pub struct UnitQuaternion<T>(/* private fields */);
Expand description
A quaternion with norm $1$.
Unit quaternions form a non-commutative group that can be conveniently used
for rotating 3D vectors. A 3D vector can be interpreted as a pure
quaternion (a quaternion with a real part of zero). Such a pure quaternion
$v$ can be rotated in 3D space by computing $q^{-1} \cdot v \cdot q$ for a
unit quaternion $q$. The resulting product is again a pure quaternion,
which is $v$ rotated around the axis given by the imaginary part of $q$.
The method rotate_vector
performs this
operation efficiently. The angle of rotation is double the angle between
$1$ and $q$ interpreted as 4D vectors.
You can create a UnitQuaternion
by normalizing a Quaternion
using the
Quaternion::normalize
method. Alternatively, you
can use from_euler_angles
,
from_rotation_vector
, or
from_rotation_matrix3x3
to
obtain one. The inverse functions
to_euler_angles
,
to_rotation_vector
, and
to_rotation_matrix3x3
are also
provided.
UnitQuaternion
offers the same arithmetic operations as Quaternion
.
Multiplying two unit quaternions yields a unit quaternion in theory.
However, due to limited machine precision, rounding errors accumulate
in practice and the resulting norm may deviate from $1$ over time.
Thus, when you multiply unit quaternions many times, you may need
to adjust the norm to maintain accuracy. This can be done by calling
the function adjust_norm
.
Furthermore, you can interpolate uniformly between two quaternions using
the slerp
method, which stands for spherical
linear interpolation. This can be used for smooth transitions between
3D rotations.
See also Quaternion
.
§Examples
Basic usage:
// Creating a UnitQuaternion from Euler angles
let (roll, pitch, yaw) = (1.5, 1.0, 3.0);
let uq = UnitQuaternion::from_euler_angles(roll, pitch, yaw);
// Rotating a vector using the UnitQuaternion
let vector = [1.0, 0.0, 0.0];
let rotated_vector = uq.rotate_vector(vector);
Implementations§
Source§impl<T> UnitQuaternion<T>where
T: Float,
impl<T> UnitQuaternion<T>where
T: Float,
Sourcepub fn from_euler_angles(roll: T, pitch: T, yaw: T) -> Self
pub fn from_euler_angles(roll: T, pitch: T, yaw: T) -> Self
Creates a new Quaternion from roll, pitch and yaw angles.
§Example
let uq = UnitQuaternion::from_euler_angles(1.5, 1.0, 3.0);
Sourcepub fn from_euler_angles_struct(angles: EulerAngles<T>) -> Self
pub fn from_euler_angles_struct(angles: EulerAngles<T>) -> Self
Creates a new Quaternion from Euler angles.
Note. The reason that this function is marked as unstable
is that I’m not 100%
confident about the naming of the function.
§Example
let angles = EulerAngles { roll: 1.5, pitch: 1.0, yaw: 3.0 };
let uq = UnitQuaternion::from_euler_angles_struct(angles);
Source§impl<T> UnitQuaternion<T>where
T: Float + FloatConst,
impl<T> UnitQuaternion<T>where
T: Float + FloatConst,
Sourcepub fn to_euler_angles(&self) -> EulerAngles<T>
pub fn to_euler_angles(&self) -> EulerAngles<T>
Converts the UnitQuaternion to roll, pitch, and yaw angles.
§Example
let uq = UnitQuaternion::from_euler_angles(1.5, 1.0, 3.0);
let angles = uq.to_euler_angles();
Source§impl<T> UnitQuaternion<T>where
T: Float,
impl<T> UnitQuaternion<T>where
T: Float,
Sourcepub fn from_rotation_vector(v: &[T; 3]) -> Self
pub fn from_rotation_vector(v: &[T; 3]) -> Self
Returns a quaternion from a vector which is parallel to the rotation axis and whose norm is the rotation angle.
This function is the inverse of
to_rotation_vector
.
The results of this function may not be accurate, if the input has a
very large norm. If the input vector is not finite (i. e. it contains
an infinite or NaN
component), then the result is filled with NaN
.
§Example
let v = [1.0, 0.0, 0.0];
let uq = UnitQuaternion::from_rotation_vector(&v);
Source§impl<T> UnitQuaternion<T>where
T: Float + FloatConst,
impl<T> UnitQuaternion<T>where
T: Float + FloatConst,
Sourcepub fn to_rotation_vector(&self) -> [T; 3]
pub fn to_rotation_vector(&self) -> [T; 3]
Returns a rotation vector which is parallel to the rotation axis and whose norm is the rotation angle.
This function is the inverse of
from_rotation_vector
.
§Example
let uq = UnitQuaternion::from_euler_angles(1.5, 1.0, 3.0);
let v = uq.to_rotation_vector();
Source§impl<T> UnitQuaternion<T>
impl<T> UnitQuaternion<T>
Sourcepub fn to_rotation_matrix3x3(self) -> [T; 9]
pub fn to_rotation_matrix3x3(self) -> [T; 9]
Computes the rotation matrix implied by a unit quaternion.
The matrix is returned in row major order, i. e. the indices into the result array yield the elements in the following order:
[0, 1, 2,
3, 4, 5,
6, 7, 8]
Multiplying by the returned matrix gives the same result as using
rotate_vector
modulo slightly
different rounding errors.
§Runtime Considerations
The matrix multiplication itself can be assumed to be more runtime
efficient than rotate_vector
.
However, computing the matrix also comes with additional cost. Thus
general advice is: Use rotate_vector
,
if you want to rotate a single vector. Perform the matrix
multiplication, if more than one vector needs to be rotated.
