Rotation in nalgebra::geometry - Rust
Description: A rotation matrix.
Keywords: rust, rustlang, rust-lang, Rotation

# Struct nalgebra::geometry::Rotation

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    #[repr(C)]pub struct Rotation<T, const D: usize> { /* private fields */ }

Expand description

A rotation matrix.

This is also known as an element of a Special Orthogonal (SO) group. The `Rotation` type can either represent a 2D or 3D rotation, represented as a matrix. For a rotation based on quaternions, see `UnitQuaternion` instead.

Note that instead of using the `Rotation` type in your code directly, you should use one of its aliases: `Rotation2`, or `Rotation3`. Though keep in mind that all the documentation of all the methods of these aliases will also appears on this page.

## Construction

- Identity `identity`
- From a 2D rotation angle `new`…
- From an existing 2D matrix or rotations `from_matrix`, `rotation_between`, `powf`…
- From a 3D axis and/or angles `new`, `from_euler_angles`, `from_axis_angle`…
- From a 3D eye position and target point `look_at`, `look_at_lh`, `rotation_between`…
- From an existing 3D matrix or rotations `from_matrix`, `rotation_between`, `powf`…

## Transformation and composition

Note that transforming vectors and points can be done by multiplication, e.g., `rotation * point`. Composing an rotation with another transformation can also be done by multiplication or division.

- 3D axis and angle extraction `angle`, `euler_angles`, `scaled_axis`, `angle_to`…
- 2D angle extraction `angle`, `angle_to`…
- Transformation of a vector or a point `transform_vector`, `inverse_transform_point`…
- Transposition and inversion `transpose`, `inverse`…
- Interpolation `slerp`…

## Conversion

- Conversion to a matrix `matrix`, `to_homogeneous`…

## Implementations§

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### impl<T, const D: usize> Rotation<T, D>

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#### pub const fn from_matrix_unchecked(matrix: SMatrix<T, D, D>) -> Self

Creates a new rotation from the given square matrix.

The matrix orthonormality is not checked.

##### Example

    let mat = Matrix3::new(0.8660254, -0.5,      0.0,
                           0.5,       0.8660254, 0.0,
                           0.0,       0.0,       1.0);
    let rot = Rotation3::from_matrix_unchecked(mat);

    assert_eq!(*rot.matrix(), mat);

    let mat = Matrix2::new(0.8660254, -0.5,
                           0.5,       0.8660254);
    let rot = Rotation2::from_matrix_unchecked(mat);

    assert_eq!(*rot.matrix(), mat);

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### impl<T: Scalar, const D: usize> Rotation<T, D>

#### Conversion to a matrix

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#### pub fn matrix(&self) -> &SMatrix<T, D, D>

A reference to the underlying matrix representation of this rotation.

##### Example

    let rot = Rotation3::from_axis_angle(&Vector3::z_axis(), 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.matrix(), expected);

    let rot = Rotation2::new(f32::consts::FRAC_PI_6);
    let expected = Matrix2::new(0.8660254, -0.5,
                                0.5,       0.8660254);
    assert_eq!(*rot.matrix(), expected);

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#### pub unsafe fn matrix_mut(&mut self) -> &mut SMatrix<T, D, D>

👎Deprecated: Use `.matrix_mut_unchecked()` instead.

A mutable reference to the underlying matrix representation of this rotation.

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#### pub fn matrix_mut_unchecked(&mut self) -> &mut SMatrix<T, D, D>

A mutable reference to the underlying matrix representation of this rotation.

This is suffixed by “_unchecked” because this allows the user to replace the matrix by another one that is non-inversible or non-orthonormal. If one of those properties is broken, subsequent method calls may return bogus results.

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#### pub fn into_inner(self) -> SMatrix<T, D, D>

Unwraps the underlying matrix.

##### Example

    let rot = Rotation3::from_axis_angle(&Vector3::z_axis(), f32::consts::FRAC_PI_6);
    let mat = rot.into_inner();
    let expected = Matrix3::new(0.8660254, -0.5,      0.0,
                                0.5,       0.8660254, 0.0,
                                0.0,       0.0,       1.0);
    assert_eq!(mat, expected);

    let rot = Rotation2::new(f32::consts::FRAC_PI_6);
    let mat = rot.into_inner();
    let expected = Matrix2::new(0.8660254, -0.5,
                                0.5,       0.8660254);
    assert_eq!(mat, expected);

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#### pub fn unwrap(self) -> SMatrix<T, D, D>

👎Deprecated: use `.into_inner()` instead

Unwraps the underlying matrix. Deprecated: Use `Rotation::into_inner` instead.

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#### pub fn to_homogeneous(
&self
) -> OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>where
T: Zero + One,
Const<D>: DimNameAdd<U1>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

Converts this rotation into its equivalent homogeneous transformation matrix.

This is the same as `self.into()`.

##### Example

    let rot = Rotation3::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_eq!(rot.to_homogeneous(), expected);

    let rot = Rotation2::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: Scalar, const D: usize> Rotation<T, D>

#### Transposition and inversion

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

Transposes `self`.

Same as `.inverse()` because the inverse of a rotation matrix is its transform.

