Unit in nalgebra::base - Rust
Description: A wrapper that ensures the underlying algebraic entity has a unit norm.
Keywords: rust, rustlang, rust-lang, Unit

# Struct nalgebra::base::Unit

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    #[repr(transparent)]pub struct Unit<T> { /* private fields */ }

Expand description

A wrapper that ensures the underlying algebraic entity has a unit norm.

It is likely that the only piece of documentation that you need in this page are:

- The construction with normalization
- Data extraction and construction without normalization
- Interpolation between two unit vectors

All the other impl blocks you will see in this page are about `UnitComplex` and `UnitQuaternion`; both built on top of `Unit`. If you are interested in their documentation, read their dedicated pages directly.

## Implementations§

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### impl<T, D, S> Unit<Vector<T, D, S>>where
T: Scalar,
D: Dim,
S: RawStorage<T, D, U1>,

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#### pub fn cast<T2: Scalar>(self) -> Unit<OVector<T2, D>>where
T: Scalar,
OVector<T2, D>: SupersetOf<Vector<T, D, S>>,
DefaultAllocator: Allocator<T2, D, U1>,

Cast the components of `self` to another type.

##### Example

    let v = Vector3::<f64>::y_axis();
    let v2 = v.cast::<f32>();
    assert_eq!(v2, Vector3::<f32>::y_axis());

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### impl<T: Normed> Unit<T>

#### Construction with normalization

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#### pub fn new_normalize(value: T) -> Self

Normalize the given vector and return it wrapped on a `Unit` structure.

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#### pub fn try_new(value: T, min_norm: T::Norm) -> Option<Self>where
T::Norm: RealField,

Attempts to normalize the given vector and return it wrapped on a `Unit` structure.

Returns `None` if the norm was smaller or equal to `min_norm`.

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#### pub fn new_and_get(value: T) -> (Self, T::Norm)

Normalize the given vector and return it wrapped on a `Unit` structure and its norm.

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#### pub fn try_new_and_get(value: T, min_norm: T::Norm) -> Option<(Self, T::Norm)>where
T::Norm: RealField,

Normalize the given vector and return it wrapped on a `Unit` structure and its norm.

Returns `None` if the norm was smaller or equal to `min_norm`.

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#### pub fn renormalize(&mut self) -> T::Norm

Normalizes this vector again. This is useful when repeated computations might cause a drift in the norm because of float inaccuracies.

Returns the norm before re-normalization. See `.renormalize_fast` for a faster alternative that may be slightly less accurate if `self` drifted significantly from having a unit length.

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#### pub fn renormalize_fast(&mut self)

Normalizes this vector again using a first-order Taylor approximation. This is useful when repeated computations might cause a drift in the norm because of float inaccuracies.

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### impl<T> Unit<T>

#### Data extraction and construction without normalization

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#### pub const fn new_unchecked(value: T) -> Self

Wraps the given value, assuming it is already normalized.

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#### pub fn from_ref_unchecked(value: &T) -> &Self

Wraps the given reference, assuming it is already normalized.

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#### pub fn into_inner(self) -> T

Retrieves the underlying value.

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#### pub fn unwrap(self) -> T

👎Deprecated: use `.into_inner()` instead

Retrieves the underlying value. Deprecated: use `Unit::into_inner` instead.

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#### pub fn as_mut_unchecked(&mut self) -> &mut T

Returns a mutable reference to the underlying value. This is `_unchecked` because modifying the underlying value in such a way that it no longer has unit length may lead to unexpected results.

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### impl<T: RealField, D: Dim, S: Storage<T, D>> Unit<Vector<T, D, S>>

#### Interpolation between two unit vectors

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#### pub fn slerp<S2: Storage<T, D>>(
&self,
rhs: &Unit<Vector<T, D, S2>>,
t: T
) -> Unit<OVector<T, D>>where
DefaultAllocator: Allocator<T, D>,

Computes the spherical linear interpolation between two unit vectors.

##### Examples:

    let v1 = Unit::new_normalize(Vector2::new(1.0, 2.0));
    let v2 = Unit::new_normalize(Vector2::new(2.0, -3.0));

    let v = v1.slerp(&v2, 1.0);

    assert_eq!(v, v2);

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#### pub fn try_slerp<S2: Storage<T, D>>(
&self,
rhs: &Unit<Vector<T, D, S2>>,
t: T,
epsilon: T
) -> Option<Unit<OVector<T, D>>>where
DefaultAllocator: Allocator<T, D>,

Computes the spherical linear interpolation between two unit vectors.

Returns `None` if the two vectors are almost collinear and with opposite direction (in this case, there is an infinity of possible results).

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### impl<T: SimdRealField> Unit<Quaternion<T>>where
T::Element: SimdRealField,

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#### pub fn angle(&self) -> T

The rotation angle in [0; pi] of this unit quaternion.

##### Example

    let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
    let rot = UnitQuaternion::from_axis_angle(&axis, 1.78);
    assert_eq!(rot.angle(), 1.78);

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#### pub fn quaternion(&self) -> &Quaternion<T>

The underlying quaternion.

Same as `self.as_ref()`.

##### Example

    let axis = UnitQuaternion::identity();
    assert_eq!(*axis.quaternion(), Quaternion::new(1.0, 0.0, 0.0, 0.0));

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#### pub fn conjugate(&self) -> Self

Compute the conjugate of this unit quaternion.

##### Example

    let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
    let rot = UnitQuaternion::from_axis_angle(&axis, 1.78);
    let conj = rot.conjugate();
    assert_eq!(conj, UnitQuaternion::from_axis_angle(&-axis, 1.78));

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#### pub fn inverse(&self) -> Self

Inverts this quaternion if it is not zero.

##### Example

    let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
    let rot = UnitQuaternion::from_axis_angle(&axis, 1.78);
    let inv = rot.inverse();
    assert_eq!(rot * inv, UnitQuaternion::identity());
    assert_eq!(inv * rot, UnitQuaternion::identity());

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#### pub fn angle_to(&self, other: &Self) -> T

The rotation angle needed to make `self` and `other` coincide.

##### Example

    let rot1 = UnitQuaternion::from_axis_angle(&Vector3::y_axis(), 1.0);
    let rot2 = UnitQuaternion::from_axis_angle(&Vector3::x_axis(), 0.1);
    assert_relative_eq!(rot1.angle_to(&rot2), 1.0045657, epsilon = 1.0e-6);

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#### pub fn rotation_to(&self, other: &Self) -> Self

The unit quaternion needed to make `self` and `other` coincide.

The result is such that: `self.rotation_to(other) * self == other`.

##### Example

    let rot1 = UnitQuaternion::from_axis_angle(&Vector3::y_axis(), 1.0);
    let rot2 = UnitQuaternion::from_axis_angle(&Vector3::x_axis(), 0.1);
    let rot_to = rot1.rotation_to(&rot2);
    assert_relative_eq!(rot_to * rot1, rot2, epsilon = 1.0e-6);

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#### pub fn lerp(&self, other: &Self, t: T) -> Quaternion<T>

Linear interpolation between two unit quaternions.

The result is not normalized.

##### Example

    let q1 = UnitQuaternion::new_normalize(Quaternion::new(1.0, 0.0, 0.0, 0.0));
    let q2 = UnitQuaternion::new_normalize(Quaternion::new(0.0, 1.0, 0.0, 0.0));
    assert_eq!(q1.lerp(&q2, 0.1), Quaternion::new(0.9, 0.1, 0.0, 0.0));

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#### pub fn nlerp(&self, other: &Self, t: T) -> Self

Normalized linear interpolation between two unit quaternions.

This is the same as `self.lerp` except that the result is normalized.

##### Example

    let q1 = UnitQuaternion::new_normalize(Quaternion::new(1.0, 0.0, 0.0, 0.0));
    let q2 = UnitQuaternion::new_normalize(Quaternion::new(0.0, 1.0, 0.0, 0.0));
    assert_eq!(q1.nlerp(&q2, 0.1), UnitQuaternion::new_normalize(Quaternion::new(0.9, 0.1, 0.0, 0.0)));

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#### pub fn slerp(&self, other: &Self, t: T) -> Selfwhere
T: RealField,

Spherical linear interpolation between two unit quaternions.

Panics if the angle between both quaternion is 180 degrees (in which case the interpolation is not well-defined). Use `.try_slerp` instead to avoid the panic.

##### Example

    let q1 = UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0);
    let q2 = UnitQuaternion::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0);

    let q = q1.slerp(&q2, 1.0 / 3.0);

    assert_eq!(q.euler_angles(), (std::f32::consts::FRAC_PI_2, 0.0, 0.0));

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#### pub fn try_slerp(&self, other: &Self, t: T, epsilon: T) -> Option<Self>where
T: RealField,

Computes the spherical linear interpolation between two unit quaternions or returns `None` if both quaternions are approximately 180 degrees apart (in which case the interpolation is not well-defined).

##### Arguments

- `self`: the first quaternion to interpolate from.
- `other`: the second quaternion to interpolate toward.
- `t`: the interpolation parameter. Should be between 0 and 1.
- `epsilon`: the value below which the sinus of the angle separating both quaternion must be to return `None`.

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#### pub fn conjugate_mut(&mut self)

Compute the conjugate of this unit quaternion in-place.

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#### pub fn inverse_mut(&mut self)

Inverts this quaternion if it is not zero.

##### Example

    let axisangle = Vector3::new(0.1, 0.2, 0.3);
    let mut rot = UnitQuaternion::new(axisangle);
    rot.inverse_mut();
    assert_relative_eq!(rot * UnitQuaternion::new(axisangle), UnitQuaternion::identity());
    assert_relative_eq!(UnitQuaternion::new(axisangle) * rot, UnitQuaternion::identity());

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#### pub fn axis(&self) -> Option<Unit<Vector3<T>>>where
T: RealField,

The rotation axis of this unit quaternion or `None` if the rotation is zero.

##### Example

    let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
    let angle = 1.2;
    let rot = UnitQuaternion::from_axis_angle(&axis, angle);
    assert_eq!(rot.axis(), Some(axis));

    // Case with a zero angle.
    let rot = UnitQuaternion::from_axis_angle(&axis, 0.0);
    assert!(rot.axis().is_none());

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#### pub fn scaled_axis(&self) -> Vector3<T>where
T: RealField,

The rotation axis of this unit quaternion multiplied by the rotation angle.

##### Example

    let axisangle = Vector3::new(0.1, 0.2, 0.3);
    let rot = UnitQuaternion::new(axisangle);
    assert_relative_eq!(rot.scaled_axis(), axisangle, epsilon = 1.0e-6);

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#### pub fn axis_angle(&self) -> Option<(Unit<Vector3<T>>, T)>where
T: RealField,

The rotation axis and angle in (0, pi] of this unit quaternion.

Returns `None` if the angle is zero.

##### Example

    let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
    let angle = 1.2;
    let rot = UnitQuaternion::from_axis_angle(&axis, angle);
    assert_eq!(rot.axis_angle(), Some((axis, angle)));

    // Case with a zero angle.
    let rot = UnitQuaternion::from_axis_angle(&axis, 0.0);
    assert!(rot.axis_angle().is_none());

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#### pub fn exp(&self) -> Quaternion<T>

Compute the exponential of a quaternion.

Note that this function yields a `Quaternion<T>` because it loses the unit property.

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#### pub fn ln(&self) -> Quaternion<T>where
T: RealField,

Compute the natural logarithm of a quaternion.

Note that this function yields a `Quaternion<T>` because it loses the unit property. The vector part of the return value corresponds to the axis-angle representation (divided by 2.0) of this unit quaternion.

##### Example

    let axisangle = Vector3::new(0.1, 0.2, 0.3);
    let q = UnitQuaternion::new(axisangle);
    assert_relative_eq!(q.ln().vector().into_owned(), axisangle, epsilon = 1.0e-6);

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#### pub fn powf(&self, n: T) -> Selfwhere
T: RealField,

Raise the quaternion to a given floating power.

This returns the unit quaternion that identifies a rotation with axis `self.axis()` and angle `self.angle() × n`.

##### Example

    let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
    let angle = 1.2;
    let rot = UnitQuaternion::from_axis_angle(&axis, angle);
    let pow = rot.powf(2.0);
    assert_relative_eq!(pow.axis().unwrap(), axis, epsilon = 1.0e-6);
    assert_eq!(pow.angle(), 2.4);

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#### pub fn to_rotation_matrix(self) -> Rotation<T, 3>

Builds a rotation matrix from this unit quaternion.

##### Example

    let q = UnitQuaternion::from_axis_angle(&Vector3::z_axis(), f32::consts::FRAC_PI_6);
    let rot = q.to_rotation_matrix();
    let expected = Matrix3::new(0.8660254, -0.5,      0.0,
                                0.5,       0.8660254, 0.0,
                                0.0,       0.0,       1.0);

    assert_relative_eq!(*rot.matrix(), expected, epsilon = 1.0e-6);

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#### pub fn to_euler_angles(self) -> (T, T, T)where
T: RealField,

👎Deprecated: This is renamed to use `.euler_angles()`.

Converts this unit quaternion into its equivalent Euler angles.

The angles are produced in the form (roll, pitch, yaw).

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#### pub fn euler_angles(&self) -> (T, T, T)where
T: RealField,

Retrieves the euler angles corresponding to this unit quaternion.

The angles are produced in the form (roll, pitch, yaw).

##### Example

    let rot = UnitQuaternion::from_euler_angles(0.1, 0.2, 0.3);
    let euler = rot.euler_angles();
    assert_relative_eq!(euler.0, 0.1, epsilon = 1.0e-6);
    assert_relative_eq!(euler.1, 0.2, epsilon = 1.0e-6);
    assert_relative_eq!(euler.2, 0.3, epsilon = 1.0e-6);

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#### pub fn to_homogeneous(self) -> Matrix4<T>

Converts this unit quaternion into its equivalent homogeneous transformation matrix.

##### Example

    let rot = UnitQuaternion::from_axis_angle(&Vector3::z_axis(), f32::consts::FRAC_PI_6);
    let expected = Matrix4::new(0.8660254, -0.5,      0.0, 0.0,
                                0.5,       0.8660254, 0.0, 0.0,
                                0.0,       0.0,       1.0, 0.0,
                                0.0,       0.0,       0.0, 1.0);

    assert_relative_eq!(rot.to_homogeneous(), expected, epsilon = 1.0e-6);

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#### pub fn transform_point(&self, pt: &Point3<T>) -> Point3<T>

Rotate a point by this unit quaternion.

This is the same as the multiplication `self * pt`.

