normal(), operator=(), Permutate(), Power(), Power(), Quaternion(), Quaternion(), Quaternion(), Subtract(), ToString(), and UnitQuaternion().

The documentation for this class was generated from the following files:

Public Member Functions

Static Public Member Functions

Public Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Quaternion() [1/4]

◆ Quaternion() [2/4]

◆ Quaternion() [3/4]

◆ Quaternion() [4/4]

Member Function Documentation

◆ Absolute() [1/2]

◆ Absolute() [2/2]

◆ Add() [1/2]

◆ Add() [2/2]

◆ AdditiveInverse() [1/2]

◆ AdditiveInverse() [2/2]

◆ Conjugate() [1/2]

◆ Conjugate() [2/2]

◆ DeltaRotation()

◆ Divide() [1/3]

◆ Divide() [2/3]

◆ Divide() [3/3]

◆ DotProduct() [1/2]

◆ DotProduct() [2/2]

◆ GetBiVector()

◆ GetNormal()

◆ IsClose()

◆ IsEqual()

◆ IsFinite()

◆ IsInfinite()

◆ IsNaN()

◆ IsNonZero()

◆ Magnitude() [1/2]

◆ Magnitude() [2/2]

◆ MultiplicativeInverse() [1/2]

◆ MultiplicativeInverse() [2/2]

◆ Multiply() [1/3]

◆ Multiply() [2/3]

◆ Multiply() [3/3]

◆ Normal() [1/2]

◆ Normal() [2/2]

◆ operator!=()

◆ operator*()

◆ operator+()

◆ operator-()

◆ operator/() [1/2]

◆ operator/() [2/2]

◆ operator=()

◆ operator==()

◆ Permutate() [1/2]

◆ Permutate() [2/2]

◆ Power() [1/4]

◆ Power() [2/4]

◆ Power() [3/4]

◆ Power() [4/4]

◆ RotateVector() [1/2]

◆ RotateVector() [2/2]

◆ RotateVectorUnit()

◆ SphericalInterpolation()

◆ Subtract() [1/2]

◆ Subtract() [2/2]

◆ ToString()

◆ UnitQuaternion() [1/2]

◆ UnitQuaternion() [2/2]

◆ UnrotateVector() [1/2]

◆ UnrotateVector() [2/2]

Friends And Related Symbol Documentation

◆ operator* [1/2]

◆ operator* [2/2]

Member Data Documentation

◆ W

◆ X

◆ Y

◆ Z