##### Example

    let rot = Rotation3::new(Vector3::new(1.0, 2.0, 3.0));
    let tr_rot = rot.transpose();
    assert_relative_eq!(rot * tr_rot, Rotation3::identity(), epsilon = 1.0e-6);
    assert_relative_eq!(tr_rot * rot, Rotation3::identity(), epsilon = 1.0e-6);

    let rot = Rotation2::new(1.2);
    let tr_rot = rot.transpose();
    assert_relative_eq!(rot * tr_rot, Rotation2::identity(), epsilon = 1.0e-6);
    assert_relative_eq!(tr_rot * rot, Rotation2::identity(), epsilon = 1.0e-6);

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

Inverts `self`.

Same as `.transpose()` because the inverse of a rotation matrix is its transform.

##### Example

    let rot = Rotation3::new(Vector3::new(1.0, 2.0, 3.0));
    let inv = rot.inverse();
    assert_relative_eq!(rot * inv, Rotation3::identity(), epsilon = 1.0e-6);
    assert_relative_eq!(inv * rot, Rotation3::identity(), epsilon = 1.0e-6);

    let rot = Rotation2::new(1.2);
    let inv = rot.inverse();
    assert_relative_eq!(rot * inv, Rotation2::identity(), epsilon = 1.0e-6);
    assert_relative_eq!(inv * rot, Rotation2::identity(), epsilon = 1.0e-6);

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

Transposes `self` in-place.

Same as `.inverse_mut()` because the inverse of a rotation matrix is its transform.

##### Example

    let rot = Rotation3::new(Vector3::new(1.0, 2.0, 3.0));
    let mut tr_rot = Rotation3::new(Vector3::new(1.0, 2.0, 3.0));
    tr_rot.transpose_mut();

    assert_relative_eq!(rot * tr_rot, Rotation3::identity(), epsilon = 1.0e-6);
    assert_relative_eq!(tr_rot * rot, Rotation3::identity(), epsilon = 1.0e-6);

    let rot = Rotation2::new(1.2);
    let mut tr_rot = Rotation2::new(1.2);
    tr_rot.transpose_mut();

    assert_relative_eq!(rot * tr_rot, Rotation2::identity(), epsilon = 1.0e-6);
    assert_relative_eq!(tr_rot * rot, Rotation2::identity(), epsilon = 1.0e-6);

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

Inverts `self` in-place.

Same as `.transpose_mut()` because the inverse of a rotation matrix is its transform.

##### Example

    let rot = Rotation3::new(Vector3::new(1.0, 2.0, 3.0));
    let mut inv = Rotation3::new(Vector3::new(1.0, 2.0, 3.0));
    inv.inverse_mut();

    assert_relative_eq!(rot * inv, Rotation3::identity(), epsilon = 1.0e-6);
    assert_relative_eq!(inv * rot, Rotation3::identity(), epsilon = 1.0e-6);

    let rot = Rotation2::new(1.2);
    let mut inv = Rotation2::new(1.2);
    inv.inverse_mut();

    assert_relative_eq!(rot * inv, Rotation2::identity(), epsilon = 1.0e-6);
    assert_relative_eq!(inv * rot, Rotation2::identity(), epsilon = 1.0e-6);

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### impl<T: SimdRealField, const D: usize> Rotation<T, D>where
T::Element: SimdRealField,

#### Transformation of a vector or a point

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

Rotate the given point.

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

##### Example

    let rot = Rotation3::new(Vector3::y() * 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: &SVector<T, D>) -> SVector<T, D>

Rotate the given vector.

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

##### Example

    let rot = Rotation3::new(Vector3::y() * 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: &Point<T, D>) -> Point<T, D>

Rotate the given point by the inverse of this rotation. This may be cheaper than inverting the rotation and then transforming the given point.

##### Example

    let rot = Rotation3::new(Vector3::y() * 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: &SVector<T, D>) -> SVector<T, D>

Rotate the given vector by the inverse of this rotation. This may be cheaper than inverting the rotation and then transforming the given vector.

##### Example

    let rot = Rotation3::new(Vector3::y() * 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<SVector<T, D>>
) -> Unit<SVector<T, D>>

Rotate the given vector by the inverse of this rotation. This may be cheaper than inverting the rotation and then transforming the given vector.

##### Example

    let rot = Rotation3::new(Vector3::z() * 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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### impl<T, const D: usize> Rotation<T, D>where
T: Scalar + Zero + One,

#### Identity

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#### pub fn identity() -> Rotation<T, D>

Creates a new square identity rotation of the given `dimension`.

##### Example

    let rot1 = Rotation2::identity();
    let rot2 = Rotation2::new(std::f32::consts::FRAC_PI_2);

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

    let rot1 = Rotation3::identity();
    let rot2 = Rotation3::from_axis_angle(&Vector3::z_axis(), std::f32::consts::FRAC_PI_2);

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

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### impl<T: Scalar, const D: usize> Rotation<T, D>

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

Cast the components of `self` to another type.

##### Example

    let rot = Rotation2::<f64>::identity();
    let rot2 = rot.cast::<f32>();
    assert_eq!(rot2, Rotation2::<f32>::identity());

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### impl<T: SimdRealField> Rotation<T, 2>

#### Interpolation

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

Spherical linear interpolation between two rotation matrices.