§Example
let uq = UQ64::I;
let matrix = uq.to_rotation_matrix3x3();
Source§impl<T> UnitQuaternion<T>where
T: Float,
impl<T> UnitQuaternion<T>where
T: Float,
Sourcepub fn from_rotation_matrix3x3(mat: &impl ReadMat3x3<T>) -> UnitQuaternion<T>
pub fn from_rotation_matrix3x3(mat: &impl ReadMat3x3<T>) -> UnitQuaternion<T>
Computes a quaternion from a 3x3 rotation matrix.
The input matrix $O$ is required to be an actual rotation matrix, i. e. $O^TO$ is the identity matrix and $\det O = 1$ (neglecting floating point rounding errors).
The quaternion solution with non-negative real part is returned. This
function reverses the method
to_rotation_matrix3x3
.
§Example
let matrix = [[0.0, 1.0, 0.0],
[0.0, 0.0, 1.0],
[1.0, 0.0, 0.0]];
let uq = UnitQuaternion::from_rotation_matrix3x3(&matrix);
Source§impl<T> UnitQuaternion<T>where
T: Float,
impl<T> UnitQuaternion<T>where
T: Float,
Sourcepub fn from_two_vectors(a: &[T; 3], b: &[T; 3]) -> UnitQuaternion<T>
pub fn from_two_vectors(a: &[T; 3], b: &[T; 3]) -> UnitQuaternion<T>
Returns a unit quaternion that rotates vector $\vec a$ to vector $\vec b$ with the minimum angle of rotation.
The method rotate_vector
can be used
to apply the rotation. The resulting unit quaternion maps the ray
${t\vec{a} : t > 0}$ to the ray ${t\vec{b} : t > 0}$.
Note that the input vectors neither need to be normalized nor have the same magnitude. In the case where the input vectors point in opposite directions, there are multiple solutions to the problem, and one will be returned. If one (or both) of the input vectors is the zero vector, the unit quaternion $1$ is returned.
§Example
let a = [1.0, 0.0, 0.0];
let b = [0.0, 1.0, 0.0];
let uq = UQ64::from_two_vectors(&a, &b);
let angles = uq.to_euler_angles();
assert!((angles.yaw - std::f64::consts::FRAC_PI_2).abs() < 1e-10);
assert!((angles.pitch).abs() < 1e-10);
assert!((angles.roll).abs() < 1e-10);
Source§impl<T> UnitQuaternion<T>where
T: Float,
impl<T> UnitQuaternion<T>where
T: Float,
Sourcepub fn normalize(q: Quaternion<T>) -> Option<Self>
pub fn normalize(q: Quaternion<T>) -> Option<Self>
Normalizes the quaternion to length $1$.
The sign of the real part will be the same as the sign of the input. If the input quaternion
- is zero, or
- has infinite length, or
- has a
NaN
value,
then None
will be returned.
Note, that it may be more natural to use the method
Quaternion::normalize
instead of this function. Both functions are
equivalent, but the method is more idiomatic in most cases.
§Example
let q = UnitQuaternion::from_euler_angles(1.5, 1.0, 3.0);
let normalized = UnitQuaternion::normalize(q.into_inner());
assert_eq!(normalized, Some(q));
Source§impl<T> UnitQuaternion<T>
impl<T> UnitQuaternion<T>
Sourcepub const ONE: Self
pub const ONE: Self
A constant UnitQuaternion
of value $1$.
See also UnitQuaternion::one
, Quaternion::ONE
.
§Example
assert_eq!(UQ32::ONE, UQ32::one());
Sourcepub const I: Self
pub const I: Self
A constant UnitQuaternion
of value $i$.
See also UnitQuaternion::i
, Quaternion::I
.
§Example
assert_eq!(UQ32::I, UQ32::i());
Sourcepub const J: Self
pub const J: Self
A constant UnitQuaternion
of value $j$.
See also UnitQuaternion::j
, Quaternion::J
.
§Example
assert_eq!(UQ32::J, UQ32::j());
Sourcepub const K: Self
pub const K: Self
A constant UnitQuaternion
of value $k$.
See also UnitQuaternion::k
, Quaternion::K
.
§Example
assert_eq!(UQ32::K, UQ32::k());
Source§impl<T> UnitQuaternion<T>
impl<T> UnitQuaternion<T>
Sourcepub fn one() -> Self
pub fn one() -> Self
Returns the identity quaternion $1$.
See also UnitQuaternion::ONE
, Quaternion::ONE
.
§Example
assert_eq!(UQ32::one().into_inner(), Q32::one());
Sourcepub fn i() -> Self
pub fn i() -> Self
Returns the imaginary unit $i$.
See also UnitQuaternion::I
, Quaternion::i
.
§Example
assert_eq!(UQ32::i().into_inner(), Q32::new(0.0, 1.0, 0.0, 0.0));
Sourcepub fn j() -> Self
pub fn j() -> Self
Returns the imaginary unit $j$.
See also UnitQuaternion::J
, Quaternion::j
.
§Example
assert_eq!(UQ32::j().into_inner(), Q32::new(0.0, 0.0, 1.0, 0.0));
Sourcepub fn k() -> Self
pub fn k() -> Self
Returns the imaginary unit $k$.
See also UnitQuaternion::K
, Quaternion::k
.
§Example
assert_eq!(UQ32::k().into_inner(), Q32::new(0.0, 0.0, 0.0, 1.0));
Source§impl<T> UnitQuaternion<T>
impl<T> UnitQuaternion<T>
Sourcepub fn into_quaternion(self) -> Quaternion<T>
pub fn into_quaternion(self) -> Quaternion<T>
Returns the inner quaternion.
This function does the same as
into_inner
. Client code can decide
which function to use based on the naming preference and context.
§Example
let uq = UQ64::I;
let q = uq.into_quaternion();
assert_eq!(q, Q64::I);
Sourcepub fn into_inner(self) -> Quaternion<T>
pub fn into_inner(self) -> Quaternion<T>
Returns the inner quaternion.
This function does the same as
into_quaternion
. Client code can
decide which function to use based on the naming preference and
context.