##### Example

    let rot = UnitQuaternion::from_axis_angle(&Vector3::y_axis(), f32::consts::FRAC_PI_2);
    let transformed_point = rot.transform_point(&Point3::new(1.0, 2.0, 3.0));

    assert_relative_eq!(transformed_point, Point3::new(3.0, 2.0, -1.0), epsilon = 1.0e-6);

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#### pub fn transform_vector(&self, v: &Vector3<T>) -> Vector3<T>

Rotate a vector by this unit quaternion.

This is the same as the multiplication `self * v`.

##### Example

    let rot = UnitQuaternion::from_axis_angle(&Vector3::y_axis(), f32::consts::FRAC_PI_2);
    let transformed_vector = rot.transform_vector(&Vector3::new(1.0, 2.0, 3.0));

    assert_relative_eq!(transformed_vector, Vector3::new(3.0, 2.0, -1.0), epsilon = 1.0e-6);

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#### pub fn inverse_transform_point(&self, pt: &Point3<T>) -> Point3<T>

Rotate a point by the inverse of this unit quaternion. This may be cheaper than inverting the unit quaternion and transforming the point.

##### Example

    let rot = UnitQuaternion::from_axis_angle(&Vector3::y_axis(), f32::consts::FRAC_PI_2);
    let transformed_point = rot.inverse_transform_point(&Point3::new(1.0, 2.0, 3.0));

    assert_relative_eq!(transformed_point, Point3::new(-3.0, 2.0, 1.0), epsilon = 1.0e-6);

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#### pub fn inverse_transform_vector(&self, v: &Vector3<T>) -> Vector3<T>

Rotate a vector by the inverse of this unit quaternion. This may be cheaper than inverting the unit quaternion and transforming the vector.

##### Example

    let rot = UnitQuaternion::from_axis_angle(&Vector3::y_axis(), f32::consts::FRAC_PI_2);
    let transformed_vector = rot.inverse_transform_vector(&Vector3::new(1.0, 2.0, 3.0));

    assert_relative_eq!(transformed_vector, Vector3::new(-3.0, 2.0, 1.0), epsilon = 1.0e-6);

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#### pub fn inverse_transform_unit_vector(
&self,
v: &Unit<Vector3<T>>
) -> Unit<Vector3<T>>

Rotate a vector by the inverse of this unit quaternion. This may be cheaper than inverting the unit quaternion and transforming the vector.

##### Example

    let rot = UnitQuaternion::from_axis_angle(&Vector3::z_axis(), f32::consts::FRAC_PI_2);
    let transformed_vector = rot.inverse_transform_unit_vector(&Vector3::x_axis());

    assert_relative_eq!(transformed_vector, -Vector3::y_axis(), epsilon = 1.0e-6);

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#### pub fn append_axisangle_linearized(&self, axisangle: &Vector3<T>) -> Self

Appends to `self` a rotation given in the axis-angle form, using a linearized formulation.

This is faster, but approximate, way to compute `UnitQuaternion::new(axisangle) * self`.

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### impl<T: SimdRealField> Unit<Quaternion<T>>where
T::Element: SimdRealField,

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#### pub fn identity() -> Self

The rotation identity.

##### Example

    let q = UnitQuaternion::identity();
    let q2 = UnitQuaternion::new(Vector3::new(1.0, 2.0, 3.0));
    let v = Vector3::new_random();
    let p = Point3::from(v);

    assert_eq!(q * q2, q2);
    assert_eq!(q2 * q, q2);
    assert_eq!(q * v, v);
    assert_eq!(q * p, p);

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#### pub fn cast<To>(self) -> UnitQuaternion<To>where
To: SupersetOf<T> + Scalar,

Cast the components of `self` to another type.

##### Example

    let q = UnitQuaternion::from_euler_angles(1.0f64, 2.0, 3.0);
    let q2 = q.cast::<f32>();
    assert_relative_eq!(q2, UnitQuaternion::from_euler_angles(1.0f32, 2.0, 3.0), epsilon = 1.0e-6);

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#### pub fn from_axis_angle<SB>(axis: &Unit<Vector<T, U3, SB>>, angle: T) -> Selfwhere
SB: Storage<T, U3>,

Creates a new quaternion from a unit vector (the rotation axis) and an angle (the rotation angle).

##### Example

    let axis = Vector3::y_axis();
    let angle = f32::consts::FRAC_PI_2;
    // Point and vector being transformed in the tests.
    let pt = Point3::new(4.0, 5.0, 6.0);
    let vec = Vector3::new(4.0, 5.0, 6.0);
    let q = UnitQuaternion::from_axis_angle(&axis, angle);

    assert_eq!(q.axis().unwrap(), axis);
    assert_eq!(q.angle(), angle);
    assert_relative_eq!(q * pt, Point3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
    assert_relative_eq!(q * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);

    // A zero vector yields an identity.
    assert_eq!(UnitQuaternion::from_scaled_axis(Vector3::<f32>::zeros()), UnitQuaternion::identity());

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#### pub fn from_quaternion(q: Quaternion<T>) -> Self

Creates a new unit quaternion from a quaternion.

The input quaternion will be normalized.

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#### pub fn from_euler_angles(roll: T, pitch: T, yaw: T) -> Self

Creates a new unit quaternion from Euler angles.

The primitive rotations are applied in order: 1 roll − 2 pitch − 3 yaw.

##### Example

    let rot = UnitQuaternion::from_euler_angles(0.1, 0.2, 0.3);
    let euler = rot.euler_angles();
    assert_relative_eq!(euler.0, 0.1, epsilon = 1.0e-6);
    assert_relative_eq!(euler.1, 0.2, epsilon = 1.0e-6);
    assert_relative_eq!(euler.2, 0.3, epsilon = 1.0e-6);

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#### pub fn from_basis_unchecked(basis: &[Vector3<T>; 3]) -> Self

Builds an unit quaternion from a basis assumed to be orthonormal.

In order to get a valid unit-quaternion, the input must be an orthonormal basis, i.e., all vectors are normalized, and the are all orthogonal to each other. These invariants are not checked by this method.

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#### pub fn from_rotation_matrix(rotmat: &Rotation3<T>) -> Self

Builds an unit quaternion from a rotation matrix.

##### Example

    let axis = Vector3::y_axis();
    let angle = 0.1;
    let rot = Rotation3::from_axis_angle(&axis, angle);
    let q = UnitQuaternion::from_rotation_matrix(&rot);
    assert_relative_eq!(q.to_rotation_matrix(), rot, epsilon = 1.0e-6);
    assert_relative_eq!(q.axis().unwrap(), rot.axis().unwrap(), epsilon = 1.0e-6);
    assert_relative_eq!(q.angle(), rot.angle(), epsilon = 1.0e-6);

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#### pub fn from_matrix(m: &Matrix3<T>) -> Selfwhere
T: RealField,

Builds an unit quaternion by extracting the rotation part of the given transformation `m`.

This is an iterative method. See `.from_matrix_eps` to provide mover convergence parameters and starting solution. This implements “A Robust Method to Extract the Rotational Part of Deformations” by Müller et al.

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#### pub fn from_matrix_eps(
m: &Matrix3<T>,
eps: T,
max_iter: usize,
guess: Self
) -> Selfwhere
T: RealField,

Builds an unit quaternion by extracting the rotation part of the given transformation `m`.

This implements “A Robust Method to Extract the Rotational Part of Deformations” by Müller et al.

##### Parameters

- `m`: the matrix from which the rotational part is to be extracted.
- `eps`: the angular errors tolerated between the current rotation and the optimal one.
- `max_iter`: the maximum number of iterations. Loops indefinitely until convergence if set to `0`.
- `guess`: an estimate of the solution. Convergence will be significantly faster if an initial solution close to the actual solution is provided. Can be set to `UnitQuaternion::identity()` if no other guesses come to mind.

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#### pub fn rotation_between<SB, SC>(
a: &Vector<T, U3, SB>,
b: &Vector<T, U3, SC>
) -> Option<Self>where
T: RealField,
SB: Storage<T, U3>,
SC: Storage<T, U3>,

The unit quaternion needed to make `a` and `b` be collinear and point toward the same direction. Returns `None` if both `a` and `b` are collinear and point to opposite directions, as then the rotation desired is not unique.

##### Example

    let a = Vector3::new(1.0, 2.0, 3.0);
    let b = Vector3::new(3.0, 1.0, 2.0);
    let q = UnitQuaternion::rotation_between(&a, &b).unwrap();
    assert_relative_eq!(q * a, b);
    assert_relative_eq!(q.inverse() * b, a);

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#### pub fn scaled_rotation_between<SB, SC>(
a: &Vector<T, U3, SB>,
b: &Vector<T, U3, SC>,
s: T
) -> Option<Self>where
T: RealField,
SB: Storage<T, U3>,
SC: Storage<T, U3>,

The smallest rotation needed to make `a` and `b` collinear and point toward the same direction, raised to the power `s`.

##### Example

    let a = Vector3::new(1.0, 2.0, 3.0);
    let b = Vector3::new(3.0, 1.0, 2.0);
    let q2 = UnitQuaternion::scaled_rotation_between(&a, &b, 0.2).unwrap();
    let q5 = UnitQuaternion::scaled_rotation_between(&a, &b, 0.5).unwrap();
    assert_relative_eq!(q2 * q2 * q2 * q2 * q2 * a, b, epsilon = 1.0e-6);
    assert_relative_eq!(q5 * q5 * a, b, epsilon = 1.0e-6);

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#### pub fn rotation_between_axis<SB, SC>(
a: &Unit<Vector<T, U3, SB>>,
b: &Unit<Vector<T, U3, SC>>
) -> Option<Self>where
T: RealField,
SB: Storage<T, U3>,
SC: Storage<T, U3>,

The unit quaternion needed to make `a` and `b` be collinear and point toward the same direction.

##### Example

    let a = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
    let b = Unit::new_normalize(Vector3::new(3.0, 1.0, 2.0));
    let q = UnitQuaternion::rotation_between(&a, &b).unwrap();
    assert_relative_eq!(q * a, b);
    assert_relative_eq!(q.inverse() * b, a);

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#### pub fn scaled_rotation_between_axis<SB, SC>(
na: &Unit<Vector<T, U3, SB>>,
nb: &Unit<Vector<T, U3, SC>>,
s: T
) -> Option<Self>where
T: RealField,
SB: Storage<T, U3>,
SC: Storage<T, U3>,

The smallest rotation needed to make `a` and `b` collinear and point toward the same direction, raised to the power `s`.

##### Example

    let a = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
    let b = Unit::new_normalize(Vector3::new(3.0, 1.0, 2.0));
    let q2 = UnitQuaternion::scaled_rotation_between(&a, &b, 0.2).unwrap();
    let q5 = UnitQuaternion::scaled_rotation_between(&a, &b, 0.5).unwrap();
    assert_relative_eq!(q2 * q2 * q2 * q2 * q2 * a, b, epsilon = 1.0e-6);
    assert_relative_eq!(q5 * q5 * a, b, epsilon = 1.0e-6);

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#### pub fn face_towards<SB, SC>(
dir: &Vector<T, U3, SB>,
up: &Vector<T, U3, SC>
) -> Selfwhere
SB: Storage<T, U3>,
SC: Storage<T, U3>,

Creates an unit quaternion that corresponds to the local frame of an observer standing at the origin and looking toward `dir`.

It maps the `z` axis to the direction `dir`.

##### Arguments

- dir - The look direction. It does not need to be normalized.
- up - The vertical direction. It does not need to be normalized. The only requirement of this parameter is to not be collinear to `dir`. Non-collinearity is not checked.

##### Example

    let dir = Vector3::new(1.0, 2.0, 3.0);
    let up = Vector3::y();

    let q = UnitQuaternion::face_towards(&dir, &up);
    assert_relative_eq!(q * Vector3::z(), dir.normalize());

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#### pub fn new_observer_frames<SB, SC>(
dir: &Vector<T, U3, SB>,
up: &Vector<T, U3, SC>
) -> Selfwhere
SB: Storage<T, U3>,
SC: Storage<T, U3>,

👎Deprecated: renamed to `face_towards`

Deprecated: Use `UnitQuaternion::face_towards` instead.

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#### pub fn look_at_rh<SB, SC>(
dir: &Vector<T, U3, SB>,
up: &Vector<T, U3, SC>
) -> Selfwhere
SB: Storage<T, U3>,
SC: Storage<T, U3>,

Builds a right-handed look-at view matrix without translation.

It maps the view direction `dir` to the negative `z` axis. This conforms to the common notion of right handed look-at matrix from the computer graphics community.

##### Arguments

- dir − The view direction. It does not need to be normalized.
- up - A vector approximately aligned with required the vertical axis. It does not need to be normalized. The only requirement of this parameter is to not be collinear to `dir`.

##### Example

    let dir = Vector3::new(1.0, 2.0, 3.0);
    let up = Vector3::y();

    let q = UnitQuaternion::look_at_rh(&dir, &up);
    assert_relative_eq!(q * dir.normalize(), -Vector3::z());

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#### pub fn look_at_lh<SB, SC>(
dir: &Vector<T, U3, SB>,
up: &Vector<T, U3, SC>
) -> Selfwhere
SB: Storage<T, U3>,
SC: Storage<T, U3>,

Builds a left-handed look-at view matrix without translation.

It maps the view direction `dir` to the positive `z` axis. This conforms to the common notion of left handed look-at matrix from the computer graphics community.

##### Arguments

- dir − The view direction. It does not need to be normalized.
- up - A vector approximately aligned with required the vertical axis. The only requirement of this parameter is to not be collinear to `dir`.

##### Example

    let dir = Vector3::new(1.0, 2.0, 3.0);
    let up = Vector3::y();

    let q = UnitQuaternion::look_at_lh(&dir, &up);
    assert_relative_eq!(q * dir.normalize(), Vector3::z());

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#### pub fn new<SB>(axisangle: Vector<T, U3, SB>) -> Selfwhere
SB: Storage<T, U3>,

Creates a new unit quaternion rotation from a rotation axis scaled by the rotation angle.

If `axisangle` has a magnitude smaller than `T::default_epsilon()`, this returns the identity rotation.

##### Example

    let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
    // Point and vector being transformed in the tests.
    let pt = Point3::new(4.0, 5.0, 6.0);
    let vec = Vector3::new(4.0, 5.0, 6.0);
    let q = UnitQuaternion::new(axisangle);

    assert_relative_eq!(q * pt, Point3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
    assert_relative_eq!(q * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);

    // A zero vector yields an identity.
    assert_eq!(UnitQuaternion::new(Vector3::<f32>::zeros()), UnitQuaternion::identity());

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#### pub fn new_eps<SB>(axisangle: Vector<T, U3, SB>, eps: T) -> Selfwhere
SB: Storage<T, U3>,

Creates a new unit quaternion rotation from a rotation axis scaled by the rotation angle.