##### Examples:

    let rot1 = Rotation2::new(std::f32::consts::FRAC_PI_4);
    let rot2 = Rotation2::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> Rotation<T, 3>

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

Spherical linear interpolation between two rotation matrices.

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

##### Examples:

    let q1 = Rotation3::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0);
    let q2 = Rotation3::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 rotation matrices or returns `None` if both rotations are approximately 180 degrees apart (in which case the interpolation is not well-defined).

##### Arguments

- `self`: the first rotation to interpolate from.
- `other`: the second rotation 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 rotations must be to return `None`.

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### impl<T: SimdRealField> Rotation<T, 2>

#### Construction from a 2D rotation angle

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

Builds a 2 dimensional rotation matrix from an angle in radian.

##### Example

    let rot = Rotation2::new(f32::consts::FRAC_PI_2);

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

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

Builds a 2 dimensional rotation matrix 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.

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### impl<T: SimdRealField> Rotation<T, 2>

#### Construction from an existing 2D matrix or rotations

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#### 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 rotation matrix, 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_matrix(m: &Matrix2<T>) -> Selfwhere
T: RealField,

Builds a rotation matrix 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: &Matrix2<T>,
eps: T,
max_iter: usize,
guess: Self
) -> Selfwhere
T: RealField,

Builds a rotation matrix 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 `Rotation2::identity()` if no other guesses come to mind.

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#### 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 rotation matrix required to align `a` and `b` but with its angle.

This is the rotation `R` such that `(R * a).angle(b) == 0 && (R * a).dot(b).is_positive()`.

##### Example

    let a = Vector2::new(1.0, 2.0);
    let b = Vector2::new(2.0, 1.0);
    let rot = Rotation2::rotation_between(&a, &b);
    assert_relative_eq!(rot * a, b);
    assert_relative_eq!(rot.inverse() * b, a);

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#### 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 = Rotation2::scaled_rotation_between(&a, &b, 0.2);
    let rot5 = Rotation2::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);

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

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

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

##### Example

    let rot1 = Rotation2::new(0.1);
    let rot2 = Rotation2::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);

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#### pub fn renormalize(&mut self)where
T: RealField,

Ensure this rotation is an orthonormal rotation matrix. This is useful when repeated computations might cause the matrix from progressively not being orthonormal anymore.

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

Raise the rotation to a given floating power, i.e., returns the rotation with the angle of `self` multiplied by `n`.

##### Example

    let rot = Rotation2::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> Rotation<T, 2>

#### 2D angle extraction

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

The rotation angle.

##### Example

    let rot = Rotation2::new(1.78);
    assert_relative_eq!(rot.angle(), 1.78);

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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 = Rotation2::new(0.1);
    let rot2 = Rotation2::new(1.7);
    assert_relative_eq!(rot1.angle_to(&rot2), 1.6);

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#### pub fn scaled_axis(&self) -> SVector<T, 1>

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.

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### impl<T: SimdRealField> Rotation<T, 3>where
T::Element: SimdRealField,

#### Construction from a 3D axis and/or angles

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

Builds a 3 dimensional rotation matrix from an axis and an angle.

##### Arguments

- `axisangle` - A vector representing the rotation. Its magnitude is the amount of rotation in radian. Its direction is the axis of 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 rot = Rotation3::new(axisangle);

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

    // A zero vector yields an identity.
    assert_eq!(Rotation3::new(Vector3::<f32>::zeros()), Rotation3::identity());

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

Builds a 3D rotation matrix from an axis scaled by the rotation angle.

This is the 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 rot = Rotation3::new(axisangle);

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

    // A zero vector yields an identity.
    assert_eq!(Rotation3::from_scaled_axis(Vector3::<f32>::zeros()), Rotation3::identity());

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

Builds a 3D rotation matrix from an axis and a 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 rot = Rotation3::from_axis_angle(&axis, angle);

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

    // A zero vector yields an identity.
    assert_eq!(Rotation3::from_scaled_axis(Vector3::<f32>::zeros()), Rotation3::identity());

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

Creates a new rotation from Euler angles.

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

##### Example

    let rot = Rotation3::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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### impl<T: SimdRealField> Rotation<T, 3>where
T::Element: SimdRealField,

#### Construction from a 3D eye position and target point

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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 a rotation 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, that is, direction the matrix `z` axis will be aligned with.
- up - The vertical direction. 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 rot = Rotation3::face_towards(&dir, &up);
    assert_relative_eq!(rot * 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 `Rotation3::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 direction toward which the camera looks.
- 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 rot = Rotation3::look_at_rh(&dir, &up);
    assert_relative_eq!(rot * dir.normalize(), -Vector3::z());

source

#### 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 direction toward which the camera looks.
- 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 rot = Rotation3::look_at_lh(&dir, &up);
    assert_relative_eq!(rot * dir.normalize(), Vector3::z());

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### impl<T: SimdRealField> Rotation<T, 3>where
T::Element: SimdRealField,

#### Construction from an existing 3D matrix or rotations

source

#### 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 rotation matrix required to align `a` and `b` but with its angle.