§Example
let uq = UQ64::I;
let q = uq.into_inner();
assert_eq!(q, Q64::I);
Sourcepub fn as_quaternion(&self) -> &Quaternion<T>
pub fn as_quaternion(&self) -> &Quaternion<T>
Returns a reference to the inner quaternion.
§Example
let uq = UQ64::I;
let q = uq.as_quaternion();
assert_eq!(q, &Q64::I);
Source§impl<T> UnitQuaternion<T>
impl<T> UnitQuaternion<T>
Source§impl<T> UnitQuaternion<T>
impl<T> UnitQuaternion<T>
Source§impl<T> UnitQuaternion<T>
impl<T> UnitQuaternion<T>
Source§impl<T> UnitQuaternion<T>where
T: Float,
impl<T> UnitQuaternion<T>where
T: Float,
Sourcepub fn adjust_norm(self) -> Self
pub fn adjust_norm(self) -> Self
Renormalizes self
.
By many multiplications of unit quaternions, round off errors can lead to norms which are deviating from $1$ significantly. This function fixes that inaccuracy.
§Panics
Panics if the norm of the quaternion is too inaccurate to be renormalized.
§Example
let uq = UnitQuaternion::from_euler_angles(1.5, 1.0, 3.0);
let adjusted = uq.adjust_norm();
assert!((adjusted - uq).norm() < 1e-10);
Source§impl<T> UnitQuaternion<T>
impl<T> UnitQuaternion<T>
Sourcepub fn rotate_vector(self, vector: [T; 3]) -> [T; 3]
pub fn rotate_vector(self, vector: [T; 3]) -> [T; 3]
Rotates a vector using a quaternion.
Given a unit quaternion $q$ and a pure quaternion $v$ (i. e. a quaternion with real part zero), the mapping $v \mapsto q^*vq$ is a 3D rotation in the space of pure quaternions. This function performs this 3D rotation efficiently.
§Example
let uq = UQ64::I;
let rotated = uq.rotate_vector([1.0, 2.0, 3.0]);
assert_eq!(rotated, [1.0, -2.0, -3.0]);
Source§impl<T> UnitQuaternion<T>where
T: Float,
impl<T> UnitQuaternion<T>where
T: Float,
Sourcepub fn slerp(&self, other: &Self, t: T) -> Self
pub fn slerp(&self, other: &Self, t: T) -> Self
Spherical linear interpolation between two unit quaternions.
t
should be in the range [0, 1], where 0 returns self
and 1 returns
other
or -other
, whichever is closer to self
.
§Example
let uq1 = UnitQuaternion::from_euler_angles(1.5, 1.0, 3.0);
let uq2 = UnitQuaternion::from_euler_angles(0.5, 2.0, 1.0);
let uq = uq1.slerp(&uq2, 0.5);
Source§impl<T> UnitQuaternion<T>where
T: Float + FloatConst,
impl<T> UnitQuaternion<T>where
T: Float + FloatConst,
Sourcepub fn sqrt(self) -> Self
pub fn sqrt(self) -> Self
Computes the square root of a unit quaternion.
Given an input unit quaternion $c$, this function returns the unit quaternion $q$ which satisfies $q^2 = c$ and has a real part with a positive sign.
For $c = -1$, there are multiple solutions to these constraints. In that case $q = \pm i$ is returned. The sign is determined by the input coefficient of the imaginary unit $i$.
In any case, the three imaginary parts of the result have the same sign as the three imaginary parts of the input.
§Example
let uq = UnitQuaternion::from_euler_angles(1.5, 1.0, 3.0);
let sqrt = uq.sqrt();
assert!((sqrt * sqrt - uq).norm() < 1e-10);
Source§impl<T> UnitQuaternion<T>where
T: Float + FloatConst,
impl<T> UnitQuaternion<T>where
T: Float + FloatConst,
Sourcepub fn ln(self) -> PureQuaternion<T>
pub fn ln(self) -> PureQuaternion<T>
Computes the natural logarithm of a unit quaternion.
The function implements the following guarantees for extreme input values:
- The function is continuous onto the branch cut taking into account the sign of the coefficient of $i$.
- For all quaternions $q$ it holds
q.conj().ln() == q.ln().conj()
. - The signs of the coefficients of the imaginary parts of the outputs
are equal to the signs of the respective coefficients of the inputs.
This also holds for signs of zeros, but not for
NaNs
. - If the input has a
NaN
value, then the result isNaN
in all components.
