Tes::Maths::Quaternion Struct Reference

A quaternion implementation for applying 3D rotations. More...

List of all members.

Public Member Functions
	Quaternion (float x, float y, float z, float w)
	Initialise a quaternion with the given component values.
	Quaternion (Vector3 axis, float angle)
	Initialise a quaternion using an axis and an angle.
void	SetFromTo (Vector3 from, Vector3 to)
	Initialise this quaternion as the rotation between from and to .
void	GetAxisAngle (ref Vector3 axis, ref float angle)
	Converts this quaternion into a axis of rotation and the rotation angle around that axis (radians).
void	SetAxisAngle (Vector3 axis, float angle)
	Sets this quaternion from an axis of rotation and the angle of rotation about that axis (radians).
void	Invert ()
	Inverts this quaternion so that it expresses the counter rotation to its current value.
void	Conjugate ()
	Sets this quaternion to its conjugate.
float	Normalise (float epsilon=Epsilon)
	Attempts to normalise this quaternion.
float	Dot (Quaternion other)
	Calculates the dot product of this and other .
Vector3	Transform (Vector3 v)
	Transforms v by this quaternion rotation.
void	Multiply (float scalar)
	Multiply all components of this quaternion by a scalar.
override bool	Equals (object obj)
	Compare two quaternions for precise numeric equality.
override int	GetHashCode ()
	Generates a simple hash code for the quaternion.
Static Public Member Functions
static Quaternion	FromTo (Vector3 from, Vector3 to)
	Static method for constructing a quaternion as a rotation between from and to .
static Quaternion	AxisAngle (Vector3 axis, float angle)
	Creates a quaternion from an axis an angle.
static Quaternion	Slerp (Quaternion from, Quaternion to, float t)
	Performs a spherical linear interpolation of one quaternion to another.
static bool	operator== (Quaternion a, Quaternion b)
	Compare two quaternions for precise numeric equality.
static bool	operator!= (Quaternion a, Quaternion b)
	Compare two quaternions for inequality using precise numeric equality.
static Quaternion	operator* (Quaternion a, Quaternion b)
	Transform (rotate) one quaternion by another.
static Vector3	operator* (Quaternion q, Vector3 v)
	Transform (rotate) a vector by a quaternion.
static Quaternion	operator* (Quaternion q, float s)
	Multiply a quaternion by a scalar.
static Quaternion	operator* (float s, Quaternion q)
	Multiply a quaternion by a scalar.
static Quaternion	operator/ (Quaternion q, float s)
	Divide a quaternion by a scalar.
Public Attributes
const float	Epsilon = 1e-6f
	Default epsilon value used in various calculations.
Static Public Attributes
static Quaternion	Identity = new Quaternion { X = 0, Y = 0, Z = 0, W = 1 }
	The identity quaternion (0, 0, 0, 1).
static Quaternion	Zero = new Quaternion { X = 0, Y = 0, Z = 0, W = 0 }
	A zero quaternion (0, 0, 0, 0).
Properties
float	X [get, set]
	The quaternion X component.
float	Y [get, set]
	The quaternion Y component.
float	Z [get, set]
	The quaternion Z component.
float	W [get, set]
	The quaternion W component.
float	this[int index] [get, set]
	Indexing accessor.
bool	IsZero [get]
	Is this quaternion exactly zero (0, 0, 0, 0)?
bool	IsIdentity [get]
	Is this quaternion exactly identity (0, 0, 0, 1)?
float	Magnitude [get]
	Returns the magnitude of this quaternion.
float	MagnitudeSquared [get]
	Returns the magnitude squared of this quaternion.
Quaternion	Inverse [get]
	Calculates and returns the inverse, or counter rotation, of this quaternion.
Quaternion	Conjugated [get]
	Calculates and returns the conjugate of this quaternion.
Quaternion	normalised [get]
	Returns a normalised copy of this quaternion.

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Detailed Description

A quaternion implementation for applying 3D rotations.

See Wikipedia or Wolfram MathWorld for technical details on quaternions.

Note that all angles expressed by this class are in radians.