This is the rotation `R` such that `(R * a).angle(b) == 0 && (R * a).dot(b).is_positive()`.

##### Example

    let a = Vector3::new(1.0, 2.0, 3.0);
    let b = Vector3::new(3.0, 1.0, 2.0);
    let rot = Rotation3::rotation_between(&a, &b).unwrap();
    assert_relative_eq!(rot * a, b, epsilon = 1.0e-6);
    assert_relative_eq!(rot.inverse() * b, a, epsilon = 1.0e-6);

source

#### pub fn scaled_rotation_between<SB, SC>(
a: &Vector<T, U3, SB>,
b: &Vector<T, U3, SC>,
n: 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 rot2 = Rotation3::scaled_rotation_between(&a, &b, 0.2).unwrap();
    let rot5 = Rotation3::scaled_rotation_between(&a, &b, 0.5).unwrap();
    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);

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

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

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

##### Example

    let rot1 = Rotation3::from_axis_angle(&Vector3::y_axis(), 1.0);
    let rot2 = Rotation3::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 powf(&self, n: T) -> Selfwhere
T: RealField,

Raise the rotation to a given floating power, i.e., returns the rotation with the same axis as `self` and an angle equal to `self.angle()` multiplied by `n`.

##### Example

    let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
    let angle = 1.2;
    let rot = Rotation3::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 from_basis_unchecked(basis: &[Vector3<T>; 3]) -> Self

Builds a rotation from a basis assumed to be orthonormal.

In order to get a valid rotation matrix, 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: &Matrix3<T>) -> Selfwhere
T: RealField,

Builds a rotation matrix 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 a rotation matrix 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`: a guess of the solution. Convergence will be significantly faster if an initial solution close to the actual solution is provided. Can be set to `Rotation3::identity()` if no other guesses come to mind.

source

#### pub fn renormalize(&mut self)where
T: RealField,

Ensure this rotation is an orthonormal rotation matrix. This is useful when repeated computations might cause the matrix from progressively not being orthonormal anymore.

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### impl<T: SimdRealField> Rotation<T, 3>

#### 3D axis and angle extraction

source

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

The rotation angle in [0; pi].

##### Example

    let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
    let rot = Rotation3::from_axis_angle(&axis, 1.78);
    assert_relative_eq!(rot.angle(), 1.78);

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

The rotation axis. Returns `None` if the rotation angle is zero or PI.

##### Example

    let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
    let angle = 1.2;
    let rot = Rotation3::from_axis_angle(&axis, angle);
    assert_relative_eq!(rot.axis().unwrap(), axis);

    // Case with a zero angle.
    let rot = Rotation3::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 multiplied by the rotation angle.

##### Example

    let axisangle = Vector3::new(0.1, 0.2, 0.3);
    let rot = Rotation3::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 rotation matrix.

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 = Rotation3::from_axis_angle(&axis, angle);
    let axis_angle = rot.axis_angle().unwrap();
    assert_relative_eq!(axis_angle.0, axis);
    assert_relative_eq!(axis_angle.1, angle);

    // Case with a zero angle.
    let rot = Rotation3::from_axis_angle(&axis, 0.0);
    assert!(rot.axis_angle().is_none());

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

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

##### Example

    let rot1 = Rotation3::from_axis_angle(&Vector3::y_axis(), 1.0);
    let rot2 = Rotation3::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 to_euler_angles(self) -> (T, T, T)where
T: RealField,

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

Creates Euler angles from a rotation.

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

source

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

Euler angles corresponding to this rotation from a rotation.

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

##### Example

    let rot = Rotation3::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);

## Trait Implementations§

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### impl<T, const D: usize> AbsDiffEq<Rotation<T, D>> for Rotation<T, D>where
T: Scalar + AbsDiffEq,
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
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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: SimdRealField, const D: usize> AbstractRotation<T, D> for Rotation<T, D>where
T::Element: SimdRealField,

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#### fn identity() -> Self

The rotation identity.
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#### fn inverse(&self) -> Self

The rotation inverse.
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#### fn inverse_mut(&mut self)

Change `self` to its inverse.
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#### fn transform_vector(&self, v: &SVector<T, D>) -> SVector<T, D>

Apply the rotation to the given vector.
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#### fn transform_point(&self, p: &Point<T, D>) -> Point<T, D>

Apply the rotation to the given point.
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#### fn inverse_transform_vector(&self, v: &SVector<T, D>) -> SVector<T, D>

Apply the inverse rotation to the given vector.
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#### fn inverse_transform_unit_vector(
&self,
v: &Unit<SVector<T, D>>
) -> Unit<SVector<T, D>>

Apply the inverse rotation to the given unit vector.
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#### fn inverse_transform_point(&self, p: &Point<T, D>) -> Point<T, D>

Apply the inverse rotation to the given point.
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### impl<T: Clone, const D: usize> Clone for Rotation<T, D>

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#### fn clone(&self) -> Rotation<T, D>

Returns a copy of the value. Read more
1.0.0 · source§

#### fn clone_from(&mut self, source: &Self)

Performs copy-assignment from `source`. Read more
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### impl<T: Debug, const D: usize> Debug for Rotation<T, D>