If `axisangle` has a magnitude smaller than `eps`, this returns the identity rotation.

##### Example

    let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
    // Point and vector being transformed in the tests.
    let pt = Point3::new(4.0, 5.0, 6.0);
    let vec = Vector3::new(4.0, 5.0, 6.0);
    let q = UnitQuaternion::new_eps(axisangle, 1.0e-6);

    assert_relative_eq!(q * pt, Point3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
    assert_relative_eq!(q * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);

    // An almost zero vector yields an identity.
    assert_eq!(UnitQuaternion::new_eps(Vector3::new(1.0e-8, 1.0e-9, 1.0e-7), 1.0e-6), UnitQuaternion::identity());

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#### pub fn from_scaled_axis<SB>(axisangle: Vector<T, U3, SB>) -> Selfwhere
SB: Storage<T, U3>,

Creates a new unit quaternion rotation from a rotation axis scaled by the rotation angle.

If `axisangle` has a magnitude smaller than `T::default_epsilon()`, this returns the identity rotation. Same as `Self::new(axisangle)`.

##### Example

    let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
    // Point and vector being transformed in the tests.
    let pt = Point3::new(4.0, 5.0, 6.0);
    let vec = Vector3::new(4.0, 5.0, 6.0);
    let q = UnitQuaternion::from_scaled_axis(axisangle);

    assert_relative_eq!(q * pt, Point3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
    assert_relative_eq!(q * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);

    // A zero vector yields an identity.
    assert_eq!(UnitQuaternion::from_scaled_axis(Vector3::<f32>::zeros()), UnitQuaternion::identity());

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#### pub fn from_scaled_axis_eps<SB>(axisangle: Vector<T, U3, SB>, eps: T) -> Selfwhere
SB: Storage<T, U3>,

Creates a new unit quaternion rotation from a rotation axis scaled by the rotation angle.

If `axisangle` has a magnitude smaller than `eps`, this returns the identity rotation. Same as `Self::new_eps(axisangle, eps)`.

##### Example

    let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
    // Point and vector being transformed in the tests.
    let pt = Point3::new(4.0, 5.0, 6.0);
    let vec = Vector3::new(4.0, 5.0, 6.0);
    let q = UnitQuaternion::from_scaled_axis_eps(axisangle, 1.0e-6);

    assert_relative_eq!(q * pt, Point3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);
    assert_relative_eq!(q * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);

    // An almost zero vector yields an identity.
    assert_eq!(UnitQuaternion::from_scaled_axis_eps(Vector3::new(1.0e-8, 1.0e-9, 1.0e-7), 1.0e-6), UnitQuaternion::identity());

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#### pub fn mean_of(unit_quaternions: impl IntoIterator<Item = Self>) -> Selfwhere
T: RealField,

Create the mean unit quaternion from a data structure implementing `IntoIterator` returning unit quaternions.

The method will panic if the iterator does not return any quaternions.

Algorithm from: Oshman, Yaakov, and Avishy Carmi. “Attitude estimation from vector observations using a genetic-algorithm-embedded quaternion particle filter.” Journal of Guidance, Control, and Dynamics 29.4 (2006): 879-891.

##### Example

    let q1 = UnitQuaternion::from_euler_angles(0.0, 0.0, 0.0);
    let q2 = UnitQuaternion::from_euler_angles(-0.1, 0.0, 0.0);
    let q3 = UnitQuaternion::from_euler_angles(0.1, 0.0, 0.0);

    let quat_vec = vec![q1, q2, q3];
    let q_mean = UnitQuaternion::mean_of(quat_vec);

    let euler_angles_mean = q_mean.euler_angles();
    assert_relative_eq!(euler_angles_mean.0, 0.0, epsilon = 1.0e-7)

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### impl<T: SimdRealField> Unit<DualQuaternion<T>>where
T::Element: SimdRealField,

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#### pub fn dual_quaternion(&self) -> &DualQuaternion<T>

The underlying dual quaternion.

Same as `self.as_ref()`.

##### Example

    let id = UnitDualQuaternion::identity();
    assert_eq!(*id.dual_quaternion(), DualQuaternion::from_real_and_dual(
        Quaternion::new(1.0, 0.0, 0.0, 0.0),
        Quaternion::new(0.0, 0.0, 0.0, 0.0)
    ));

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#### pub fn conjugate(&self) -> Self

Compute the conjugate of this unit quaternion.

##### Example

    let qr = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    let qd = Quaternion::new(5.0, 6.0, 7.0, 8.0);
    let unit = UnitDualQuaternion::new_normalize(
        DualQuaternion::from_real_and_dual(qr, qd)
    );
    let conj = unit.conjugate();
    assert_eq!(conj.real, unit.real.conjugate());
    assert_eq!(conj.dual, unit.dual.conjugate());

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#### pub fn conjugate_mut(&mut self)

Compute the conjugate of this unit quaternion in-place.

##### Example

    let qr = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    let qd = Quaternion::new(5.0, 6.0, 7.0, 8.0);
    let unit = UnitDualQuaternion::new_normalize(
        DualQuaternion::from_real_and_dual(qr, qd)
    );
    let mut conj = unit.clone();
    conj.conjugate_mut();
    assert_eq!(conj.as_ref().real, unit.as_ref().real.conjugate());
    assert_eq!(conj.as_ref().dual, unit.as_ref().dual.conjugate());

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#### pub fn inverse(&self) -> Self

Inverts this dual quaternion if it is not zero.

##### Example

    let qr = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    let qd = Quaternion::new(5.0, 6.0, 7.0, 8.0);
    let unit = UnitDualQuaternion::new_normalize(DualQuaternion::from_real_and_dual(qr, qd));
    let inv = unit.inverse();
    assert_relative_eq!(unit * inv, UnitDualQuaternion::identity(), epsilon = 1.0e-6);
    assert_relative_eq!(inv * unit, UnitDualQuaternion::identity(), epsilon = 1.0e-6);

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#### pub fn inverse_mut(&mut self)

Inverts this dual quaternion in place if it is not zero.

##### Example

    let qr = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    let qd = Quaternion::new(5.0, 6.0, 7.0, 8.0);
    let unit = UnitDualQuaternion::new_normalize(DualQuaternion::from_real_and_dual(qr, qd));
    let mut inv = unit.clone();
    inv.inverse_mut();
    assert_relative_eq!(unit * inv, UnitDualQuaternion::identity(), epsilon = 1.0e-6);
    assert_relative_eq!(inv * unit, UnitDualQuaternion::identity(), epsilon = 1.0e-6);

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#### pub fn isometry_to(&self, other: &Self) -> Self

The unit dual quaternion needed to make `self` and `other` coincide.

The result is such that: `self.isometry_to(other) * self == other`.

##### Example

    let qr = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    let qd = Quaternion::new(5.0, 6.0, 7.0, 8.0);
    let dq1 = UnitDualQuaternion::new_normalize(DualQuaternion::from_real_and_dual(qr, qd));
    let dq2 = UnitDualQuaternion::new_normalize(DualQuaternion::from_real_and_dual(qd, qr));
    let dq_to = dq1.isometry_to(&dq2);
    assert_relative_eq!(dq_to * dq1, dq2, epsilon = 1.0e-6);

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#### pub fn lerp(&self, other: &Self, t: T) -> DualQuaternion<T>

Linear interpolation between two unit dual quaternions.

The result is not normalized.

##### Example

    let dq1 = UnitDualQuaternion::new_normalize(DualQuaternion::from_real_and_dual(
        Quaternion::new(0.5, 0.0, 0.5, 0.0),
        Quaternion::new(0.0, 0.5, 0.0, 0.5)
    ));
    let dq2 = UnitDualQuaternion::new_normalize(DualQuaternion::from_real_and_dual(
        Quaternion::new(0.5, 0.0, 0.0, 0.5),
        Quaternion::new(0.5, 0.0, 0.5, 0.0)
    ));
    assert_relative_eq!(
        UnitDualQuaternion::new_normalize(dq1.lerp(&dq2, 0.5)),
        UnitDualQuaternion::new_normalize(
            DualQuaternion::from_real_and_dual(
                Quaternion::new(0.5, 0.0, 0.25, 0.25),
                Quaternion::new(0.25, 0.25, 0.25, 0.25)
            )
        ),
        epsilon = 1.0e-6
    );

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#### pub fn nlerp(&self, other: &Self, t: T) -> Self

Normalized linear interpolation between two unit quaternions.

This is the same as `self.lerp` except that the result is normalized.

##### Example

    let dq1 = UnitDualQuaternion::new_normalize(DualQuaternion::from_real_and_dual(
        Quaternion::new(0.5, 0.0, 0.5, 0.0),
        Quaternion::new(0.0, 0.5, 0.0, 0.5)
    ));
    let dq2 = UnitDualQuaternion::new_normalize(DualQuaternion::from_real_and_dual(
        Quaternion::new(0.5, 0.0, 0.0, 0.5),
        Quaternion::new(0.5, 0.0, 0.5, 0.0)
    ));
    assert_relative_eq!(dq1.nlerp(&dq2, 0.2), UnitDualQuaternion::new_normalize(
        DualQuaternion::from_real_and_dual(
            Quaternion::new(0.5, 0.0, 0.4, 0.1),
            Quaternion::new(0.1, 0.4, 0.1, 0.4)
        )
    ), epsilon = 1.0e-6);

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#### pub fn sclerp(&self, other: &Self, t: T) -> Selfwhere
T: RealField,

Screw linear interpolation between two unit quaternions. This creates a smooth arc from one dual-quaternion to another.

Panics if the angle between both quaternion is 180 degrees (in which case the interpolation is not well-defined). Use `.try_sclerp` instead to avoid the panic.

##### Example

    let dq1 = UnitDualQuaternion::from_parts(
        Vector3::new(0.0, 3.0, 0.0).into(),
        UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0),
    );

    let dq2 = UnitDualQuaternion::from_parts(
        Vector3::new(0.0, 0.0, 3.0).into(),
        UnitQuaternion::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0),
    );

    let dq = dq1.sclerp(&dq2, 1.0 / 3.0);

    assert_relative_eq!(
        dq.rotation().euler_angles().0, std::f32::consts::FRAC_PI_2, epsilon = 1.0e-6
    );
    assert_relative_eq!(dq.translation().vector.y, 3.0, epsilon = 1.0e-6);

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#### pub fn try_sclerp(&self, other: &Self, t: T, epsilon: T) -> Option<Self>where
T: RealField,

Computes the screw-linear interpolation between two unit quaternions or returns `None` if both quaternions are approximately 180 degrees apart (in which case the interpolation is not well-defined).

##### Arguments

- `self`: the first quaternion to interpolate from.
- `other`: the second quaternion to interpolate toward.
- `t`: the interpolation parameter. Should be between 0 and 1.
- `epsilon`: the value below which the sinus of the angle separating both quaternion must be to return `None`.

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#### pub fn rotation(&self) -> UnitQuaternion<T>

Return the rotation part of this unit dual quaternion.

##### Example

    let dq = UnitDualQuaternion::from_parts(
        Vector3::new(0.0, 3.0, 0.0).into(),
        UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0)
    );

    assert_relative_eq!(
        dq.rotation().angle(), std::f32::consts::FRAC_PI_4, epsilon = 1.0e-6
    );

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#### pub fn translation(&self) -> Translation3<T>

Return the translation part of this unit dual quaternion.

##### Example

    let dq = UnitDualQuaternion::from_parts(
        Vector3::new(0.0, 3.0, 0.0).into(),
        UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0)
    );

    assert_relative_eq!(
        dq.translation().vector, Vector3::new(0.0, 3.0, 0.0), epsilon = 1.0e-6
    );

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#### pub fn to_isometry(self) -> Isometry3<T>

Builds an isometry from this unit dual quaternion.

##### Example

    let rotation = UnitQuaternion::from_euler_angles(std::f32::consts::PI, 0.0, 0.0);
    let translation = Vector3::new(1.0, 3.0, 2.5);
    let dq = UnitDualQuaternion::from_parts(
        translation.into(),
        rotation
    );
    let iso = dq.to_isometry();

    assert_relative_eq!(iso.rotation.angle(), std::f32::consts::PI, epsilon = 1.0e-6);
    assert_relative_eq!(iso.translation.vector, translation, epsilon = 1.0e-6);

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#### pub fn transform_point(&self, pt: &Point3<T>) -> Point3<T>

Rotate and translate a point by this unit dual quaternion interpreted as an isometry.

This is the same as the multiplication `self * pt`.

##### Example

    let dq = UnitDualQuaternion::from_parts(
        Vector3::new(0.0, 3.0, 0.0).into(),
        UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_2, 0.0, 0.0)
    );
    let point = Point3::new(1.0, 2.0, 3.0);

    assert_relative_eq!(
        dq.transform_point(&point), Point3::new(1.0, 0.0, 2.0), epsilon = 1.0e-6
    );

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#### pub fn transform_vector(&self, v: &Vector3<T>) -> Vector3<T>

Rotate a vector by this unit dual quaternion, ignoring the translational component.

This is the same as the multiplication `self * v`.

##### Example

    let dq = UnitDualQuaternion::from_parts(
        Vector3::new(0.0, 3.0, 0.0).into(),
        UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_2, 0.0, 0.0)
    );
    let vector = Vector3::new(1.0, 2.0, 3.0);

    assert_relative_eq!(
        dq.transform_vector(&vector), Vector3::new(1.0, -3.0, 2.0), epsilon = 1.0e-6
    );

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#### pub fn inverse_transform_point(&self, pt: &Point3<T>) -> Point3<T>

Rotate and translate a point by the inverse of this unit quaternion.

This may be cheaper than inverting the unit dual quaternion and transforming the point.

##### Example

    let dq = UnitDualQuaternion::from_parts(
        Vector3::new(0.0, 3.0, 0.0).into(),
        UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_2, 0.0, 0.0)
    );
    let point = Point3::new(1.0, 2.0, 3.0);

    assert_relative_eq!(
        dq.inverse_transform_point(&point), Point3::new(1.0, 3.0, 1.0), epsilon = 1.0e-6
    );

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#### pub fn inverse_transform_vector(&self, v: &Vector3<T>) -> Vector3<T>

Rotate a vector by the inverse of this unit quaternion, ignoring the translational component.

This may be cheaper than inverting the unit dual quaternion and transforming the vector.