§Example
let q = Quaternion::new(1.0f32, 2.0, 3.0, 4.0).normalize().unwrap();
let ln_q = q.ln();
Trait Implementations§
Source§impl<T> Add<&PureQuaternion<T>> for &UnitQuaternion<T>
impl<T> Add<&PureQuaternion<T>> for &UnitQuaternion<T>
Source§type Output = <UnitQuaternion<T> as Add<PureQuaternion<T>>>::Output
type Output = <UnitQuaternion<T> as Add<PureQuaternion<T>>>::Output
+
operator.Source§impl<T> Add<&PureQuaternion<T>> for UnitQuaternion<T>
impl<T> Add<&PureQuaternion<T>> for UnitQuaternion<T>
Source§type Output = <UnitQuaternion<T> as Add<PureQuaternion<T>>>::Output
type Output = <UnitQuaternion<T> as Add<PureQuaternion<T>>>::Output
+
operator.Source§impl<T> Add<&Quaternion<T>> for &UnitQuaternion<T>
impl<T> Add<&Quaternion<T>> for &UnitQuaternion<T>
Source§type Output = <UnitQuaternion<T> as Add<Quaternion<T>>>::Output
type Output = <UnitQuaternion<T> as Add<Quaternion<T>>>::Output
+
operator.Source§impl<T> Add<&Quaternion<T>> for UnitQuaternion<T>
impl<T> Add<&Quaternion<T>> for UnitQuaternion<T>
Source§type Output = <UnitQuaternion<T> as Add<Quaternion<T>>>::Output
type Output = <UnitQuaternion<T> as Add<Quaternion<T>>>::Output
+
operator.Source§impl<T> Add<&T> for &UnitQuaternion<T>
impl<T> Add<&T> for &UnitQuaternion<T>
Source§impl<T> Add<&T> for UnitQuaternion<T>
impl<T> Add<&T> for UnitQuaternion<T>
Source§impl<T> Add<&UnitQuaternion<T>> for &PureQuaternion<T>
impl<T> Add<&UnitQuaternion<T>> for &PureQuaternion<T>
Source§type Output = <PureQuaternion<T> as Add<UnitQuaternion<T>>>::Output
type Output = <PureQuaternion<T> as Add<UnitQuaternion<T>>>::Output
+
operator.Source§impl<T> Add<&UnitQuaternion<T>> for &Quaternion<T>
impl<T> Add<&UnitQuaternion<T>> for &Quaternion<T>
Source§type Output = <Quaternion<T> as Add<UnitQuaternion<T>>>::Output
type Output = <Quaternion<T> as Add<UnitQuaternion<T>>>::Output
+
operator.Source§impl<T> Add<&UnitQuaternion<T>> for &UnitQuaternion<T>
impl<T> Add<&UnitQuaternion<T>> for &UnitQuaternion<T>
Source§impl<T> Add<&UnitQuaternion<T>> for PureQuaternion<T>
impl<T> Add<&UnitQuaternion<T>> for PureQuaternion<T>
Source§type Output = <PureQuaternion<T> as Add<UnitQuaternion<T>>>::Output
type Output = <PureQuaternion<T> as Add<UnitQuaternion<T>>>::Output
+
operator.Source§impl<T> Add<&UnitQuaternion<T>> for Quaternion<T>
impl<T> Add<&UnitQuaternion<T>> for Quaternion<T>
Source§type Output = <Quaternion<T> as Add<UnitQuaternion<T>>>::Output
type Output = <Quaternion<T> as Add<UnitQuaternion<T>>>::Output
+
operator.Source§impl<T> Add<&UnitQuaternion<T>> for UnitQuaternion<T>
impl<T> Add<&UnitQuaternion<T>> for UnitQuaternion<T>
Source§impl<T> Add<PureQuaternion<T>> for &UnitQuaternion<T>
impl<T> Add<PureQuaternion<T>> for &UnitQuaternion<T>
Source§type Output = <UnitQuaternion<T> as Add<PureQuaternion<T>>>::Output
type Output = <UnitQuaternion<T> as Add<PureQuaternion<T>>>::Output
+
operator.Source§impl<T> Add<PureQuaternion<T>> for UnitQuaternion<T>
impl<T> Add<PureQuaternion<T>> for UnitQuaternion<T>
Source§type Output = Quaternion<T>
type Output = Quaternion<T>
+
operator.Source§impl<T> Add<Quaternion<T>> for &UnitQuaternion<T>
impl<T> Add<Quaternion<T>> for &UnitQuaternion<T>
Source§type Output = <UnitQuaternion<T> as Add<Quaternion<T>>>::Output
type Output = <UnitQuaternion<T> as Add<Quaternion<T>>>::Output
+
operator.Source§impl<T> Add<Quaternion<T>> for UnitQuaternion<T>
impl<T> Add<Quaternion<T>> for UnitQuaternion<T>
Source§type Output = Quaternion<T>
type Output = Quaternion<T>
+
operator.Source§impl<T> Add<T> for &UnitQuaternion<T>
impl<T> Add<T> for &UnitQuaternion<T>
Source§impl<T> Add<T> for UnitQuaternion<T>
impl<T> Add<T> for UnitQuaternion<T>
Source§impl<T> Add<UnitQuaternion<T>> for &PureQuaternion<T>
impl<T> Add<UnitQuaternion<T>> for &PureQuaternion<T>
Source§type Output = <PureQuaternion<T> as Add<UnitQuaternion<T>>>::Output
type Output = <PureQuaternion<T> as Add<UnitQuaternion<T>>>::Output
+
operator.Source§impl<T> Add<UnitQuaternion<T>> for &Quaternion<T>
impl<T> Add<UnitQuaternion<T>> for &Quaternion<T>
Source§type Output = <Quaternion<T> as Add<UnitQuaternion<T>>>::Output
type Output = <Quaternion<T> as Add<UnitQuaternion<T>>>::Output
+
operator.Source§impl<T> Add<UnitQuaternion<T>> for &UnitQuaternion<T>
impl<T> Add<UnitQuaternion<T>> for &UnitQuaternion<T>
Source§impl<T> Add<UnitQuaternion<T>> for PureQuaternion<T>where