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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, const D: usize> Default for Rotation<T, D>where
T: Scalar + Zero + One,

source§

#### fn default() -> Self

Returns the “default value” for a type. Read more
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### impl<T, const D: usize> Display for Rotation<T, D>where
T: RealField + Display,

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

Formats the value using the given formatter. Read more
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### impl<'a, 'b, T: SimdRealField, const D: usize> Div<&'b Isometry<T, Rotation<T, D>, D>> for &'a Rotation<T, D>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Rotation<T, D>, D>

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

Performs the `/` operation. Read more
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### impl<'b, T: SimdRealField, const D: usize> Div<&'b Isometry<T, Rotation<T, D>, D>> for Rotation<T, D>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Rotation<T, D>, D>

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

Performs the `/` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Div<&'b Rotation<T, 2>> 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 Rotation<T, 2>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'b, T: SimdRealField> Div<&'b Rotation<T, 2>> 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 Rotation<T, 2>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Div<&'b Rotation<T, 3>> 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 div(self, rhs: &'b Rotation<T, 3>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'b, T: SimdRealField> Div<&'b Rotation<T, 3>> 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 div(self, rhs: &'b Rotation<T, 3>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'a, 'b, T: SimdRealField, const D: usize> Div<&'b Rotation<T, D>> for &'a Isometry<T, Rotation<T, D>, D>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Rotation<T, D>, D>

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

Performs the `/` operation. Read more
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### impl<'a, 'b, T, const D: usize> Div<&'b Rotation<T, D>> for &'a Rotation<T, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,

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#### type Output = Rotation<T, D>

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

Performs the `/` operation. Read more
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### impl<'a, 'b, T: SimdRealField, const D: usize> Div<&'b Rotation<T, D>> for &'a Similarity<T, Rotation<T, D>, D>where
T::Element: SimdRealField,

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#### type Output = Similarity<T, Rotation<T, D>, D>

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

Performs the `/` operation. Read more
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### impl<'a, 'b, T, C, const D: usize> Div<&'b Rotation<T, D>> for &'a Transform<T, C, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

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

Performs the `/` operation. Read more
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### impl<'b, T: SimdRealField, const D: usize> Div<&'b Rotation<T, D>> for Isometry<T, Rotation<T, D>, D>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Rotation<T, D>, D>

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

Performs the `/` operation. Read more
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### impl<'b, T, const D: usize> Div<&'b Rotation<T, D>> for Rotation<T, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,

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#### type Output = Rotation<T, D>

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

Performs the `/` operation. Read more
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### impl<'b, T: SimdRealField, const D: usize> Div<&'b Rotation<T, D>> for Similarity<T, Rotation<T, D>, D>where
T::Element: SimdRealField,

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#### type Output = Similarity<T, Rotation<T, D>, D>

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

Performs the `/` operation. Read more
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### impl<'b, T, C, const D: usize> Div<&'b Rotation<T, D>> for Transform<T, C, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

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

Performs the `/` operation. Read more
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### impl<'a, 'b, T, R1, C1, SA, const D2: usize> Div<&'b Rotation<T, D2>> for &'a Matrix<T, R1, C1, SA>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,
R1: Dim,
C1: Dim,
SA: Storage<T, R1, C1>,
DefaultAllocator: Allocator<T, R1, Const<D2>>,
ShapeConstraint: AreMultipliable<R1, C1, Const<D2>, Const<D2>>,

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#### type Output = Matrix<T, R1, Const<D2>, <DefaultAllocator as Allocator<T, R1, Const<D2>>>::Buffer>

The resulting type after applying the `/` operator.
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#### fn div(self, right: &'b Rotation<T, D2>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'b, T, R1, C1, SA, const D2: usize> Div<&'b Rotation<T, D2>> for Matrix<T, R1, C1, SA>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,
R1: Dim,
C1: Dim,
SA: Storage<T, R1, C1>,
DefaultAllocator: Allocator<T, R1, Const<D2>>,
ShapeConstraint: AreMultipliable<R1, C1, Const<D2>, Const<D2>>,

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#### type Output = Matrix<T, R1, Const<D2>, <DefaultAllocator as Allocator<T, R1, Const<D2>>>::Buffer>

The resulting type after applying the `/` operator.
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#### fn div(self, right: &'b Rotation<T, D2>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'a, 'b, T: SimdRealField, const D: usize> Div<&'b Similarity<T, Rotation<T, D>, D>> for &'a Rotation<T, D>where
T::Element: SimdRealField,

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#### type Output = Similarity<T, Rotation<T, D>, D>

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

Performs the `/` operation. Read more
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### impl<'b, T: SimdRealField, const D: usize> Div<&'b Similarity<T, Rotation<T, D>, D>> for Rotation<T, D>where
T::Element: SimdRealField,

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#### type Output = Similarity<T, Rotation<T, D>, D>

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

Performs the `/` operation. Read more
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### impl<'a, 'b, T, C, const D: usize> Div<&'b Transform<T, C, D>> for &'a Rotation<T, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