##### Example

    let dq = UnitDualQuaternion::from_parts(
        Vector3::new(0.0, 3.0, 0.0).into(),
        UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_2, 0.0, 0.0)
    );
    let vector = Vector3::new(1.0, 2.0, 3.0);

    assert_relative_eq!(
        dq.inverse_transform_vector(&vector), Vector3::new(1.0, 3.0, -2.0), epsilon = 1.0e-6
    );

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#### pub fn inverse_transform_unit_vector(
&self,
v: &Unit<Vector3<T>>
) -> Unit<Vector3<T>>

Rotate a unit vector by the inverse of this unit quaternion, ignoring the translational component. This may be cheaper than inverting the unit dual quaternion and transforming the vector.

##### Example

    let dq = UnitDualQuaternion::from_parts(
        Vector3::new(0.0, 3.0, 0.0).into(),
        UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_2, 0.0, 0.0)
    );
    let vector = Unit::new_unchecked(Vector3::new(0.0, 1.0, 0.0));

    assert_relative_eq!(
        dq.inverse_transform_unit_vector(&vector),
        Unit::new_unchecked(Vector3::new(0.0, 0.0, -1.0)),
        epsilon = 1.0e-6
    );

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### impl<T: SimdRealField + RealField> Unit<DualQuaternion<T>>where
T::Element: SimdRealField,

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#### pub fn to_homogeneous(self) -> Matrix4<T>

Converts this unit dual quaternion interpreted as an isometry into its equivalent homogeneous transformation matrix.

##### Example

    let dq = UnitDualQuaternion::from_parts(
        Vector3::new(1.0, 3.0, 2.0).into(),
        UnitQuaternion::from_axis_angle(&Vector3::z_axis(), std::f32::consts::FRAC_PI_6)
    );
    let expected = Matrix4::new(0.8660254, -0.5,      0.0, 1.0,
                                0.5,       0.8660254, 0.0, 3.0,
                                0.0,       0.0,       1.0, 2.0,
                                0.0,       0.0,       0.0, 1.0);

    assert_relative_eq!(dq.to_homogeneous(), expected, epsilon = 1.0e-6);

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### impl<T: SimdRealField> Unit<DualQuaternion<T>>

source

#### pub fn identity() -> Self

The unit dual quaternion multiplicative identity, which also represents the identity transformation as an isometry.

##### Example

    let ident = UnitDualQuaternion::identity();
    let point = Point3::new(1.0, -4.3, 3.33);

    assert_eq!(ident * point, point);
    assert_eq!(ident, ident.inverse());

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#### pub fn cast<To: Scalar>(self) -> UnitDualQuaternion<To>where
UnitDualQuaternion<To>: SupersetOf<Self>,

Cast the components of `self` to another type.

##### Example

    let q = UnitDualQuaternion::<f64>::identity();
    let q2 = q.cast::<f32>();
    assert_eq!(q2, UnitDualQuaternion::<f32>::identity());

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### impl<T: SimdRealField> Unit<DualQuaternion<T>>where
T::Element: SimdRealField,

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#### pub fn from_parts(
translation: Translation3<T>,
rotation: UnitQuaternion<T>
) -> Self

Return a dual quaternion representing the translation and orientation given by the provided rotation quaternion and translation vector.

##### Example

    let dq = UnitDualQuaternion::from_parts(
        Vector3::new(0.0, 3.0, 0.0).into(),
        UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_2, 0.0, 0.0)
    );
    let point = Point3::new(1.0, 2.0, 3.0);

    assert_relative_eq!(dq * point, Point3::new(1.0, 0.0, 2.0), epsilon = 1.0e-6);

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#### pub fn from_isometry(isometry: &Isometry3<T>) -> Self

Return a unit dual quaternion representing the translation and orientation given by the provided isometry.

##### Example

    let iso = Isometry3::from_parts(
        Vector3::new(0.0, 3.0, 0.0).into(),
        UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_2, 0.0, 0.0)
    );
    let dq = UnitDualQuaternion::from_isometry(&iso);
    let point = Point3::new(1.0, 2.0, 3.0);

    assert_relative_eq!(dq * point, iso * point, epsilon = 1.0e-6);

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#### pub fn from_rotation(rotation: UnitQuaternion<T>) -> Self

Creates a dual quaternion from a unit quaternion rotation.

##### Example

    let q = Quaternion::new(1.0, 2.0, 3.0, 4.0);
    let rot = UnitQuaternion::new_normalize(q);

    let dq = UnitDualQuaternion::from_rotation(rot);
    assert_relative_eq!(dq.as_ref().real.norm(), 1.0, epsilon = 1.0e-6);
    assert_eq!(dq.as_ref().dual.norm(), 0.0);

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### impl<T: SimdRealField> Unit<Complex<T>>where
T::Element: SimdRealField,

#### Angle extraction

source

#### pub fn angle(&self) -> T

The rotation angle in `]-pi; pi]` of this unit complex number.

##### Example

    let rot = UnitComplex::new(1.78);
    assert_eq!(rot.angle(), 1.78);

source

#### pub fn sin_angle(&self) -> T

The sine of the rotation angle.

##### Example

    let angle = 1.78f32;
    let rot = UnitComplex::new(angle);
    assert_eq!(rot.sin_angle(), angle.sin());

source

#### pub fn cos_angle(&self) -> T

The cosine of the rotation angle.

##### Example

    let angle = 1.78f32;
    let rot = UnitComplex::new(angle);
    assert_eq!(rot.cos_angle(),angle.cos());

source

#### pub fn scaled_axis(&self) -> Vector1<T>

The rotation angle returned as a 1-dimensional vector.

This is generally used in the context of generic programming. Using the `.angle()` method instead is more common.

source

#### pub fn axis_angle(&self) -> Option<(Unit<Vector1<T>>, T)>where
T: RealField,

The rotation axis and angle in (0, pi] of this complex number.

This is generally used in the context of generic programming. Using the `.angle()` method instead is more common. Returns `None` if the angle is zero.

source

#### pub fn angle_to(&self, other: &Self) -> T

The rotation angle needed to make `self` and `other` coincide.

##### Example

    let rot1 = UnitComplex::new(0.1);
    let rot2 = UnitComplex::new(1.7);
    assert_relative_eq!(rot1.angle_to(&rot2), 1.6);

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### impl<T: SimdRealField> Unit<Complex<T>>where
T::Element: SimdRealField,

#### Conjugation and inversion

source

#### pub fn conjugate(&self) -> Self

Compute the conjugate of this unit complex number.

##### Example

    let rot = UnitComplex::new(1.78);
    let conj = rot.conjugate();
    assert_eq!(rot.complex().im, -conj.complex().im);
    assert_eq!(rot.complex().re, conj.complex().re);

source

#### pub fn inverse(&self) -> Self

Inverts this complex number if it is not zero.

##### Example

    let rot = UnitComplex::new(1.2);
    let inv = rot.inverse();
    assert_relative_eq!(rot * inv, UnitComplex::identity(), epsilon = 1.0e-6);
    assert_relative_eq!(inv * rot, UnitComplex::identity(), epsilon = 1.0e-6);

source

#### pub fn conjugate_mut(&mut self)

Compute in-place the conjugate of this unit complex number.

##### Example

    let angle = 1.7;
    let rot = UnitComplex::new(angle);
    let mut conj = UnitComplex::new(angle);
    conj.conjugate_mut();
    assert_eq!(rot.complex().im, -conj.complex().im);
    assert_eq!(rot.complex().re, conj.complex().re);

source

#### pub fn inverse_mut(&mut self)

Inverts in-place this unit complex number.

##### Example

    let angle = 1.7;
    let mut rot = UnitComplex::new(angle);
    rot.inverse_mut();
    assert_relative_eq!(rot * UnitComplex::new(angle), UnitComplex::identity());
    assert_relative_eq!(UnitComplex::new(angle) * rot, UnitComplex::identity());

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### impl<T: SimdRealField> Unit<Complex<T>>where
T::Element: SimdRealField,

#### Conversion to a matrix

source

#### pub fn to_rotation_matrix(self) -> Rotation2<T>

Builds the rotation matrix corresponding to this unit complex number.

##### Example

    let rot = UnitComplex::new(f32::consts::FRAC_PI_6);
    let expected = Rotation2::new(f32::consts::FRAC_PI_6);
    assert_eq!(rot.to_rotation_matrix(), expected);

source

#### pub fn to_homogeneous(self) -> Matrix3<T>

Converts this unit complex number into its equivalent homogeneous transformation matrix.

##### Example

    let rot = UnitComplex::new(f32::consts::FRAC_PI_6);
    let expected = Matrix3::new(0.8660254, -0.5,      0.0,
                                0.5,       0.8660254, 0.0,
                                0.0,       0.0,       1.0);
    assert_eq!(rot.to_homogeneous(), expected);

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### impl<T: SimdRealField> Unit<Complex<T>>where
T::Element: SimdRealField,

#### Transformation of a vector or a point

source

#### pub fn transform_point(&self, pt: &Point2<T>) -> Point2<T>

Rotate the given point by this unit complex number.

This is the same as the multiplication `self * pt`.

##### Example

    let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
    let transformed_point = rot.transform_point(&Point2::new(1.0, 2.0));
    assert_relative_eq!(transformed_point, Point2::new(-2.0, 1.0), epsilon = 1.0e-6);

source

#### pub fn transform_vector(&self, v: &Vector2<T>) -> Vector2<T>

Rotate the given vector by this unit complex number.

This is the same as the multiplication `self * v`.

##### Example

    let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
    let transformed_vector = rot.transform_vector(&Vector2::new(1.0, 2.0));
    assert_relative_eq!(transformed_vector, Vector2::new(-2.0, 1.0), epsilon = 1.0e-6);

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#### pub fn inverse_transform_point(&self, pt: &Point2<T>) -> Point2<T>

Rotate the given point by the inverse of this unit complex number.

##### Example

    let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
    let transformed_point = rot.inverse_transform_point(&Point2::new(1.0, 2.0));
    assert_relative_eq!(transformed_point, Point2::new(2.0, -1.0), epsilon = 1.0e-6);

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#### pub fn inverse_transform_vector(&self, v: &Vector2<T>) -> Vector2<T>

Rotate the given vector by the inverse of this unit complex number.

##### Example

    let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
    let transformed_vector = rot.inverse_transform_vector(&Vector2::new(1.0, 2.0));
    assert_relative_eq!(transformed_vector, Vector2::new(2.0, -1.0), epsilon = 1.0e-6);

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#### pub fn inverse_transform_unit_vector(
&self,
v: &Unit<Vector2<T>>
) -> Unit<Vector2<T>>

Rotate the given vector by the inverse of this unit complex number.

##### Example

    let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
    let transformed_vector = rot.inverse_transform_unit_vector(&Vector2::x_axis());
    assert_relative_eq!(transformed_vector, -Vector2::y_axis(), epsilon = 1.0e-6);

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### impl<T: SimdRealField> Unit<Complex<T>>where
T::Element: SimdRealField,

#### Interpolation

source

#### pub fn slerp(&self, other: &Self, t: T) -> Self

Spherical linear interpolation between two rotations represented as unit complex numbers.

##### Examples:

    let rot1 = UnitComplex::new(std::f32::consts::FRAC_PI_4);
    let rot2 = UnitComplex::new(-std::f32::consts::PI);

    let rot = rot1.slerp(&rot2, 1.0 / 3.0);

    assert_relative_eq!(rot.angle(), std::f32::consts::FRAC_PI_2);

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### impl<T: SimdRealField> Unit<Complex<T>>where
T::Element: SimdRealField,

#### Identity

source

#### pub fn identity() -> Self

The unit complex number multiplicative identity.

##### Example

    let rot1 = UnitComplex::identity();
    let rot2 = UnitComplex::new(1.7);

    assert_eq!(rot1 * rot2, rot2);
    assert_eq!(rot2 * rot1, rot2);

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### impl<T: SimdRealField> Unit<Complex<T>>where
T::Element: SimdRealField,

#### Construction from a 2D rotation angle

source

#### pub fn new(angle: T) -> Self

Builds the unit complex number corresponding to the rotation with the given angle.

##### Example

    let rot = UnitComplex::new(f32::consts::FRAC_PI_2);

    assert_relative_eq!(rot * Point2::new(3.0, 4.0), Point2::new(-4.0, 3.0));

source

#### pub fn from_angle(angle: T) -> Self

Builds the unit complex number corresponding to the rotation with the angle.

Same as `Self::new(angle)`.

##### Example

    let rot = UnitComplex::from_angle(f32::consts::FRAC_PI_2);

    assert_relative_eq!(rot * Point2::new(3.0, 4.0), Point2::new(-4.0, 3.0));

source

#### pub fn from_cos_sin_unchecked(cos: T, sin: T) -> Self

Builds the unit complex number from the sinus and cosinus of the rotation angle.

The input values are not checked to actually be cosines and sine of the same value. Is is generally preferable to use the `::new(angle)` constructor instead.

##### Example

    let angle = f32::consts::FRAC_PI_2;
    let rot = UnitComplex::from_cos_sin_unchecked(angle.cos(), angle.sin());

    assert_relative_eq!(rot * Point2::new(3.0, 4.0), Point2::new(-4.0, 3.0));

source

#### pub fn from_scaled_axis<SB: Storage<T, U1>>(
axisangle: Vector<T, U1, SB>
) -> Self

Builds a unit complex rotation from an angle in radian wrapped in a 1-dimensional vector.

This is generally used in the context of generic programming. Using the `::new(angle)` method instead is more common.

source§

### impl<T: SimdRealField> Unit<Complex<T>>where
T::Element: SimdRealField,

#### Construction from an existing 2D matrix or complex number

source

#### pub fn cast<To: Scalar>(self) -> UnitComplex<To>where
UnitComplex<To>: SupersetOf<Self>,

Cast the components of `self` to another type.

##### Example

    #[macro_use] extern crate approx;
    let c = UnitComplex::new(1.0f64);
    let c2 = c.cast::<f32>();
    assert_relative_eq!(c2, UnitComplex::new(1.0f32));

source

#### pub fn complex(&self) -> &Complex<T>

The underlying complex number.

Same as `self.as_ref()`.

##### Example

    let angle = 1.78f32;
    let rot = UnitComplex::new(angle);
    assert_eq!(*rot.complex(), Complex::new(angle.cos(), angle.sin()));

source

#### pub fn from_complex(q: Complex<T>) -> Self

Creates a new unit complex number from a complex number.

The input complex number will be normalized.

source

#### pub fn from_complex_and_get(q: Complex<T>) -> (Self, T)

Creates a new unit complex number from a complex number.

The input complex number will be normalized. Returns the norm of the complex number as well.

source

#### pub fn from_rotation_matrix(rotmat: &Rotation2<T>) -> Self

Builds the unit complex number from the corresponding 2D rotation matrix.