T: Add<T, Output = T>,
impl<T> Add<UnitQuaternion<T>> for PureQuaternion<T>where
T: Add<T, Output = T>,
Source§type Output = Quaternion<T>
type Output = Quaternion<T>
+
operator.Source§impl<T> Add<UnitQuaternion<T>> for Quaternion<T>where
T: Add<T, Output = T>,
impl<T> Add<UnitQuaternion<T>> for Quaternion<T>where
T: Add<T, Output = T>,
Source§type Output = Quaternion<T>
type Output = Quaternion<T>
+
operator.Source§fn add(self, rhs: UnitQuaternion<T>) -> Self
fn add(self, rhs: UnitQuaternion<T>) -> Self
+
operation. Read moreSource§impl<T> Add for UnitQuaternion<T>
impl<T> Add for UnitQuaternion<T>
Source§type Output = Quaternion<T>
type Output = Quaternion<T>
+
operator.Source§impl<T> Borrow<Quaternion<T>> for UnitQuaternion<T>
impl<T> Borrow<Quaternion<T>> for UnitQuaternion<T>
Source§fn borrow(&self) -> &Quaternion<T>
fn borrow(&self) -> &Quaternion<T>
Source§impl<T: Clone> Clone for UnitQuaternion<T>
impl<T: Clone> Clone for UnitQuaternion<T>
Source§fn clone(&self) -> UnitQuaternion<T>
fn clone(&self) -> UnitQuaternion<T>
1.0.0 · Source§fn clone_from(&mut self, source: &Self)
fn clone_from(&mut self, source: &Self)
source
. Read moreSource§impl<T> ConstOne for UnitQuaternion<T>
impl<T> ConstOne for UnitQuaternion<T>
Source§impl<T: Debug> Debug for UnitQuaternion<T>
impl<T: Debug> Debug for UnitQuaternion<T>
Source§impl<T> Default for UnitQuaternion<T>
impl<T> Default for UnitQuaternion<T>
Source§impl<'de, T> Deserialize<'de> for UnitQuaternion<T>where
T: Deserialize<'de>,
impl<'de, T> Deserialize<'de> for UnitQuaternion<T>where
T: Deserialize<'de>,
Source§fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>where
D: Deserializer<'de>,
fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>where
D: Deserializer<'de>,
Source§impl<T> Div<&PureQuaternion<T>> for &UnitQuaternion<T>
impl<T> Div<&PureQuaternion<T>> for &UnitQuaternion<T>
Source§type Output = <UnitQuaternion<T> as Div<PureQuaternion<T>>>::Output
type Output = <UnitQuaternion<T> as Div<PureQuaternion<T>>>::Output
/
operator.Source§impl<T> Div<&PureQuaternion<T>> for UnitQuaternion<T>
impl<T> Div<&PureQuaternion<T>> for UnitQuaternion<T>
Source§type Output = <UnitQuaternion<T> as Div<PureQuaternion<T>>>::Output
type Output = <UnitQuaternion<T> as Div<PureQuaternion<T>>>::Output
/
operator.Source§impl<T> Div<&Quaternion<T>> for &UnitQuaternion<T>
impl<T> Div<&Quaternion<T>> for &UnitQuaternion<T>
Source§type Output = <UnitQuaternion<T> as Div<Quaternion<T>>>::Output
type Output = <UnitQuaternion<T> as Div<Quaternion<T>>>::Output
/
operator.Source§impl<T> Div<&Quaternion<T>> for UnitQuaternion<T>
impl<T> Div<&Quaternion<T>> for UnitQuaternion<T>
Source§type Output = <UnitQuaternion<T> as Div<Quaternion<T>>>::Output
type Output = <UnitQuaternion<T> as Div<Quaternion<T>>>::Output
/
operator.Source§impl<T> Div<&T> for &UnitQuaternion<T>
impl<T> Div<&T> for &UnitQuaternion<T>
Source§impl<T> Div<&T> for UnitQuaternion<T>
impl<T> Div<&T> for UnitQuaternion<T>
Source§impl<T> Div<&UnitQuaternion<T>> for &PureQuaternion<T>
impl<T> Div<&UnitQuaternion<T>> for &PureQuaternion<T>
Source§type Output = <PureQuaternion<T> as Div<UnitQuaternion<T>>>::Output
type Output = <PureQuaternion<T> as Div<UnitQuaternion<T>>>::Output
/
operator.Source§impl<T> Div<&UnitQuaternion<T>> for &Quaternion<T>
impl<T> Div<&UnitQuaternion<T>> for &Quaternion<T>
Source§type Output = <Quaternion<T> as Div<UnitQuaternion<T>>>::Output
type Output = <Quaternion<T> as Div<UnitQuaternion<T>>>::Output
/
operator.Source§impl<T> Div<&UnitQuaternion<T>> for &UnitQuaternion<T>
impl<T> Div<&UnitQuaternion<T>> for &UnitQuaternion<T>
Source§impl<T> Div<&UnitQuaternion<T>> for PureQuaternion<T>
impl<T> Div<&UnitQuaternion<T>> for PureQuaternion<T>
Source§type Output = <PureQuaternion<T> as Div<UnitQuaternion<T>>>::Output
type Output = <PureQuaternion<T> as Div<UnitQuaternion<T>>>::Output
/
operator.Source§impl<T> Div<&UnitQuaternion<T>> for Quaternion<T>
impl<T> Div<&UnitQuaternion<T>> for Quaternion<T>
Source§type Output = <Quaternion<T> as Div<UnitQuaternion<T>>>::Output
type Output = <Quaternion<T> as Div<UnitQuaternion<T>>>::Output
/
operator.Source§impl<T> Div<&UnitQuaternion<T>> for UnitQuaternion<T>
impl<T> Div<&UnitQuaternion<T>> for UnitQuaternion<T>
Source§impl<T> Div<PureQuaternion<T>> for &UnitQuaternion<T>
impl<T> Div<PureQuaternion<T>> for &UnitQuaternion<T>