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

Performs the `/` operation. Read more
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### impl<'b, T, C, const D: usize> Div<&'b Transform<T, C, D>> for Rotation<T, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: &'b Transform<T, C, D>) -> 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<'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<'a, 'b, T: SimdRealField> Div<&'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 div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'b, T: SimdRealField> Div<&'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 div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'a, T: SimdRealField, const D: usize> Div<Isometry<T, Rotation<T, D>, D>> for &'a Rotation<T, D>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Rotation<T, D>, D>

The resulting type after applying the `/` operator.
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#### fn div(self, right: Isometry<T, Rotation<T, D>, D>) -> Self::Output

Performs the `/` operation. Read more
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### impl<T: SimdRealField, const D: usize> Div<Isometry<T, Rotation<T, D>, D>> for Rotation<T, D>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Rotation<T, D>, D>

The resulting type after applying the `/` operator.
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#### fn div(self, right: Isometry<T, Rotation<T, D>, D>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'a, T: SimdRealField> Div<Rotation<T, 2>> 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: Rotation<T, 2>) -> Self::Output

Performs the `/` operation. Read more
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### impl<T: SimdRealField> Div<Rotation<T, 2>> 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: Rotation<T, 2>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'a, T: SimdRealField> Div<Rotation<T, 3>> 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 div(self, rhs: Rotation<T, 3>) -> Self::Output

Performs the `/` operation. Read more
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### impl<T: SimdRealField> Div<Rotation<T, 3>> 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 div(self, rhs: Rotation<T, 3>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'a, T: SimdRealField, const D: usize> Div<Rotation<T, D>> for &'a Isometry<T, Rotation<T, D>, D>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Rotation<T, D>, D>

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: Rotation<T, D>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'a, T, const D: usize> Div<Rotation<T, D>> for &'a Rotation<T, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,

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#### type Output = Rotation<T, D>

The resulting type after applying the `/` operator.
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#### fn div(self, right: Rotation<T, D>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'a, T: SimdRealField, const D: usize> Div<Rotation<T, D>> for &'a Similarity<T, Rotation<T, D>, D>where
T::Element: SimdRealField,

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#### type Output = Similarity<T, Rotation<T, D>, D>

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: Rotation<T, D>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'a, T, C, const D: usize> Div<Rotation<T, D>> for &'a Transform<T, C, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: Rotation<T, D>) -> Self::Output

Performs the `/` operation. Read more
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### impl<T: SimdRealField, const D: usize> Div<Rotation<T, D>> for Isometry<T, Rotation<T, D>, D>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Rotation<T, D>, D>

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: Rotation<T, D>) -> Self::Output

Performs the `/` operation. Read more
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### impl<T, const D: usize> Div<Rotation<T, D>> for Rotation<T, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,

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#### type Output = Rotation<T, D>

The resulting type after applying the `/` operator.
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#### fn div(self, right: Rotation<T, D>) -> Self::Output

Performs the `/` operation. Read more
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### impl<T: SimdRealField, const D: usize> Div<Rotation<T, D>> for Similarity<T, Rotation<T, D>, D>where
T::Element: SimdRealField,

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#### type Output = Similarity<T, Rotation<T, D>, D>

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: Rotation<T, D>) -> Self::Output

Performs the `/` operation. Read more
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### impl<T, C, const D: usize> Div<Rotation<T, D>> for Transform<T, C, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: Rotation<T, D>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'a, T, R1, C1, SA, const D2: usize> Div<Rotation<T, D2>> for &'a Matrix<T, R1, C1, SA>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,
R1: Dim,
C1: Dim,
SA: Storage<T, R1, C1>,
DefaultAllocator: Allocator<T, R1, Const<D2>>,
ShapeConstraint: AreMultipliable<R1, C1, Const<D2>, Const<D2>>,

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#### type Output = Matrix<T, R1, Const<D2>, <DefaultAllocator as Allocator<T, R1, Const<D2>>>::Buffer>

The resulting type after applying the `/` operator.
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#### fn div(self, right: Rotation<T, D2>) -> Self::Output

Performs the `/` operation. Read more
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### impl<T, R1, C1, SA, const D2: usize> Div<Rotation<T, D2>> for Matrix<T, R1, C1, SA>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,
R1: Dim,
C1: Dim,
SA: Storage<T, R1, C1>,
DefaultAllocator: Allocator<T, R1, Const<D2>>,
ShapeConstraint: AreMultipliable<R1, C1, Const<D2>, Const<D2>>,

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#### type Output = Matrix<T, R1, Const<D2>, <DefaultAllocator as Allocator<T, R1, Const<D2>>>::Buffer>

The resulting type after applying the `/` operator.
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#### fn div(self, right: Rotation<T, D2>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'a, T: SimdRealField, const D: usize> Div<Similarity<T, Rotation<T, D>, D>> for &'a Rotation<T, D>where
T::Element: SimdRealField,

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#### type Output = Similarity<T, Rotation<T, D>, D>

The resulting type after applying the `/` operator.
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#### fn div(self, right: Similarity<T, Rotation<T, D>, D>) -> Self::Output