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Constructor & Destructor Documentation

Tes::Maths::Quaternion::Quaternion	(	float	x,
		float	y,
		float	z,
		float	w
	)		[inline]

Initialise a quaternion with the given component values.

Parameters:

x	X component value.
y	Y component value.
z	Z component value.
w	W component value.

Tes::Maths::Quaternion::Quaternion	(	Vector3	axis,
		float	angle
	)		[inline]

Initialise a quaternion using an axis and an angle.

Parameters:

axis	The quaternion rotation axis. Must be a unity vector for well defined behaviour.
angle	The rotation angle around axis (radians).

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Member Function Documentation

static Quaternion Tes::Maths::Quaternion::AxisAngle	(	Vector3	axis,
		float	angle
	)		[inline, static]

Creates a quaternion from an axis an angle.

This provides a static alternative to SetAxisAngle(Vector3, float).

Parameters:

axis	The axis of rotation. Must be a unit vector.
angle	The rotation angle around axis (radians).

Returns:

The quaternion expressing the desired axis rotation.

void Tes::Maths::Quaternion::Conjugate

(

)

[inline]

Sets this quaternion to its conjugate.

The conjugate is the same quaternion with x, y, z values negated, but w remains as is.

float Tes::Maths::Quaternion::Dot

(

Quaternion

other

)

[inline]

Calculates the dot product of

this

and other .

Returns:

The dot product.

override bool Tes::Maths::Quaternion::Equals

(

object

obj

)

[inline]

Compare two quaternions for precise numeric equality.

Parameters:

obj	The quaternion to compare to.

Returns:

True if the quaternions are precisely equal.

Exceptions:

InvalidCastException

When obj is not a Quaternion.

static Quaternion Tes::Maths::Quaternion::FromTo	(	Vector3	from,
		Vector3	to
	)		[inline, static]

Static method for constructing a quaternion as a rotation between from and to .

Parameters:

from	The vector to rotate from. Should ideally be normalised.
to	The vector to rotate to. Should ideally be normalised.

Returns:

The rotation quaternion between the given vectors.

void Tes::Maths::Quaternion::GetAxisAngle	(	ref Vector3	axis,
		ref float	angle
	)		[inline]

Converts this quaternion into a axis of rotation and the rotation angle around that axis (radians).

Parameters:

angle	Set to the rotation angle (radians). Zero if this quaternion is identity.
axis	Set to the axis of rotation. Set to (0, 0, 1) if this quaternion is identity or near zero length.

override int Tes::Maths::Quaternion::GetHashCode

(

)

[inline]

Generates a simple hash code for the quaternion.

Not a very good hash.

Returns:

The hash code for this quaternion.

void Tes::Maths::Quaternion::Multiply

(

float

scalar

)

[inline]

Multiply all components of this quaternion by a scalar.

Generally not a very useful operation for a quaternion as quaternions should stay normalised.

Parameters:

scalar

The scalar to multiply the vector components by.

float Tes::Maths::Quaternion::Normalise

(

float

epsilon = Epsilon

)

[inline]

Attempts to normalise this quaternion.

Normalisation fails if the length of this quaternion is less than or equal to epsilon . In this case, the quaternion becomes identity.

Returns:

The magnitude of this quaternion before normalisation or zero if normalisation failed.

static bool Tes::Maths::Quaternion::operator!=	(	Quaternion	a,
		Quaternion	b
	)		[inline, static]

Compare two quaternions for inequality using precise numeric equality.

Parameters:

a	A quaternion to compare.
b	A quaternion to compare.

Returns:

True if the quaternions are not precisely equal.

static Vector3 Tes::Maths::Quaternion::operator*	(	Quaternion	q,
		Vector3	v
	)		[inline, static]

Transform (rotate) a vector by a quaternion.

Parameters:

q	The quaternion to rotate by.
v	The vector to rotate.

Returns:

The vector v rotated by q .

static Quaternion Tes::Maths::Quaternion::operator*	(	float	s,
		Quaternion	q
	)		[inline, static]

Multiply a quaternion by a scalar.

Not a very useful operation for a quaternion as they should stay normalised. Provided for completeness.

Parameters:

s	The scalar to multiply by.
q	The quaternion to operate on.