Source§type Output = <UnitQuaternion<T> as Div<PureQuaternion<T>>>::Output
type Output = <UnitQuaternion<T> as Div<PureQuaternion<T>>>::Output
/
operator.Source§impl<T> Div<PureQuaternion<T>> for UnitQuaternion<T>
impl<T> Div<PureQuaternion<T>> for UnitQuaternion<T>
Source§type Output = Quaternion<T>
type Output = Quaternion<T>
/
operator.Source§impl<T> Div<Quaternion<T>> for &UnitQuaternion<T>
impl<T> Div<Quaternion<T>> for &UnitQuaternion<T>
Source§type Output = <UnitQuaternion<T> as Div<Quaternion<T>>>::Output
type Output = <UnitQuaternion<T> as Div<Quaternion<T>>>::Output
/
operator.Source§impl<T> Div<Quaternion<T>> for UnitQuaternion<T>
impl<T> Div<Quaternion<T>> for UnitQuaternion<T>
Source§type Output = Quaternion<T>
type Output = Quaternion<T>
/
operator.Source§impl<T> Div<T> for &UnitQuaternion<T>
impl<T> Div<T> for &UnitQuaternion<T>
Source§impl<T> Div<T> for UnitQuaternion<T>
impl<T> Div<T> for UnitQuaternion<T>
Source§impl<T> Div<UnitQuaternion<T>> for &PureQuaternion<T>
impl<T> Div<UnitQuaternion<T>> for &PureQuaternion<T>
Source§type Output = <PureQuaternion<T> as Div<UnitQuaternion<T>>>::Output
type Output = <PureQuaternion<T> as Div<UnitQuaternion<T>>>::Output
/
operator.Source§impl<T> Div<UnitQuaternion<T>> for &Quaternion<T>
impl<T> Div<UnitQuaternion<T>> for &Quaternion<T>
Source§type Output = <Quaternion<T> as Div<UnitQuaternion<T>>>::Output
type Output = <Quaternion<T> as Div<UnitQuaternion<T>>>::Output
/
operator.Source§impl<T> Div<UnitQuaternion<T>> for &UnitQuaternion<T>
impl<T> Div<UnitQuaternion<T>> for &UnitQuaternion<T>
Source§impl<T> Div<UnitQuaternion<T>> for PureQuaternion<T>
impl<T> Div<UnitQuaternion<T>> for PureQuaternion<T>
Source§type Output = Quaternion<T>
type Output = Quaternion<T>
/
operator.Source§impl<T> Div<UnitQuaternion<T>> for Quaternion<T>
impl<T> Div<UnitQuaternion<T>> for Quaternion<T>
Source§type Output = Quaternion<T>
type Output = Quaternion<T>
/
operator.Source§impl<T> Div for UnitQuaternion<T>
impl<T> Div for UnitQuaternion<T>
Source§type Output = UnitQuaternion<T>
type Output = UnitQuaternion<T>
/
operator.Source§impl<T, S> DivAssign<S> for UnitQuaternion<T>
impl<T, S> DivAssign<S> for UnitQuaternion<T>
Source§fn div_assign(&mut self, other: S)
fn div_assign(&mut self, other: S)
/=
operation. Read moreSource§impl<'a, T> From<&'a UnitQuaternion<T>> for &'a Quaternion<T>
impl<'a, T> From<&'a UnitQuaternion<T>> for &'a Quaternion<T>
Source§fn from(q: &'a UnitQuaternion<T>) -> Self
fn from(q: &'a UnitQuaternion<T>) -> Self
Source§impl<T> From<UnitQuaternion<T>> for Quaternion<T>
impl<T> From<UnitQuaternion<T>> for Quaternion<T>
Source§fn from(q: UnitQuaternion<T>) -> Self
fn from(q: UnitQuaternion<T>) -> Self
Source§impl<T: Hash> Hash for UnitQuaternion<T>
impl<T: Hash> Hash for UnitQuaternion<T>
Source§impl<T> Inv for &UnitQuaternion<T>
impl<T> Inv for &UnitQuaternion<T>
Source§impl<T> Inv for UnitQuaternion<T>
impl<T> Inv for UnitQuaternion<T>
Source§impl<T> Mul<&PureQuaternion<T>> for &UnitQuaternion<T>
impl<T> Mul<&PureQuaternion<T>> for &UnitQuaternion<T>
Source§type Output = <UnitQuaternion<T> as Mul<PureQuaternion<T>>>::Output
type Output = <UnitQuaternion<T> as Mul<PureQuaternion<T>>>::Output
*
operator.Source§impl<T> Mul<&PureQuaternion<T>> for UnitQuaternion<T>
impl<T> Mul<&PureQuaternion<T>> for UnitQuaternion<T>
Source§type Output = <UnitQuaternion<T> as Mul<PureQuaternion<T>>>::Output
type Output = <UnitQuaternion<T> as Mul<PureQuaternion<T>>>::Output
*
operator.Source§impl<T> Mul<&Quaternion<T>> for &UnitQuaternion<T>
impl<T> Mul<&Quaternion<T>> for &UnitQuaternion<T>
Source§type Output = <UnitQuaternion<T> as Mul<Quaternion<T>>>::Output
type Output = <UnitQuaternion<T> as Mul<Quaternion<T>>>::Output
*
operator.Source§impl<T> Mul<&Quaternion<T>> for UnitQuaternion<T>
impl<T> Mul<&Quaternion<T>> for UnitQuaternion<T>
Source§type Output = <UnitQuaternion<T> as Mul<Quaternion<T>>>::Output
type Output = <UnitQuaternion<T> as Mul<Quaternion<T>>>::Output
*
operator.Source§impl<T> Mul<&T> for &UnitQuaternion<T>
impl<T> Mul<&T> for &UnitQuaternion<T>
Source§impl<T> Mul<&T> for UnitQuaternion<T>
impl<T> Mul<&T> for UnitQuaternion<T>
Source§impl<T> Mul<&UnitQuaternion<T>> for &PureQuaternion<T>
impl<T> Mul<&UnitQuaternion<T>> for &PureQuaternion<T>
Source§type Output = <PureQuaternion<T> as Mul<UnitQuaternion<T>>>::Output
type Output = <PureQuaternion<T> as Mul<UnitQuaternion<T>>>::Output