Performs the `/` operation. Read more
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### impl<T: SimdRealField, const D: usize> Div<Similarity<T, Rotation<T, D>, D>> for Rotation<T, D>where
T::Element: SimdRealField,

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#### type Output = Similarity<T, Rotation<T, D>, D>

The resulting type after applying the `/` operator.
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#### fn div(self, right: Similarity<T, Rotation<T, D>, D>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'a, T, C, const D: usize> Div<Transform<T, C, D>> for &'a Rotation<T, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: Transform<T, C, D>) -> Self::Output

Performs the `/` operation. Read more
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### impl<T, C, const D: usize> Div<Transform<T, C, D>> for Rotation<T, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

The resulting type after applying the `/` operator.
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#### fn div(self, rhs: Transform<T, C, D>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'a, T: SimdRealField> Div<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: UnitComplex<T>) -> Self::Output

Performs the `/` operation. Read more
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### impl<T: SimdRealField> Div<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: UnitComplex<T>) -> Self::Output

Performs the `/` operation. Read more
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### impl<'a, T: SimdRealField> Div<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 div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
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### impl<T: SimdRealField> Div<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 div(self, rhs: UnitQuaternion<T>) -> Self::Output

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

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#### fn div_assign(&mut self, rhs: &'b Rotation<T, 2>)

Performs the `/=` operation. Read more
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### impl<'b, T: SimdRealField> DivAssign<&'b Rotation<T, 3>> for UnitQuaternion<T>where
T::Element: SimdRealField,

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#### fn div_assign(&mut self, rhs: &'b Rotation<T, 3>)

Performs the `/=` operation. Read more
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### impl<'b, T, const R1: usize, const C1: usize> DivAssign<&'b Rotation<T, C1>> for SMatrix<T, R1, C1>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,

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#### fn div_assign(&mut self, right: &'b Rotation<T, C1>)

Performs the `/=` operation. Read more
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### impl<'b, T, const D: usize> DivAssign<&'b Rotation<T, D>> for Isometry<T, Rotation<T, D>, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

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

Performs the `/=` operation. Read more
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### impl<'b, T, const D: usize> DivAssign<&'b Rotation<T, D>> for Rotation<T, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,

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#### fn div_assign(&mut self, right: &'b Rotation<T, D>)

Performs the `/=` operation. Read more
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### impl<'b, T, const D: usize> DivAssign<&'b Rotation<T, D>> for Similarity<T, Rotation<T, D>, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

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

Performs the `/=` operation. Read more
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### impl<'b, T, C, const D: usize> DivAssign<&'b Rotation<T, D>> for Transform<T, C, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategory,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

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

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

Performs the `/=` operation. Read more
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### impl<T: SimdRealField> DivAssign<Rotation<T, 2>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### fn div_assign(&mut self, rhs: Rotation<T, 2>)

Performs the `/=` operation. Read more
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### impl<T: SimdRealField> DivAssign<Rotation<T, 3>> for UnitQuaternion<T>where
T::Element: SimdRealField,

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#### fn div_assign(&mut self, rhs: Rotation<T, 3>)

Performs the `/=` operation. Read more
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### impl<T, const R1: usize, const C1: usize> DivAssign<Rotation<T, C1>> for SMatrix<T, R1, C1>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,

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#### fn div_assign(&mut self, right: Rotation<T, C1>)

Performs the `/=` operation. Read more
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### impl<T, const D: usize> DivAssign<Rotation<T, D>> for Isometry<T, Rotation<T, D>, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

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

Performs the `/=` operation. Read more
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### impl<T, const D: usize> DivAssign<Rotation<T, D>> for Rotation<T, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,

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#### fn div_assign(&mut self, right: Rotation<T, D>)

Performs the `/=` operation. Read more
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### impl<T, const D: usize> DivAssign<Rotation<T, D>> for Similarity<T, Rotation<T, D>, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

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

Performs the `/=` operation. Read more
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### impl<T, C, const D: usize> DivAssign<Rotation<T, D>> for Transform<T, C, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategory,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

Performs the `/=` operation. Read more
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### impl<T: SimdRealField> DivAssign<Unit<Complex<T>>> for Rotation<T, 2>where
T::Element: SimdRealField,

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

Performs the `/=` operation. Read more
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### impl<T, const D: usize> From<[Rotation<<T as SimdValue>::Element, D>; 16]> for Rotation<T, D>where
T: From<[<T as SimdValue>::Element; 16]> + Scalar + PrimitiveSimdValue,
T::Element: Scalar + Copy,

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#### fn from(arr: [Rotation<T::Element, D>; 16]) -> Self

Converts to this type from the input type.
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### impl<T, const D: usize> From<[Rotation<<T as SimdValue>::Element, D>; 2]> for Rotation<T, D>where
T: From<[<T as SimdValue>::Element; 2]> + Scalar + PrimitiveSimdValue,
T::Element: Scalar + Copy,

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#### fn from(arr: [Rotation<T::Element, D>; 2]) -> Self

Converts to this type from the input type.
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### impl<T, const D: usize> From<[Rotation<<T as SimdValue>::Element, D>; 4]> for Rotation<T, D>where
T: From<[<T as SimdValue>::Element; 4]> + Scalar + PrimitiveSimdValue,
T::Element: Scalar + Copy,