Returns:

The scaled quaternion.

static Quaternion Tes::Maths::Quaternion::operator*	(	Quaternion	a,
		Quaternion	b
	)		[inline, static]

Transform (rotate) one quaternion by another.

The resulting quaternion represents a combined rotation, applying b then a .

Parameters:

a	The quaternion to rotate by.
b	The quaternion to rotate

Returns:

The quaternion a rotated by b .

static Quaternion Tes::Maths::Quaternion::operator*	(	Quaternion	q,
		float	s
	)		[inline, static]

Multiply a quaternion by a scalar.

Not a very useful operation for a quaternion as they should stay normalised. Provided for completeness.

Parameters:

q	The quaternion to operate on.
s	The scalar to multiply by.

Returns:

The scaled quaternion.

static Quaternion Tes::Maths::Quaternion::operator/	(	Quaternion	q,
		float	s
	)		[inline, static]

Divide a quaternion by a scalar.

Not a very useful operation for a quaternion as they should stay normalised. Provided for completeness.

Parameters:

q	The quaternion to operate on.
s	The scalar to divide by.

Returns:

The scaled quaternion.

static bool Tes::Maths::Quaternion::operator==	(	Quaternion	a,
		Quaternion	b
	)		[inline, static]

Compare two quaternions for precise numeric equality.

Parameters:

a	A quaternion to compare.
b	A quaternion to compare.

Returns:

True if the quaternions are precisely equal.

void Tes::Maths::Quaternion::SetAxisAngle	(	Vector3	axis,
		float	angle
	)		[inline]

Sets this quaternion from an axis of rotation and the angle of rotation about that axis (radians).

Parameters:

axis	The axis of rotation. Must be a unit vector.
angle	The rotation angle around axis (radians).

void Tes::Maths::Quaternion::SetFromTo	(	Vector3	from,
		Vector3	to
	)		[inline]

Initialise this quaternion as the rotation between from and to .

Parameters:

from	The vector to rotate from. Should ideally be normalised.
to	The vector to rotate to. Should ideally be normalised.

static Quaternion Tes::Maths::Quaternion::Slerp	(	Quaternion	from,
		Quaternion	to,
		float	t
	)		[inline, static]

Performs a spherical linear interpolation of one quaternion to another.

This results in a quaternion which rotates partway between from and to .

This is an ambiguity in rotation when from and to are exactly opposed and the resulting quaternion is not well defined.

Parameters:

from	The quaternion rotation to interpolate from.
to	The quaternion rotation to interpolate to.
t	The interpolation "time", [0, 1]. Zero selects from while one selects to .

Returns:

The interpolated result.

Vector3 Tes::Maths::Quaternion::Transform

(

Vector3

v

)

[inline]

Transforms v by this quaternion rotation.

The transformation signifies a rotation of v by this quaternion.

Returns:

The transformed vector.

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Property Documentation

Quaternion Tes::Maths::Quaternion::Conjugated [get]

Calculates and returns the conjugate of this quaternion.

The conjugate is the same quaternion with x, y, z values negated, but w remains as is.

Returns:

This quaternion's conjugate.

Quaternion Tes::Maths::Quaternion::Inverse [get]

Calculates and returns the inverse, or counter rotation, of this quaternion.

Returns:

The inverse of this quaternion.

bool Tes::Maths::Quaternion::IsIdentity [get]

Is this quaternion exactly identity (0, 0, 0, 1)?

bool Tes::Maths::Quaternion::IsZero [get]

Is this quaternion exactly zero (0, 0, 0, 0)?

Quaternion Tes::Maths::Quaternion::normalised [get]

Returns a normalised copy of this quaternion.

Normalisation fails if the length of this quaternion is less than or equal to epsilon.

Returns:

A normalised copy of this quaternion, or a zero quaternion if if normalisation failed.

float Tes::Maths::Quaternion::this[int index] [get, set]

Indexing accessor.

Indexes X, Y, Z, W across the range [0, 3].

Parameters:

index

The component index [0, 3].

Returns:

The requested component.

Exceptions:

IndexOutOfRangeException

Thrown when index is out of range.

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The documentation for this struct was generated from the following file:

• Quaternion.cs