*
operator.Source§impl<T> Mul<&UnitQuaternion<T>> for &Quaternion<T>
impl<T> Mul<&UnitQuaternion<T>> for &Quaternion<T>
Source§type Output = <Quaternion<T> as Mul<UnitQuaternion<T>>>::Output
type Output = <Quaternion<T> as Mul<UnitQuaternion<T>>>::Output
*
operator.Source§impl<T> Mul<&UnitQuaternion<T>> for &UnitQuaternion<T>
impl<T> Mul<&UnitQuaternion<T>> for &UnitQuaternion<T>
Source§impl<T> Mul<&UnitQuaternion<T>> for PureQuaternion<T>
impl<T> Mul<&UnitQuaternion<T>> for PureQuaternion<T>
Source§type Output = <PureQuaternion<T> as Mul<UnitQuaternion<T>>>::Output
type Output = <PureQuaternion<T> as Mul<UnitQuaternion<T>>>::Output
*
operator.Source§impl<T> Mul<&UnitQuaternion<T>> for Quaternion<T>
impl<T> Mul<&UnitQuaternion<T>> for Quaternion<T>
Source§type Output = <Quaternion<T> as Mul<UnitQuaternion<T>>>::Output
type Output = <Quaternion<T> as Mul<UnitQuaternion<T>>>::Output
*
operator.Source§impl<T> Mul<&UnitQuaternion<T>> for UnitQuaternion<T>
impl<T> Mul<&UnitQuaternion<T>> for UnitQuaternion<T>
Source§impl<T> Mul<PureQuaternion<T>> for &UnitQuaternion<T>
impl<T> Mul<PureQuaternion<T>> for &UnitQuaternion<T>
Source§type Output = <UnitQuaternion<T> as Mul<PureQuaternion<T>>>::Output
type Output = <UnitQuaternion<T> as Mul<PureQuaternion<T>>>::Output
*
operator.Source§impl<T> Mul<PureQuaternion<T>> for UnitQuaternion<T>
impl<T> Mul<PureQuaternion<T>> for UnitQuaternion<T>
Source§type Output = Quaternion<T>
type Output = Quaternion<T>
*
operator.Source§impl<T> Mul<Quaternion<T>> for &UnitQuaternion<T>
impl<T> Mul<Quaternion<T>> for &UnitQuaternion<T>
Source§type Output = <UnitQuaternion<T> as Mul<Quaternion<T>>>::Output
type Output = <UnitQuaternion<T> as Mul<Quaternion<T>>>::Output
*
operator.Source§impl<T> Mul<Quaternion<T>> for UnitQuaternion<T>
impl<T> Mul<Quaternion<T>> for UnitQuaternion<T>
Source§type Output = Quaternion<T>
type Output = Quaternion<T>
*
operator.Source§impl<T> Mul<T> for &UnitQuaternion<T>
impl<T> Mul<T> for &UnitQuaternion<T>
Source§impl<T> Mul<T> for UnitQuaternion<T>
impl<T> Mul<T> for UnitQuaternion<T>
Source§impl<T> Mul<UnitQuaternion<T>> for &PureQuaternion<T>
impl<T> Mul<UnitQuaternion<T>> for &PureQuaternion<T>
Source§type Output = <PureQuaternion<T> as Mul<UnitQuaternion<T>>>::Output
type Output = <PureQuaternion<T> as Mul<UnitQuaternion<T>>>::Output
*
operator.Source§impl<T> Mul<UnitQuaternion<T>> for &Quaternion<T>
impl<T> Mul<UnitQuaternion<T>> for &Quaternion<T>
Source§type Output = <Quaternion<T> as Mul<UnitQuaternion<T>>>::Output
type Output = <Quaternion<T> as Mul<UnitQuaternion<T>>>::Output
*
operator.Source§impl<T> Mul<UnitQuaternion<T>> for &UnitQuaternion<T>
impl<T> Mul<UnitQuaternion<T>> for &UnitQuaternion<T>
Source§impl<T> Mul<UnitQuaternion<T>> for PureQuaternion<T>
impl<T> Mul<UnitQuaternion<T>> for PureQuaternion<T>
Source§type Output = Quaternion<T>
type Output = Quaternion<T>
*
operator.Source§impl<T> Mul<UnitQuaternion<T>> for Quaternion<T>
impl<T> Mul<UnitQuaternion<T>> for Quaternion<T>
Source§type Output = Quaternion<T>
type Output = Quaternion<T>
*
operator.Source§impl<T> Mul for UnitQuaternion<T>
impl<T> Mul for UnitQuaternion<T>
Source§type Output = UnitQuaternion<T>
type Output = UnitQuaternion<T>
*
operator.Source§impl<T, S> MulAssign<S> for UnitQuaternion<T>
impl<T, S> MulAssign<S> for UnitQuaternion<T>
Source§fn mul_assign(&mut self, other: S)
fn mul_assign(&mut self, other: S)
*=
operation. Read moreSource§impl<T> Neg for UnitQuaternion<T>where
T: Neg<Output = T>,
impl<T> Neg for UnitQuaternion<T>where
T: Neg<Output = T>,
Source§impl<T> One for UnitQuaternion<T>
impl<T> One for UnitQuaternion<T>
Source§impl<T: PartialEq> PartialEq for UnitQuaternion<T>
impl<T: PartialEq> PartialEq for UnitQuaternion<T>
Source§impl<T> Serialize for UnitQuaternion<T>where
T: Serialize,
impl<T> Serialize for UnitQuaternion<T>where
T: Serialize,
Source§impl<T> Sub<&PureQuaternion<T>> for &UnitQuaternion<T>
impl<T> Sub<&PureQuaternion<T>> for &UnitQuaternion<T>
Source§type Output = <UnitQuaternion<T> as Sub<PureQuaternion<T>>>::Output
type Output = <UnitQuaternion<T> as Sub<PureQuaternion<T>>>::Output
-
operator.Source§impl<T> Sub<&PureQuaternion<T>> for UnitQuaternion<T>
impl<T> Sub<&PureQuaternion<T>> for UnitQuaternion<T>
Source§type Output = <UnitQuaternion<T> as Sub<PureQuaternion<T>>>::Output
type Output = <UnitQuaternion<T> as Sub<PureQuaternion<T>>>::Output