##### Example

    let rot = Rotation2::new(1.7);
    let complex = UnitComplex::from_rotation_matrix(&rot);
    assert_eq!(complex, UnitComplex::new(1.7));

source

#### pub fn from_basis_unchecked(basis: &[Vector2<T>; 2]) -> Self

Builds a rotation from a basis assumed to be orthonormal.

In order to get a valid unit-quaternion, the input must be an orthonormal basis, i.e., all vectors are normalized, and the are all orthogonal to each other. These invariants are not checked by this method.

source

#### pub fn from_matrix(m: &Matrix2<T>) -> Selfwhere
T: RealField,

Builds an unit complex by extracting the rotation part of the given transformation `m`.

This is an iterative method. See `.from_matrix_eps` to provide mover convergence parameters and starting solution. This implements “A Robust Method to Extract the Rotational Part of Deformations” by Müller et al.

source

#### pub fn from_matrix_eps(
m: &Matrix2<T>,
eps: T,
max_iter: usize,
guess: Self
) -> Selfwhere
T: RealField,

Builds an unit complex by extracting the rotation part of the given transformation `m`.

This implements “A Robust Method to Extract the Rotational Part of Deformations” by Müller et al.

##### Parameters

- `m`: the matrix from which the rotational part is to be extracted.
- `eps`: the angular errors tolerated between the current rotation and the optimal one.
- `max_iter`: the maximum number of iterations. Loops indefinitely until convergence if set to `0`.
- `guess`: an estimate of the solution. Convergence will be significantly faster if an initial solution close to the actual solution is provided. Can be set to `UnitQuaternion::identity()` if no other guesses come to mind.

source

#### pub fn rotation_to(&self, other: &Self) -> Self

The unit complex number needed to make `self` and `other` coincide.

The result is such that: `self.rotation_to(other) * self == other`.

##### Example

    let rot1 = UnitComplex::new(0.1);
    let rot2 = UnitComplex::new(1.7);
    let rot_to = rot1.rotation_to(&rot2);

    assert_relative_eq!(rot_to * rot1, rot2);
    assert_relative_eq!(rot_to.inverse() * rot2, rot1);

source

#### pub fn powf(&self, n: T) -> Self

Raise this unit complex number to a given floating power.

This returns the unit complex number that identifies a rotation angle equal to `self.angle() × n`.

##### Example

    let rot = UnitComplex::new(0.78);
    let pow = rot.powf(2.0);
    assert_relative_eq!(pow.angle(), 2.0 * 0.78);

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### impl<T: SimdRealField> Unit<Complex<T>>where
T::Element: SimdRealField,

#### Construction from two vectors

source

#### pub fn rotation_between<SB, SC>(
a: &Vector<T, U2, SB>,
b: &Vector<T, U2, SC>
) -> Selfwhere
T: RealField,
SB: Storage<T, U2>,
SC: Storage<T, U2>,

The unit complex needed to make `a` and `b` be collinear and point toward the same direction.

##### Example

    let a = Vector2::new(1.0, 2.0);
    let b = Vector2::new(2.0, 1.0);
    let rot = UnitComplex::rotation_between(&a, &b);
    assert_relative_eq!(rot * a, b);
    assert_relative_eq!(rot.inverse() * b, a);

source

#### pub fn scaled_rotation_between<SB, SC>(
a: &Vector<T, U2, SB>,
b: &Vector<T, U2, SC>,
s: T
) -> Selfwhere
T: RealField,
SB: Storage<T, U2>,
SC: Storage<T, U2>,

The smallest rotation needed to make `a` and `b` collinear and point toward the same direction, raised to the power `s`.

##### Example

    let a = Vector2::new(1.0, 2.0);
    let b = Vector2::new(2.0, 1.0);
    let rot2 = UnitComplex::scaled_rotation_between(&a, &b, 0.2);
    let rot5 = UnitComplex::scaled_rotation_between(&a, &b, 0.5);
    assert_relative_eq!(rot2 * rot2 * rot2 * rot2 * rot2 * a, b, epsilon = 1.0e-6);
    assert_relative_eq!(rot5 * rot5 * a, b, epsilon = 1.0e-6);

source

#### pub fn rotation_between_axis<SB, SC>(
a: &Unit<Vector<T, U2, SB>>,
b: &Unit<Vector<T, U2, SC>>
) -> Selfwhere
SB: Storage<T, U2>,
SC: Storage<T, U2>,

The unit complex needed to make `a` and `b` be collinear and point toward the same direction.

##### Example

    let a = Unit::new_normalize(Vector2::new(1.0, 2.0));
    let b = Unit::new_normalize(Vector2::new(2.0, 1.0));
    let rot = UnitComplex::rotation_between_axis(&a, &b);
    assert_relative_eq!(rot * a, b);
    assert_relative_eq!(rot.inverse() * b, a);

source

#### pub fn scaled_rotation_between_axis<SB, SC>(
na: &Unit<Vector<T, U2, SB>>,
nb: &Unit<Vector<T, U2, SC>>,
s: T
) -> Selfwhere
SB: Storage<T, U2>,
SC: Storage<T, U2>,

The smallest rotation needed to make `a` and `b` collinear and point toward the same direction, raised to the power `s`.

##### Example

    let a = Unit::new_normalize(Vector2::new(1.0, 2.0));
    let b = Unit::new_normalize(Vector2::new(2.0, 1.0));
    let rot2 = UnitComplex::scaled_rotation_between_axis(&a, &b, 0.2);
    let rot5 = UnitComplex::scaled_rotation_between_axis(&a, &b, 0.5);
    assert_relative_eq!(rot2 * rot2 * rot2 * rot2 * rot2 * a, b, epsilon = 1.0e-6);
    assert_relative_eq!(rot5 * rot5 * a, b, epsilon = 1.0e-6);

## Trait Implementations§

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### impl<T: RealField> AbsDiffEq<Unit<Complex<T>>> for UnitComplex<T>

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#### type Epsilon = T

Used for specifying relative comparisons.
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#### fn default_epsilon() -> Self::Epsilon

The default tolerance to use when testing values that are close together. Read more
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#### fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool

A test for equality that uses the absolute difference to compute the approximate equality of two numbers. Read more
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#### fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of `AbsDiffEq::abs_diff_eq`.
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### impl<T: RealField + AbsDiffEq<Epsilon = T>> AbsDiffEq<Unit<DualQuaternion<T>>> for UnitDualQuaternion<T>

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#### type Epsilon = T

Used for specifying relative comparisons.
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#### fn default_epsilon() -> Self::Epsilon

The default tolerance to use when testing values that are close together. Read more
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#### fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool

A test for equality that uses the absolute difference to compute the approximate equality of two numbers. Read more
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#### fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of `AbsDiffEq::abs_diff_eq`.
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### impl<T, R: Dim, C: Dim, S> AbsDiffEq<Unit<Matrix<T, R, C, S>>> for Unit<Matrix<T, R, C, S>>where
T: Scalar + AbsDiffEq,
S: RawStorage<T, R, C>,
T::Epsilon: Clone,

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#### type Epsilon = <T as AbsDiffEq<T>>::Epsilon

Used for specifying relative comparisons.
source§

#### fn default_epsilon() -> Self::Epsilon

The default tolerance to use when testing values that are close together. Read more
source§

#### fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool

A test for equality that uses the absolute difference to compute the approximate equality of two numbers. Read more
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#### fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of `AbsDiffEq::abs_diff_eq`.
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### impl<T: RealField + AbsDiffEq<Epsilon = T>> AbsDiffEq<Unit<Quaternion<T>>> for UnitQuaternion<T>

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#### type Epsilon = T

Used for specifying relative comparisons.
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#### fn default_epsilon() -> Self::Epsilon

The default tolerance to use when testing values that are close together. Read more
source§

#### fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool

A test for equality that uses the absolute difference to compute the approximate equality of two numbers. Read more
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#### fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of `AbsDiffEq::abs_diff_eq`.
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### impl<T> AsRef<T> for Unit<T>

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#### fn as_ref(&self) -> &T

Converts this type into a shared reference of the (usually inferred) input type.
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### impl<T: Clone> Clone for Unit<T>

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#### fn clone(&self) -> Unit<T>

Returns a copy of the value. Read more
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#### fn clone_from(&mut self, source: &Self)

Performs copy-assignment from `source`. Read more
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### impl<T: Debug> Debug for Unit<T>

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#### fn fmt(&self, formatter: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter. Read more
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### impl<T> Deref for Unit<T>

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#### type Target = T

The resulting type after dereferencing.
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#### fn deref(&self) -> &T

Dereferences the value.
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### impl<'a, 'b, T: SimdRealField> Div<&'a Unit<DualQuaternion<T>>> for &'b Translation3<T>where
T::Element: SimdRealField,

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#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: &'a UnitDualQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for &'a Isometry<T, UnitComplex<T>, 2>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for &'a Rotation<T, 2>where
T::Element: SimdRealField,

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#### type Output = Unit<Complex<T>>

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for &'a Similarity<T, UnitComplex<T>, 2>where
T::Element: SimdRealField,

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#### type Output = Similarity<T, Unit<Complex<T>>, 2>

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for &'a UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Complex<T>>

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for Rotation<T, 2>where
T::Element: SimdRealField,

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#### type Output = Unit<Complex<T>>

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>where
T::Element: SimdRealField,

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#### type Output = Similarity<T, Unit<Complex<T>>, 2>

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Complex<T>>

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for &'a DualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = DualQuaternion<T>

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for &'a Isometry3<T>where
T::Element: SimdRealField,

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#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for &'a UnitDualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for &'a UnitQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for DualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = DualQuaternion<T>

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for Isometry3<T>where
T::Element: SimdRealField,

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#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for Translation3<T>where
T::Element: SimdRealField,

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#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for UnitDualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'b, T: SimdRealField> Div<&'b Unit<DualQuaternion<T>>> for UnitQuaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for &'a Isometry<T, UnitQuaternion<T>, 3>where
T::Element: SimdRealField,

§

#### type Output = Isometry<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for &'a Rotation<T, 3>where
T::Element: SimdRealField,

§

#### type Output = Unit<Quaternion<T>>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for &'a Similarity<T, UnitQuaternion<T>, 3>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'a, 'b, T, C> Div<&'b Unit<Quaternion<T>>> for &'a Transform<T, C, 3>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
C: TCategoryMul<TAffine>,

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#### type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 3>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for &'a UnitDualQuaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for &'a UnitQuaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Unit<Quaternion<T>>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for Isometry<T, UnitQuaternion<T>, 3>where
T::Element: SimdRealField,

§

#### type Output = Isometry<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for Rotation<T, 3>where
T::Element: SimdRealField,

§

#### type Output = Unit<Quaternion<T>>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'b, T, C> Div<&'b Unit<Quaternion<T>>> for Transform<T, C, 3>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
C: TCategoryMul<TAffine>,

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#### type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 3>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for UnitDualQuaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for UnitQuaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Unit<Quaternion<T>>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'a, T: SimdRealField> Div<Unit<Complex<T>>> for &'a Isometry<T, UnitComplex<T>, 2>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitComplex<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'a, T: SimdRealField> Div<Unit<Complex<T>>> for &'a Rotation<T, 2>where
T::Element: SimdRealField,

§

#### type Output = Unit<Complex<T>>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitComplex<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'a, T: SimdRealField> Div<Unit<Complex<T>>> for &'a Similarity<T, UnitComplex<T>, 2>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Complex<T>>, 2>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitComplex<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'a, T: SimdRealField> Div<Unit<Complex<T>>> for &'a UnitComplex<T>where
T::Element: SimdRealField,

§

#### type Output = Unit<Complex<T>>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitComplex<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<T: SimdRealField> Div<Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>where
T::Element: SimdRealField,

§

#### type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitComplex<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<T: SimdRealField> Div<Unit<Complex<T>>> for Rotation<T, 2>where
T::Element: SimdRealField,

§

#### type Output = Unit<Complex<T>>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitComplex<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<T: SimdRealField> Div<Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Complex<T>>, 2>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitComplex<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<T: SimdRealField> Div<Unit<Complex<T>>> for UnitComplex<T>where
T::Element: SimdRealField,

§

#### type Output = Unit<Complex<T>>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: Self) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'a, T: SimdRealField> Div<Unit<DualQuaternion<T>>> for &'a DualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = DualQuaternion<T>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'a, T: SimdRealField> Div<Unit<DualQuaternion<T>>> for &'a Isometry3<T>where
T::Element: SimdRealField,

§

#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'a, T: SimdRealField> Div<Unit<DualQuaternion<T>>> for &'a Translation3<T>where
T::Element: SimdRealField,

§

#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'a, T: SimdRealField> Div<Unit<DualQuaternion<T>>> for &'a UnitDualQuaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'a, T: SimdRealField> Div<Unit<DualQuaternion<T>>> for &'a UnitQuaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<T: SimdRealField> Div<Unit<DualQuaternion<T>>> for DualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = DualQuaternion<T>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<T: SimdRealField> Div<Unit<DualQuaternion<T>>> for Isometry3<T>where
T::Element: SimdRealField,

§

#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<T: SimdRealField> Div<Unit<DualQuaternion<T>>> for Translation3<T>where
T::Element: SimdRealField,

§

#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<T: SimdRealField> Div<Unit<DualQuaternion<T>>> for UnitDualQuaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<T: SimdRealField> Div<Unit<DualQuaternion<T>>> for UnitQuaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'a, T: SimdRealField> Div<Unit<Quaternion<T>>> for &'a Isometry<T, UnitQuaternion<T>, 3>where
T::Element: SimdRealField,

§

#### type Output = Isometry<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'a, T: SimdRealField> Div<Unit<Quaternion<T>>> for &'a Rotation<T, 3>where
T::Element: SimdRealField,

§

#### type Output = Unit<Quaternion<T>>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'a, T: SimdRealField> Div<Unit<Quaternion<T>>> for &'a Similarity<T, UnitQuaternion<T>, 3>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'a, T, C> Div<Unit<Quaternion<T>>> for &'a Transform<T, C, 3>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
C: TCategoryMul<TAffine>,

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#### type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 3>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'a, T: SimdRealField> Div<Unit<Quaternion<T>>> for &'a UnitDualQuaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'a, T: SimdRealField> Div<Unit<Quaternion<T>>> for &'a UnitQuaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Unit<Quaternion<T>>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<T: SimdRealField> Div<Unit<Quaternion<T>>> for Isometry<T, UnitQuaternion<T>, 3>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<T: SimdRealField> Div<Unit<Quaternion<T>>> for Rotation<T, 3>where
T::Element: SimdRealField,