-
operator.Source§impl<T> Sub<&Quaternion<T>> for &UnitQuaternion<T>
impl<T> Sub<&Quaternion<T>> for &UnitQuaternion<T>
Source§type Output = <UnitQuaternion<T> as Sub<Quaternion<T>>>::Output
type Output = <UnitQuaternion<T> as Sub<Quaternion<T>>>::Output
-
operator.Source§impl<T> Sub<&Quaternion<T>> for UnitQuaternion<T>
impl<T> Sub<&Quaternion<T>> for UnitQuaternion<T>
Source§type Output = <UnitQuaternion<T> as Sub<Quaternion<T>>>::Output
type Output = <UnitQuaternion<T> as Sub<Quaternion<T>>>::Output
-
operator.Source§impl<T> Sub<&T> for &UnitQuaternion<T>
impl<T> Sub<&T> for &UnitQuaternion<T>
Source§impl<T> Sub<&T> for UnitQuaternion<T>
impl<T> Sub<&T> for UnitQuaternion<T>
Source§impl<T> Sub<&UnitQuaternion<T>> for &PureQuaternion<T>
impl<T> Sub<&UnitQuaternion<T>> for &PureQuaternion<T>
Source§type Output = <PureQuaternion<T> as Sub<UnitQuaternion<T>>>::Output
type Output = <PureQuaternion<T> as Sub<UnitQuaternion<T>>>::Output
-
operator.Source§impl<T> Sub<&UnitQuaternion<T>> for &Quaternion<T>
impl<T> Sub<&UnitQuaternion<T>> for &Quaternion<T>
Source§type Output = <Quaternion<T> as Sub<UnitQuaternion<T>>>::Output
type Output = <Quaternion<T> as Sub<UnitQuaternion<T>>>::Output
-
operator.Source§impl<T> Sub<&UnitQuaternion<T>> for &UnitQuaternion<T>
impl<T> Sub<&UnitQuaternion<T>> for &UnitQuaternion<T>
Source§impl<T> Sub<&UnitQuaternion<T>> for PureQuaternion<T>
impl<T> Sub<&UnitQuaternion<T>> for PureQuaternion<T>
Source§type Output = <PureQuaternion<T> as Sub<UnitQuaternion<T>>>::Output
type Output = <PureQuaternion<T> as Sub<UnitQuaternion<T>>>::Output
-
operator.Source§impl<T> Sub<&UnitQuaternion<T>> for Quaternion<T>
impl<T> Sub<&UnitQuaternion<T>> for Quaternion<T>
Source§type Output = <Quaternion<T> as Sub<UnitQuaternion<T>>>::Output
type Output = <Quaternion<T> as Sub<UnitQuaternion<T>>>::Output
-
operator.Source§impl<T> Sub<&UnitQuaternion<T>> for UnitQuaternion<T>
impl<T> Sub<&UnitQuaternion<T>> for UnitQuaternion<T>
Source§impl<T> Sub<PureQuaternion<T>> for &UnitQuaternion<T>
impl<T> Sub<PureQuaternion<T>> for &UnitQuaternion<T>
Source§type Output = <UnitQuaternion<T> as Sub<PureQuaternion<T>>>::Output
type Output = <UnitQuaternion<T> as Sub<PureQuaternion<T>>>::Output
-
operator.Source§impl<T> Sub<PureQuaternion<T>> for UnitQuaternion<T>
impl<T> Sub<PureQuaternion<T>> for UnitQuaternion<T>
Source§type Output = Quaternion<T>
type Output = Quaternion<T>
-
operator.Source§impl<T> Sub<Quaternion<T>> for &UnitQuaternion<T>
impl<T> Sub<Quaternion<T>> for &UnitQuaternion<T>
Source§type Output = <UnitQuaternion<T> as Sub<Quaternion<T>>>::Output
type Output = <UnitQuaternion<T> as Sub<Quaternion<T>>>::Output
-
operator.Source§impl<T> Sub<Quaternion<T>> for UnitQuaternion<T>
impl<T> Sub<Quaternion<T>> for UnitQuaternion<T>
Source§type Output = Quaternion<T>
type Output = Quaternion<T>
-
operator.Source§impl<T> Sub<T> for &UnitQuaternion<T>
impl<T> Sub<T> for &UnitQuaternion<T>
Source§impl<T> Sub<T> for UnitQuaternion<T>
impl<T> Sub<T> for UnitQuaternion<T>
Source§impl<T> Sub<UnitQuaternion<T>> for &PureQuaternion<T>
impl<T> Sub<UnitQuaternion<T>> for &PureQuaternion<T>
Source§type Output = <PureQuaternion<T> as Sub<UnitQuaternion<T>>>::Output
type Output = <PureQuaternion<T> as Sub<UnitQuaternion<T>>>::Output
-
operator.Source§impl<T> Sub<UnitQuaternion<T>> for &Quaternion<T>
impl<T> Sub<UnitQuaternion<T>> for &Quaternion<T>
Source§type Output = <Quaternion<T> as Sub<UnitQuaternion<T>>>::Output
type Output = <Quaternion<T> as Sub<UnitQuaternion<T>>>::Output
-
operator.Source§impl<T> Sub<UnitQuaternion<T>> for &UnitQuaternion<T>
impl<T> Sub<UnitQuaternion<T>> for &UnitQuaternion<T>
Source§impl<T> Sub<UnitQuaternion<T>> for PureQuaternion<T>
impl<T> Sub<UnitQuaternion<T>> for PureQuaternion<T>
Source§type Output = Quaternion<T>
type Output = Quaternion<T>
-
operator.Source§impl<T> Sub<UnitQuaternion<T>> for Quaternion<T>where
T: Sub<T, Output = T>,
impl<T> Sub<UnitQuaternion<T>> for Quaternion<T>where
T: Sub<T, Output = T>,
Source§type Output = Quaternion<T>
type Output = Quaternion<T>
-
operator.Source§fn sub(self, rhs: UnitQuaternion<T>) -> Self
fn sub(self, rhs: UnitQuaternion<T>) -> Self
-
operation. Read moreSource§impl<T> Sub for UnitQuaternion<T>
impl<T> Sub for UnitQuaternion<T>
Source§type Output = Quaternion<T>
type Output = Quaternion<T>
-
operator.