§

#### type Output = Unit<Quaternion<T>>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<T: SimdRealField> Div<Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>where
T::Element: SimdRealField,

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#### type Output = Similarity<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<T, C> Div<Unit<Quaternion<T>>> for Transform<T, C, 3>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
C: TCategoryMul<TAffine>,

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#### type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 3>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<T: SimdRealField> Div<Unit<Quaternion<T>>> for UnitDualQuaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<T: SimdRealField> Div<Unit<Quaternion<T>>> for UnitQuaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Unit<Quaternion<T>>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'b, T> DivAssign<&'b Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

source§

#### fn div_assign(&mut self, rhs: &'b UnitComplex<T>)

Performs the `/=` operation. Read more
source§

### impl<'b, T: SimdRealField> DivAssign<&'b Unit<Complex<T>>> for Rotation<T, 2>where
T::Element: SimdRealField,

source§

#### fn div_assign(&mut self, rhs: &'b UnitComplex<T>)

Performs the `/=` operation. Read more
source§

### impl<'b, T> DivAssign<&'b Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

source§

#### fn div_assign(&mut self, rhs: &'b UnitComplex<T>)

Performs the `/=` operation. Read more
source§

### impl<'b, T, C> DivAssign<&'b Unit<Complex<T>>> for Transform<T, C, 2>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
C: TCategory,

source§

#### fn div_assign(&mut self, rhs: &'b UnitComplex<T>)

Performs the `/=` operation. Read more
source§

### impl<'b, T: SimdRealField> DivAssign<&'b Unit<Complex<T>>> for UnitComplex<T>where
T::Element: SimdRealField,

source§

#### fn div_assign(&mut self, rhs: &'b UnitComplex<T>)

Performs the `/=` operation. Read more
source§

### impl<'b, T: SimdRealField> DivAssign<&'b Unit<DualQuaternion<T>>> for DualQuaternion<T>where
T::Element: SimdRealField,

source§

#### fn div_assign(&mut self, rhs: &'b UnitDualQuaternion<T>)

Performs the `/=` operation. Read more
source§

### impl<'b, T: SimdRealField> DivAssign<&'b Unit<DualQuaternion<T>>> for UnitDualQuaternion<T>where
T::Element: SimdRealField,

source§

#### fn div_assign(&mut self, rhs: &'b UnitDualQuaternion<T>)

Performs the `/=` operation. Read more
source§

### impl<'b, T> DivAssign<&'b Unit<Quaternion<T>>> for Isometry<T, UnitQuaternion<T>, 3>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

source§

#### fn div_assign(&mut self, rhs: &'b UnitQuaternion<T>)

Performs the `/=` operation. Read more
source§

### impl<'b, T> DivAssign<&'b Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

source§

#### fn div_assign(&mut self, rhs: &'b UnitQuaternion<T>)

Performs the `/=` operation. Read more
source§

### impl<'b, T, C> DivAssign<&'b Unit<Quaternion<T>>> for Transform<T, C, 3>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
C: TCategory,

source§

#### fn div_assign(&mut self, rhs: &'b UnitQuaternion<T>)

Performs the `/=` operation. Read more
source§

### impl<'b, T: SimdRealField> DivAssign<&'b Unit<Quaternion<T>>> for UnitDualQuaternion<T>where
T::Element: SimdRealField,

source§

#### fn div_assign(&mut self, rhs: &'b UnitQuaternion<T>)

Performs the `/=` operation. Read more
source§

### impl<'b, T: SimdRealField> DivAssign<&'b Unit<Quaternion<T>>> for UnitQuaternion<T>where
T::Element: SimdRealField,

source§

#### fn div_assign(&mut self, rhs: &'b UnitQuaternion<T>)

Performs the `/=` operation. Read more
source§

### impl<T> DivAssign<Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

source§

#### fn div_assign(&mut self, rhs: UnitComplex<T>)

Performs the `/=` operation. Read more
source§

### impl<T: SimdRealField> DivAssign<Unit<Complex<T>>> for Rotation<T, 2>where
T::Element: SimdRealField,

source§

#### fn div_assign(&mut self, rhs: UnitComplex<T>)

Performs the `/=` operation. Read more
source§

### impl<T> DivAssign<Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

source§

#### fn div_assign(&mut self, rhs: UnitComplex<T>)

Performs the `/=` operation. Read more
source§

### impl<T, C> DivAssign<Unit<Complex<T>>> for Transform<T, C, 2>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
C: TCategory,

source§

#### fn div_assign(&mut self, rhs: UnitComplex<T>)

Performs the `/=` operation. Read more
source§

### impl<T: SimdRealField> DivAssign<Unit<Complex<T>>> for UnitComplex<T>where
T::Element: SimdRealField,

source§

#### fn div_assign(&mut self, rhs: UnitComplex<T>)

Performs the `/=` operation. Read more
source§

### impl<T: SimdRealField> DivAssign<Unit<DualQuaternion<T>>> for DualQuaternion<T>where
T::Element: SimdRealField,

source§

#### fn div_assign(&mut self, rhs: UnitDualQuaternion<T>)

Performs the `/=` operation. Read more
source§

### impl<T: SimdRealField> DivAssign<Unit<DualQuaternion<T>>> for UnitDualQuaternion<T>where
T::Element: SimdRealField,

source§

#### fn div_assign(&mut self, rhs: UnitDualQuaternion<T>)

Performs the `/=` operation. Read more
source§

### impl<T> DivAssign<Unit<Quaternion<T>>> for Isometry<T, UnitQuaternion<T>, 3>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

source§

#### fn div_assign(&mut self, rhs: UnitQuaternion<T>)

Performs the `/=` operation. Read more
source§

### impl<T> DivAssign<Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

source§

#### fn div_assign(&mut self, rhs: UnitQuaternion<T>)

Performs the `/=` operation. Read more
source§

### impl<T, C> DivAssign<Unit<Quaternion<T>>> for Transform<T, C, 3>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
C: TCategory,

source§

#### fn div_assign(&mut self, rhs: UnitQuaternion<T>)

Performs the `/=` operation. Read more
source§

### impl<T: SimdRealField> DivAssign<Unit<Quaternion<T>>> for UnitDualQuaternion<T>where
T::Element: SimdRealField,

source§

#### fn div_assign(&mut self, rhs: UnitQuaternion<T>)

Performs the `/=` operation. Read more
source§

### impl<T: SimdRealField> DivAssign<Unit<Quaternion<T>>> for UnitQuaternion<T>where
T::Element: SimdRealField,

source§

#### fn div_assign(&mut self, rhs: UnitQuaternion<T>)

Performs the `/=` operation. Read more
source§

### impl<T, R: Dim, C: Dim> From<[Unit<Matrix<<T as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<<T as SimdValue>::Element, R, C>>::Buffer>>; 16]> for Unit<OMatrix<T, R, C>>where
T: From<[<T as SimdValue>::Element; 16]> + Scalar + PrimitiveSimdValue,
T::Element: Scalar,
DefaultAllocator: Allocator<T, R, C> + Allocator<T::Element, R, C>,

source§

#### fn from(arr: [Unit<OMatrix<T::Element, R, C>>; 16]) -> Self

Converts to this type from the input type.
source§

### impl<T, R: Dim, C: Dim> From<[Unit<Matrix<<T as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<<T as SimdValue>::Element, R, C>>::Buffer>>; 2]> for Unit<OMatrix<T, R, C>>where
T: From<[<T as SimdValue>::Element; 2]> + Scalar + PrimitiveSimdValue,
T::Element: Scalar,
DefaultAllocator: Allocator<T, R, C> + Allocator<T::Element, R, C>,

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#### fn from(arr: [Unit<OMatrix<T::Element, R, C>>; 2]) -> Self

Converts to this type from the input type.
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### impl<T, R: Dim, C: Dim> From<[Unit<Matrix<<T as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<<T as SimdValue>::Element, R, C>>::Buffer>>; 4]> for Unit<OMatrix<T, R, C>>where
T: From<[<T as SimdValue>::Element; 4]> + Scalar + PrimitiveSimdValue,
T::Element: Scalar,
DefaultAllocator: Allocator<T, R, C> + Allocator<T::Element, R, C>,

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#### fn from(arr: [Unit<OMatrix<T::Element, R, C>>; 4]) -> Self

Converts to this type from the input type.
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### impl<T, R: Dim, C: Dim> From<[Unit<Matrix<<T as SimdValue>::Element, R, C, <DefaultAllocator as Allocator<<T as SimdValue>::Element, R, C>>::Buffer>>; 8]> for Unit<OMatrix<T, R, C>>where
T: From<[<T as SimdValue>::Element; 8]> + Scalar + PrimitiveSimdValue,
T::Element: Scalar,
DefaultAllocator: Allocator<T, R, C> + Allocator<T::Element, R, C>,

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#### fn from(arr: [Unit<OMatrix<T::Element, R, C>>; 8]) -> Self

Converts to this type from the input type.
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### impl<T: SimdRealField> From<Unit<Complex<T>>> for Matrix2<T>where
T::Element: SimdRealField,

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#### fn from(q: UnitComplex<T>) -> Self

Converts to this type from the input type.
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### impl<T: SimdRealField> From<Unit<Complex<T>>> for Matrix3<T>where
T::Element: SimdRealField,

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#### fn from(q: UnitComplex<T>) -> Matrix3<T>

Converts to this type from the input type.
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### impl<T: SimdRealField> From<Unit<Complex<T>>> for Rotation2<T>where
T::Element: SimdRealField,

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#### fn from(q: UnitComplex<T>) -> Self

Converts to this type from the input type.
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### impl<T: SimdRealField> From<Unit<DualQuaternion<T>>> for Isometry3<T>where
T::Element: SimdRealField,

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#### fn from(dq: UnitDualQuaternion<T>) -> Self

Converts to this type from the input type.
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### impl<T: SimdRealField + RealField> From<Unit<DualQuaternion<T>>> for Matrix4<T>where
T::Element: SimdRealField,

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#### fn from(dq: UnitDualQuaternion<T>) -> Self

Converts to this type from the input type.
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### impl<T: SimdRealField> From<Unit<Quaternion<T>>> for Matrix3<T>where
T::Element: SimdRealField,

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#### fn from(q: UnitQuaternion<T>) -> Self

Converts to this type from the input type.
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### impl<T: SimdRealField> From<Unit<Quaternion<T>>> for Matrix4<T>where
T::Element: SimdRealField,

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#### fn from(q: UnitQuaternion<T>) -> Self

Converts to this type from the input type.
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### impl<T: SimdRealField> From<Unit<Quaternion<T>>> for Rotation3<T>where
T::Element: SimdRealField,

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#### fn from(q: UnitQuaternion<T>) -> Self

Converts to this type from the input type.
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### impl<T: Hash> Hash for Unit<T>

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#### fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given `Hasher`. Read more
1.3.0 · source§

#### fn hash_slice<H>(data: &[Self], state: &mut H)where
H: Hasher,
Self: Sized,

Feeds a slice of this type into the given `Hasher`. Read more
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### impl<'a, 'b, T: SimdRealField> Mul<&'a Unit<DualQuaternion<T>>> for &'b Translation3<T>where
T::Element: SimdRealField,

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#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'a UnitDualQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for &'a Isometry<T, UnitComplex<T>, 2>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for &'a Rotation<T, 2>where
T::Element: SimdRealField,

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#### type Output = Unit<Complex<T>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for &'a Similarity<T, UnitComplex<T>, 2>where
T::Element: SimdRealField,

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#### type Output = Similarity<T, Unit<Complex<T>>, 2>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T, C> Mul<&'b Unit<Complex<T>>> for &'a Transform<T, C, 2>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
C: TCategoryMul<TAffine>,

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#### type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 2>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for &'a Translation<T, 2>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: &'b UnitComplex<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for &'a UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Complex<T>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for Rotation<T, 2>where
T::Element: SimdRealField,

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#### type Output = Unit<Complex<T>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>where
T::Element: SimdRealField,

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#### type Output = Similarity<T, Unit<Complex<T>>, 2>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T, C> Mul<&'b Unit<Complex<T>>> for Transform<T, C, 2>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
C: TCategoryMul<TAffine>,

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#### type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 2>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for Translation<T, 2>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: &'b UnitComplex<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Complex<T>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for &'a DualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = DualQuaternion<T>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for &'a Isometry3<T>where
T::Element: SimdRealField,

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#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for &'a UnitDualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for &'a UnitQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for DualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = DualQuaternion<T>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for Isometry3<T>where
T::Element: SimdRealField,

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#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for Translation3<T>where
T::Element: SimdRealField,

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#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for UnitDualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField> Mul<&'b Unit<DualQuaternion<T>>> for UnitQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitDualQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField, S: Storage<T, Const<2>>> Mul<&'b Unit<Matrix<T, Const<2>, Const<1>, S>>> for &'a UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b Unit<Vector<T, Const<2>, S>>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField, S: Storage<T, Const<2>>> Mul<&'b Unit<Matrix<T, Const<2>, Const<1>, S>>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b Unit<Vector<T, Const<2>, S>>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField, SB: Storage<T, U3>> Mul<&'b Unit<Matrix<T, Const<3>, Const<1>, SB>>> for &'a UnitDualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b Unit<Vector<T, U3, SB>>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField, SB: Storage<T, Const<3>>> Mul<&'b Unit<Matrix<T, Const<3>, Const<1>, SB>>> for &'a UnitQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b Unit<Vector<T, U3, SB>>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField, SB: Storage<T, U3>> Mul<&'b Unit<Matrix<T, Const<3>, Const<1>, SB>>> for UnitDualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b Unit<Vector<T, U3, SB>>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField, SB: Storage<T, Const<3>>> Mul<&'b Unit<Matrix<T, Const<3>, Const<1>, SB>>> for UnitQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b Unit<Vector<T, U3, SB>>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField, R, const D: usize> Mul<&'b Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>> for &'a Isometry<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

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#### type Output = Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: &'b Unit<SVector<T, D>>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField, R, const D: usize> Mul<&'b Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>> for Isometry<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

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#### type Output = Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: &'b Unit<SVector<T, D>>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T, S, const D: usize> Mul<&'b Unit<Matrix<T, Const<D>, Const<1>, S>>> for &'a Rotation<T, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,
S: Storage<T, Const<D>>,
ShapeConstraint: AreMultipliable<Const<D>, Const<D>, Const<D>, U1>,

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#### type Output = Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: &'b Unit<Vector<T, Const<D>, S>>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T, S, const D: usize> Mul<&'b Unit<Matrix<T, Const<D>, Const<1>, S>>> for Rotation<T, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,
S: Storage<T, Const<D>>,
ShapeConstraint: AreMultipliable<Const<D>, Const<D>, Const<D>, U1>,

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#### type Output = Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: &'b Unit<Vector<T, Const<D>, S>>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for &'a Isometry<T, UnitQuaternion<T>, 3>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for &'a Rotation<T, 3>where
T::Element: SimdRealField,

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#### type Output = Unit<Quaternion<T>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for &'a Similarity<T, UnitQuaternion<T>, 3>where
T::Element: SimdRealField,

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#### type Output = Similarity<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T, C> Mul<&'b Unit<Quaternion<T>>> for &'a Transform<T, C, 3>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
C: TCategoryMul<TAffine>,

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#### type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 3>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for &'a Translation<T, 3>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: &'b UnitQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for &'a UnitDualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for &'a UnitQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Quaternion<T>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for Isometry<T, UnitQuaternion<T>, 3>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for Rotation<T, 3>where
T::Element: SimdRealField,

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#### type Output = Unit<Quaternion<T>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>where
T::Element: SimdRealField,

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#### type Output = Similarity<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T, C> Mul<&'b Unit<Quaternion<T>>> for Transform<T, C, 3>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
C: TCategoryMul<TAffine>,

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#### type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 3>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for Translation<T, 3>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: &'b UnitQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for UnitDualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for UnitQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Quaternion<T>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField> Mul<Unit<Complex<T>>> for &'a Isometry<T, UnitComplex<T>, 2>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField> Mul<Unit<Complex<T>>> for &'a Rotation<T, 2>where
T::Element: SimdRealField,

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#### type Output = Unit<Complex<T>>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField> Mul<Unit<Complex<T>>> for &'a Similarity<T, UnitComplex<T>, 2>where
T::Element: SimdRealField,

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#### type Output = Similarity<T, Unit<Complex<T>>, 2>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T, C> Mul<Unit<Complex<T>>> for &'a Transform<T, C, 2>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
C: TCategoryMul<TAffine>,

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#### type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 2>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'a, T: SimdRealField> Mul<Unit<Complex<T>>> for &'a Translation<T, 2>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, right: UnitComplex<T>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'a, T: SimdRealField> Mul<Unit<Complex<T>>> for &'a UnitComplex<T>where
T::Element: SimdRealField,

§

#### type Output = Unit<Complex<T>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<T: SimdRealField> Mul<Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField> Mul<Unit<Complex<T>>> for Rotation<T, 2>where
T::Element: SimdRealField,

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#### type Output = Unit<Complex<T>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<T: SimdRealField> Mul<Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>where
T::Element: SimdRealField,

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#### type Output = Similarity<T, Unit<Complex<T>>, 2>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T, C> Mul<Unit<Complex<T>>> for Transform<T, C, 2>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
C: TCategoryMul<TAffine>,

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#### type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 2>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<T: SimdRealField> Mul<Unit<Complex<T>>> for Translation<T, 2>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, right: UnitComplex<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField> Mul<Unit<Complex<T>>> for UnitComplex<T>

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#### type Output = Unit<Complex<T>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: Self) -> Self

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for &'a DualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = DualQuaternion<T>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for &'a Isometry3<T>where
T::Element: SimdRealField,

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#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for &'a Translation3<T>where
T::Element: SimdRealField,

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#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for &'a UnitDualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for &'a UnitQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for DualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = DualQuaternion<T>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for Isometry3<T>where
T::Element: SimdRealField,

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#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for Translation3<T>where
T::Element: SimdRealField,

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#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for UnitDualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField> Mul<Unit<DualQuaternion<T>>> for UnitQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: UnitDualQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField, S: Storage<T, Const<2>>> Mul<Unit<Matrix<T, Const<2>, Const<1>, S>>> for &'a UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: Unit<Vector<T, Const<2>, S>>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField, S: Storage<T, Const<2>>> Mul<Unit<Matrix<T, Const<2>, Const<1>, S>>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Matrix<T, Const<2>, Const<1>, ArrayStorage<T, 2, 1>>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: Unit<Vector<T, Const<2>, S>>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField, SB: Storage<T, U3>> Mul<Unit<Matrix<T, Const<3>, Const<1>, SB>>> for &'a UnitDualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: Unit<Vector<T, U3, SB>>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField, SB: Storage<T, Const<3>>> Mul<Unit<Matrix<T, Const<3>, Const<1>, SB>>> for &'a UnitQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: Unit<Vector<T, U3, SB>>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField, SB: Storage<T, U3>> Mul<Unit<Matrix<T, Const<3>, Const<1>, SB>>> for UnitDualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: Unit<Vector<T, U3, SB>>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField, SB: Storage<T, Const<3>>> Mul<Unit<Matrix<T, Const<3>, Const<1>, SB>>> for UnitQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Matrix<T, Const<3>, Const<1>, ArrayStorage<T, 3, 1>>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: Unit<Vector<T, U3, SB>>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField, R, const D: usize> Mul<Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>> for &'a Isometry<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

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#### type Output = Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, right: Unit<SVector<T, D>>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField, R, const D: usize> Mul<Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>> for Isometry<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

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#### type Output = Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, right: Unit<SVector<T, D>>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T, S, const D: usize> Mul<Unit<Matrix<T, Const<D>, Const<1>, S>>> for &'a Rotation<T, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,
S: Storage<T, Const<D>>,
ShapeConstraint: AreMultipliable<Const<D>, Const<D>, Const<D>, U1>,

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#### type Output = Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, right: Unit<Vector<T, Const<D>, S>>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T, S, const D: usize> Mul<Unit<Matrix<T, Const<D>, Const<1>, S>>> for Rotation<T, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,
S: Storage<T, Const<D>>,
ShapeConstraint: AreMultipliable<Const<D>, Const<D>, Const<D>, U1>,

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#### type Output = Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, right: Unit<Vector<T, Const<D>, S>>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField> Mul<Unit<Quaternion<T>>> for &'a Isometry<T, UnitQuaternion<T>, 3>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField> Mul<Unit<Quaternion<T>>> for &'a Rotation<T, 3>where
T::Element: SimdRealField,

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#### type Output = Unit<Quaternion<T>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField> Mul<Unit<Quaternion<T>>> for &'a Similarity<T, UnitQuaternion<T>, 3>where
T::Element: SimdRealField,

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#### type Output = Similarity<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T, C> Mul<Unit<Quaternion<T>>> for &'a Transform<T, C, 3>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
C: TCategoryMul<TAffine>,

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#### type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 3>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField> Mul<Unit<Quaternion<T>>> for &'a Translation<T, 3>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, right: UnitQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField> Mul<Unit<Quaternion<T>>> for &'a UnitDualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField> Mul<Unit<Quaternion<T>>> for &'a UnitQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Quaternion<T>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField> Mul<Unit<Quaternion<T>>> for Isometry<T, UnitQuaternion<T>, 3>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField> Mul<Unit<Quaternion<T>>> for Rotation<T, 3>where
T::Element: SimdRealField,

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#### type Output = Unit<Quaternion<T>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField> Mul<Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>where
T::Element: SimdRealField,

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#### type Output = Similarity<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T, C> Mul<Unit<Quaternion<T>>> for Transform<T, C, 3>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
C: TCategoryMul<TAffine>,

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#### type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 3>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField> Mul<Unit<Quaternion<T>>> for Translation<T, 3>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, right: UnitQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField> Mul<Unit<Quaternion<T>>> for UnitDualQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = Unit<DualQuaternion<T>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField> Mul<Unit<Quaternion<T>>> for UnitQuaternion<T>where
T::Element: SimdRealField,

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#### type Output = Unit<Quaternion<T>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T> MulAssign<&'b Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

source§

#### fn mul_assign(&mut self, rhs: &'b UnitComplex<T>)

Performs the `*=` operation. Read more
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### impl<'b, T: SimdRealField> MulAssign<&'b Unit<Complex<T>>> for Rotation<T, 2>where
T::Element: SimdRealField,

source§

#### fn mul_assign(&mut self, rhs: &'b UnitComplex<T>)

Performs the `*=` operation. Read more
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### impl<'b, T> MulAssign<&'b Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

source§

#### fn mul_assign(&mut self, rhs: &'b UnitComplex<T>)

Performs the `*=` operation. Read more
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### impl<'b, T, C> MulAssign<&'b Unit<Complex<T>>> for Transform<T, C, 2>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
C: TCategory,

source§

#### fn mul_assign(&mut self, rhs: &'b UnitComplex<T>)

Performs the `*=` operation. Read more
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### impl<'b, T: SimdRealField> MulAssign<&'b Unit<Complex<T>>> for UnitComplex<T>where
T::Element: SimdRealField,

source§

#### fn mul_assign(&mut self, rhs: &'b UnitComplex<T>)

Performs the `*=` operation. Read more
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### impl<'b, T: SimdRealField> MulAssign<&'b Unit<DualQuaternion<T>>> for DualQuaternion<T>where
T::Element: SimdRealField,

source§

#### fn mul_assign(&mut self, rhs: &'b UnitDualQuaternion<T>)

Performs the `*=` operation. Read more
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### impl<'b, T: SimdRealField> MulAssign<&'b Unit<DualQuaternion<T>>> for UnitDualQuaternion<T>where
T::Element: SimdRealField,

source§

#### fn mul_assign(&mut self, rhs: &'b UnitDualQuaternion<T>)

Performs the `*=` operation. Read more
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### impl<'b, T> MulAssign<&'b Unit<Quaternion<T>>> for Isometry<T, UnitQuaternion<T>, 3>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

source§

#### fn mul_assign(&mut self, rhs: &'b UnitQuaternion<T>)

Performs the `*=` operation. Read more
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### impl<'b, T> MulAssign<&'b Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

source§

#### fn mul_assign(&mut self, rhs: &'b UnitQuaternion<T>)

Performs the `*=` operation. Read more
source§

### impl<'b, T, C> MulAssign<&'b Unit<Quaternion<T>>> for Transform<T, C, 3>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
C: TCategory,

source§

#### fn mul_assign(&mut self, rhs: &'b UnitQuaternion<T>)

Performs the `*=` operation. Read more
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### impl<'b, T: SimdRealField> MulAssign<&'b Unit<Quaternion<T>>> for UnitDualQuaternion<T>where
T::Element: SimdRealField,

source§

#### fn mul_assign(&mut self, rhs: &'b UnitQuaternion<T>)

Performs the `*=` operation. Read more
source§

### impl<'b, T: SimdRealField> MulAssign<&'b Unit<Quaternion<T>>> for UnitQuaternion<T>where
T::Element: SimdRealField,

source§

#### fn mul_assign(&mut self, rhs: &'b UnitQuaternion<T>)

Performs the `*=` operation. Read more
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### impl<T> MulAssign<Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

source§

#### fn mul_assign(&mut self, rhs: UnitComplex<T>)

Performs the `*=` operation. Read more
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### impl<T: SimdRealField> MulAssign<Unit<Complex<T>>> for Rotation<T, 2>where
T::Element: SimdRealField,

source§

#### fn mul_assign(&mut self, rhs: UnitComplex<T>)

Performs the `*=` operation. Read more
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### impl<T> MulAssign<Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

source§

#### fn mul_assign(&mut self, rhs: UnitComplex<T>)

Performs the `*=` operation. Read more
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### impl<T, C> MulAssign<Unit<Complex<T>>> for Transform<T, C, 2>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
C: TCategory,

source§

#### fn mul_assign(&mut self, rhs: UnitComplex<T>)

Performs the `*=` operation. Read more
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### impl<T: SimdRealField> MulAssign<Unit<Complex<T>>> for UnitComplex<T>where
T::Element: SimdRealField,

source§

#### fn mul_assign(&mut self, rhs: UnitComplex<T>)

Performs the `*=` operation. Read more
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### impl<T: SimdRealField> MulAssign<Unit<DualQuaternion<T>>> for DualQuaternion<T>where
T::Element: SimdRealField,

source§

#### fn mul_assign(&mut self, rhs: UnitDualQuaternion<T>)

Performs the `*=` operation. Read more
source§

### impl<T: SimdRealField> MulAssign<Unit<DualQuaternion<T>>> for UnitDualQuaternion<T>where
T::Element: SimdRealField,

source§

#### fn mul_assign(&mut self, rhs: UnitDualQuaternion<T>)

Performs the `*=` operation. Read more
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### impl<T> MulAssign<Unit<Quaternion<T>>> for Isometry<T, UnitQuaternion<T>, 3>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

source§

#### fn mul_assign(&mut self, rhs: UnitQuaternion<T>)

Performs the `*=` operation. Read more
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### impl<T> MulAssign<Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

source§

#### fn mul_assign(&mut self, rhs: UnitQuaternion<T>)

Performs the `*=` operation. Read more
source§

### impl<T, C> MulAssign<Unit<Quaternion<T>>> for Transform<T, C, 3>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
C: TCategory,

source§

#### fn mul_assign(&mut self, rhs: UnitQuaternion<T>)

Performs the `*=` operation. Read more
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### impl<T: SimdRealField> MulAssign<Unit<Quaternion<T>>> for UnitDualQuaternion<T>where
T::Element: SimdRealField,

source§

#### fn mul_assign(&mut self, rhs: UnitQuaternion<T>)

Performs the `*=` operation. Read more
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### impl<T: SimdRealField> MulAssign<Unit<Quaternion<T>>> for UnitQuaternion<T>where
T::Element: SimdRealField,

source§

#### fn mul_assign(&mut self, rhs: UnitQuaternion<T>)

Performs the `*=` operation. Read more
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### impl<T: Scalar + ClosedNeg, R: Dim, C: Dim> Neg for Unit<OMatrix<T, R, C>>where
DefaultAllocator: Allocator<T, R, C>,

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#### type Output = Unit<Matrix<T, R, C, <DefaultAllocator as Allocator<T, R, C>>::Buffer>>

The resulting type after applying the `-` operator.
source§

#### fn neg(self) -> Self::Output

Performs the unary `-` operation. Read more
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### impl<T: Scalar + PartialEq> PartialEq<Unit<Complex<T>>> for UnitComplex<T>

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#### fn eq(&self, rhs: &Self) -> bool

This method tests for `self` and `other` values to be equal, and is used by `==`. Read more
1.0.0 · source§

#### fn ne(&self, other: &Rhs) -> bool

This method tests for `!=`. The default implementation is almost always sufficient, and should not be overridden without very good reason. Read more
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### impl<T: Scalar + ClosedNeg + PartialEq + SimdRealField> PartialEq<Unit<DualQuaternion<T>>> for UnitDualQuaternion<T>

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#### fn eq(&self, rhs: &Self) -> bool

This method tests for `self` and `other` values to be equal, and is used by `==`. Read more
1.0.0 · source§

#### fn ne(&self, other: &Rhs) -> bool

This method tests for `!=`. The default implementation is almost always sufficient, and should not be overridden without very good reason. Read more
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### impl<T, R, C, S> PartialEq<Unit<Matrix<T, R, C, S>>> for Unit<Matrix<T, R, C, S>>where
T: Scalar + PartialEq,
R: Dim,
C: Dim,
S: RawStorage<T, R, C>,

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#### fn eq(&self, rhs: &Self) -> bool

This method tests for `self` and `other` values to be equal, and is used by `==`. Read more
1.0.0 · source§

#### fn ne(&self, other: &Rhs) -> bool

This method tests for `!=`. The default implementation is almost always sufficient, and should not be overridden without very good reason. Read more
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### impl<T: Scalar + ClosedNeg + PartialEq> PartialEq<Unit<Quaternion<T>>> for UnitQuaternion<T>

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#### fn eq(&self, rhs: &Self) -> bool

This method tests for `self` and `other` values to be equal, and is used by `==`. Read more
1.0.0 · source§

#### fn ne(&self, other: &Rhs) -> bool

This method tests for `!=`. The default implementation is almost always sufficient, and should not be overridden without very good reason. Read more
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### impl<T: RealField> RelativeEq<Unit<Complex<T>>> for UnitComplex<T>

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#### fn default_max_relative() -> Self::Epsilon

The default relative tolerance for testing values that are far-apart. Read more
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#### fn relative_eq(
&self,
other: &Self,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool

A test for equality that uses a relative comparison if the values are far apart.
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#### fn relative_ne(
&self,
other: &Rhs,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool

The inverse of `RelativeEq::relative_eq`.
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### impl<T: RealField + RelativeEq<Epsilon = T>> RelativeEq<Unit<DualQuaternion<T>>> for UnitDualQuaternion<T>

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#### fn default_max_relative() -> Self::Epsilon

The default relative tolerance for testing values that are far-apart. Read more
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#### fn relative_eq(
&self,
other: &Self,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool

A test for equality that uses a relative comparison if the values are far apart.
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#### fn relative_ne(
&self,
other: &Rhs,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool

The inverse of `RelativeEq::relative_eq`.
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### impl<T, R: Dim, C: Dim, S> RelativeEq<Unit<Matrix<T, R, C, S>>> for Unit<Matrix<T, R, C, S>>where
T: Scalar + RelativeEq,
S: Storage<T, R, C>,
T::Epsilon: Clone,

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#### fn default_max_relative() -> Self::Epsilon

The default relative tolerance for testing values that are far-apart. Read more
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#### fn relative_eq(
&self,
other: &Self,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool

A test for equality that uses a relative comparison if the values are far apart.
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#### fn relative_ne(
&self,
other: &Rhs,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool

The inverse of `RelativeEq::relative_eq`.
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### impl<T: RealField + RelativeEq<Epsilon = T>> RelativeEq<Unit<Quaternion<T>>> for UnitQuaternion<T>

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#### fn default_max_relative() -> Self::Epsilon

The default relative tolerance for testing values that are far-apart. Read more
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#### fn relative_eq(
&self,
other: &Self,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool

A test for equality that uses a relative comparison if the values are far apart.
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#### fn relative_ne(
&self,
other: &Rhs,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool

The inverse of `RelativeEq::relative_eq`.
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### impl<T1, T2> SubsetOf<Unit<Complex<T2>>> for Rotation2<T1>where
T1: RealField,
T2: RealField + SupersetOf<T1>,

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#### fn to_superset(&self) -> UnitComplex<T2>

The inclusion map: converts `self` to the equivalent element of its superset.
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#### fn is_in_subset(q: &UnitComplex<T2>) -> bool

Checks if `element` is actually part of the subset `Self` (and can be converted to it).
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#### fn from_superset_unchecked(q: &UnitComplex<T2>) -> Self

Use with care! Same as `self.to_superset` but without any property checks. Always succeeds.
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#### fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
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### impl<T1, T2> SubsetOf<Unit<Complex<T2>>> for UnitComplex<T1>where
T1: RealField,
T2: RealField + SupersetOf<T1>,

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#### fn to_superset(&self) -> UnitComplex<T2>

The inclusion map: converts `self` to the equivalent element of its superset.
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#### fn is_in_subset(uq: &UnitComplex<T2>) -> bool

Checks if `element` is actually part of the subset `Self` (and can be converted to it).
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#### fn from_superset_unchecked(uq: &UnitComplex<T2>) -> Self

Use with care! Same as `self.to_superset` but without any property checks. Always succeeds.
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#### fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
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### impl<T1, T2> SubsetOf<Unit<DualQuaternion<T2>>> for Isometry3<T1>where
T1: RealField,
T2: RealField + SupersetOf<T1>,

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#### fn to_superset(&self) -> UnitDualQuaternion<T2>

The inclusion map: converts `self` to the equivalent element of its superset.
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#### fn is_in_subset(dq: &UnitDualQuaternion<T2>) -> bool

Checks if `element` is actually part of the subset `Self` (and can be converted to it).
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#### fn from_superset_unchecked(dq: &UnitDualQuaternion<T2>) -> Self

Use with care! Same as `self.to_superset` but without any property checks. Always succeeds.
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#### fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
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### impl<T1, T2> SubsetOf<Unit<DualQuaternion<T2>>> for Rotation3<T1>where
T1: RealField,
T2: RealField + SupersetOf<T1>,

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#### fn to_superset(&self) -> UnitDualQuaternion<T2>

The inclusion map: converts `self` to the equivalent element of its superset.
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#### fn is_in_subset(dq: &UnitDualQuaternion<T2>) -> bool

Checks if `element` is actually part of the subset `Self` (and can be converted to it).
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#### fn from_superset_unchecked(dq: &UnitDualQuaternion<T2>) -> Self

Use with care! Same as `self.to_superset` but without any property checks. Always succeeds.
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#### fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
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### impl<T1, T2> SubsetOf<Unit<DualQuaternion<T2>>> for Translation3<T1>where
T1: RealField,
T2: RealField + SupersetOf<T1>,

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#### fn to_superset(&self) -> UnitDualQuaternion<T2>

The inclusion map: converts `self` to the equivalent element of its superset.
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#### fn is_in_subset(dq: &UnitDualQuaternion<T2>) -> bool

Checks if `element` is actually part of the subset `Self` (and can be converted to it).
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#### fn from_superset_unchecked(dq: &UnitDualQuaternion<T2>) -> Self

Use with care! Same as `self.to_superset` but without any property checks. Always succeeds.
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#### fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
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### impl<T1, T2> SubsetOf<Unit<DualQuaternion<T2>>> for UnitDualQuaternion<T1>where
T1: SimdRealField,
T2: SimdRealField + SupersetOf<T1>,

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#### fn to_superset(&self) -> UnitDualQuaternion<T2>

The inclusion map: converts `self` to the equivalent element of its superset.
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#### fn is_in_subset(dq: &UnitDualQuaternion<T2>) -> bool

Checks if `element` is actually part of the subset `Self` (and can be converted to it).
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#### fn from_superset_unchecked(dq: &UnitDualQuaternion<T2>) -> Self

Use with care! Same as `self.to_superset` but without any property checks. Always succeeds.
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#### fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
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### impl<T1, T2> SubsetOf<Unit<DualQuaternion<T2>>> for UnitQuaternion<T1>where
T1: RealField,
T2: RealField + SupersetOf<T1>,

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#### fn to_superset(&self) -> UnitDualQuaternion<T2>

The inclusion map: converts `self` to the equivalent element of its superset.
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#### fn is_in_subset(dq: &UnitDualQuaternion<T2>) -> bool

Checks if `element` is actually part of the subset `Self` (and can be converted to it).
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#### fn from_superset_unchecked(dq: &UnitDualQuaternion<T2>) -> Self

Use with care! Same as `self.to_superset` but without any property checks. Always succeeds.
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#### fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
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### impl<T1, T2> SubsetOf<Unit<Quaternion<T2>>> for Rotation3<T1>where
T1: RealField,
T2: RealField + SupersetOf<T1>,

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#### fn to_superset(&self) -> UnitQuaternion<T2>

The inclusion map: converts `self` to the equivalent element of its superset.
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#### fn is_in_subset(q: &UnitQuaternion<T2>) -> bool

Checks if `element` is actually part of the subset `Self` (and can be converted to it).
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#### fn from_superset_unchecked(q: &UnitQuaternion<T2>) -> Self

Use with care! Same as `self.to_superset` but without any property checks. Always succeeds.
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#### fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
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### impl<T1, T2> SubsetOf<Unit<Quaternion<T2>>> for UnitQuaternion<T1>where
T1: Scalar,
T2: Scalar + SupersetOf<T1>,

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#### fn to_superset(&self) -> UnitQuaternion<T2>

The inclusion map: converts `self` to the equivalent element of its superset.
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#### fn is_in_subset(uq: &UnitQuaternion<T2>) -> bool

Checks if `element` is actually part of the subset `Self` (and can be converted to it).
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#### fn from_superset_unchecked(uq: &UnitQuaternion<T2>) -> Self

Use with care! Same as `self.to_superset` but without any property checks. Always succeeds.
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#### fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
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### impl<T: RealField> UlpsEq<Unit<Complex<T>>> for UnitComplex<T>

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#### fn default_max_ulps() -> u32

The default ULPs to tolerate when testing values that are far-apart. Read more
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#### fn ulps_eq(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool

A test for equality that uses units in the last place (ULP) if the values are far apart.
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#### fn ulps_ne(&self, other: &Rhs, epsilon: Self::Epsilon, max_ulps: u32) -> bool

The inverse of `UlpsEq::ulps_eq`.
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### impl<T: RealField + UlpsEq<Epsilon = T>> UlpsEq<Unit<DualQuaternion<T>>> for UnitDualQuaternion<T>

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#### fn default_max_ulps() -> u32

The default ULPs to tolerate when testing values that are far-apart. Read more
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#### fn ulps_eq(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool

A test for equality that uses units in the last place (ULP) if the values are far apart.
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#### fn ulps_ne(&self, other: &Rhs, epsilon: Self::Epsilon, max_ulps: u32) -> bool

The inverse of `UlpsEq::ulps_eq`.
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### impl<T, R: Dim, C: Dim, S> UlpsEq<Unit<Matrix<T, R, C, S>>> for Unit<Matrix<T, R, C, S>>where
T: Scalar + UlpsEq,
S: RawStorage<T, R, C>,
T::Epsilon: Clone,

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#### fn default_max_ulps() -> u32

The default ULPs to tolerate when testing values that are far-apart. Read more
source§

#### fn ulps_eq(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool

A test for equality that uses units in the last place (ULP) if the values are far apart.
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#### fn ulps_ne(&self, other: &Rhs, epsilon: Self::Epsilon, max_ulps: u32) -> bool

The inverse of `UlpsEq::ulps_eq`.
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### impl<T: RealField + UlpsEq<Epsilon = T>> UlpsEq<Unit<Quaternion<T>>> for UnitQuaternion<T>

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#### fn default_max_ulps() -> u32

The default ULPs to tolerate when testing values that are far-apart. Read more
source§

#### fn ulps_eq(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: u32) -> bool

A test for equality that uses units in the last place (ULP) if the values are far apart.
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#### fn ulps_ne(&self, other: &Rhs, epsilon: Self::Epsilon, max_ulps: u32) -> bool

The inverse of `UlpsEq::ulps_eq`.
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### impl<T: Copy> Copy for Unit<T>

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### impl<T, R, C, S> Eq for Unit<Matrix<T, R, C, S>>where
T: Scalar + Eq,
R: Dim,
C: Dim,
S: RawStorage<T, R, C>,

## Auto Trait Implementations§

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### impl<T> RefUnwindSafe for Unit<T>where
T: RefUnwindSafe,

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### impl<T> Send for Unit<T>where
T: Send,

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### impl<T> Sync for Unit<T>where
T: Sync,

§

### impl<T> Unpin for Unit<T>where
T: Unpin,

§

### impl<T> UnwindSafe for Unit<T>where
T: UnwindSafe,

## Blanket Implementations§

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### impl<T> Any for Twhere
T: 'static + ?Sized,

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#### fn type_id(&self) -> TypeId

Gets the `TypeId` of `self`. Read more
source§

### impl<T> Borrow<T> for Twhere
T: ?Sized,

const: unstable · source§

#### fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
source§

### impl<T> BorrowMut<T> for Twhere
T: ?Sized,

const: unstable · source§

#### fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more
source§

### impl<T> From<T> for T

const: unstable · source§

#### fn from(t: T) -> T

Returns the argument unchanged.

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### impl<T, U> Into<U> for Twhere
U: From<T>,

const: unstable · source§

#### fn into(self) -> U

Calls `U::from(self)`.

That is, this conversion is whatever the implementation of `From<T> for U` chooses to do.

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### impl<T> Same<T> for T

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#### type Output = T

Should always be `Self`
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### impl<SS, SP> SupersetOf<SS> for SPwhere
SS: SubsetOf<SP>,

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#### fn to_subset(&self) -> Option<SS>

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
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#### fn is_in_subset(&self) -> bool

Checks if `self` is actually part of its subset `T` (and can be converted to it).
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#### fn to_subset_unchecked(&self) -> SS

Use with care! Same as `self.to_subset` but without any property checks. Always succeeds.
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#### fn from_subset(element: &SS) -> SP

The inclusion map: converts `self` to the equivalent element of its superset.
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### impl<T> ToOwned for Twhere
T: Clone,

§

#### type Owned = T

The resulting type after obtaining ownership.
source§

#### fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more
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#### fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more
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### impl<T> ToString for Twhere
T: Display + ?Sized,

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#### default fn to_string(&self) -> String

Converts the given value to a `String`. Read more
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### impl<T, U> TryFrom<U> for Twhere
U: Into<T>,

§

#### type Error = Infallible

The type returned in the event of a conversion error.
const: unstable · source§

#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
source§

### impl<T, U> TryInto<U> for Twhere
U: TryFrom<T>,

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#### type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.
const: unstable · source§

#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.
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### impl<T, Right> ClosedDiv<Right> for Twhere
T: Div<Right, Output = T> + DivAssign<Right>,

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### impl<T, Right> ClosedMul<Right> for Twhere
T: Mul<Right, Output = T> + MulAssign<Right>,

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### impl<T> ClosedNeg for Twhere
T: Neg<Output = T>,