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#### fn from(arr: [Rotation<T::Element, D>; 4]) -> Self

Converts to this type from the input type.
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### impl<T, const D: usize> From<[Rotation<<T as SimdValue>::Element, D>; 8]> for Rotation<T, D>where
T: From<[<T as SimdValue>::Element; 8]> + Scalar + PrimitiveSimdValue,
T::Element: Scalar + Copy,

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#### fn from(arr: [Rotation<T::Element, D>; 8]) -> Self

Converts to this type from the input type.
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### impl<T: RealField> From<Rotation<T, 2>> for Matrix2<T>

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#### fn from(q: Rotation2<T>) -> Self

Converts to this type from the input type.
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### impl<T: RealField> From<Rotation<T, 2>> for Matrix3<T>

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#### fn from(q: Rotation2<T>) -> Self

Converts to this type from the input type.
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### impl<T: SimdRealField> From<Rotation<T, 2>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### fn from(q: Rotation2<T>) -> Self

Converts to this type from the input type.
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### impl<T: RealField> From<Rotation<T, 3>> for Matrix3<T>

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#### fn from(q: Rotation3<T>) -> Self

Converts to this type from the input type.
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### impl<T: RealField> From<Rotation<T, 3>> for Matrix4<T>

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#### fn from(q: Rotation3<T>) -> Self

Converts to this type from the input type.
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### impl<T: SimdRealField> From<Rotation<T, 3>> for UnitQuaternion<T>where
T::Element: SimdRealField,

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#### fn from(q: Rotation3<T>) -> Self

Converts to this type from the input type.
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### impl<T: Scalar + Hash, const D: usize> Hash for Rotation<T, D>where
<DefaultAllocator as Allocator<T, Const<D>, Const<D>>>::Buffer: Hash,

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

Feeds this value into the given `Hasher`. Read more
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#### 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<T: Scalar, const D: usize> Index<(usize, usize)> for Rotation<T, D>

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#### type Output = T

The returned type after indexing.
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#### fn index(&self, row_col: (usize, usize)) -> &T

Performs the indexing (`container[index]`) operation. Read more
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### impl<'a, 'b, T: SimdRealField, const D: usize> Mul<&'b Isometry<T, Rotation<T, D>, D>> for &'a Rotation<T, D>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Rotation<T, D>, D>

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

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField, const D: usize> Mul<&'b Isometry<T, Rotation<T, D>, D>> for Rotation<T, D>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Rotation<T, D>, D>

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

Performs the `*` operation. Read more
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### impl<'a, 'b, T, R2, C2, SB, const D1: usize> Mul<&'b Matrix<T, R2, C2, SB>> for &'a Rotation<T, D1>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,
R2: Dim,
C2: Dim,
SB: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, Const<D1>, C2>,
ShapeConstraint: AreMultipliable<Const<D1>, Const<D1>, R2, C2>,

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#### type Output = Matrix<T, Const<D1>, C2, <DefaultAllocator as Allocator<T, Const<D1>, C2>>::Buffer>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: &'b Matrix<T, R2, C2, SB>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T, R2, C2, SB, const D1: usize> Mul<&'b Matrix<T, R2, C2, SB>> for Rotation<T, D1>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,
R2: Dim,
C2: Dim,
SB: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, Const<D1>, C2>,
ShapeConstraint: AreMultipliable<Const<D1>, Const<D1>, R2, C2>,

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#### type Output = Matrix<T, Const<D1>, C2, <DefaultAllocator as Allocator<T, Const<D1>, C2>>::Buffer>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: &'b Matrix<T, R2, C2, SB>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T, const D: usize> Mul<&'b OPoint<T, Const<D>>> for &'a Rotation<T, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,
ShapeConstraint: AreMultipliable<Const<D>, Const<D>, Const<D>, U1>,

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#### type Output = OPoint<T, Const<D>>

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

Performs the `*` operation. Read more
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### impl<'b, T, const D: usize> Mul<&'b OPoint<T, Const<D>>> for Rotation<T, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,
ShapeConstraint: AreMultipliable<Const<D>, Const<D>, Const<D>, U1>,

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#### type Output = OPoint<T, Const<D>>

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

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Mul<&'b Rotation<T, 2>> 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 Rotation<T, 2>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField> Mul<&'b Rotation<T, 2>> 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 Rotation<T, 2>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField> Mul<&'b Rotation<T, 3>> 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 Rotation<T, 3>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField> Mul<&'b Rotation<T, 3>> 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 Rotation<T, 3>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField, const D: usize> Mul<&'b Rotation<T, D>> for &'a Isometry<T, Rotation<T, D>, D>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Rotation<T, D>, D>

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

Performs the `*` operation. Read more
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### impl<'a, 'b, T, const D: usize> Mul<&'b Rotation<T, D>> for &'a Rotation<T, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,

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#### type Output = Rotation<T, D>

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

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField, const D: usize> Mul<&'b Rotation<T, D>> for &'a Similarity<T, Rotation<T, D>, D>where
T::Element: SimdRealField,

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#### type Output = Similarity<T, Rotation<T, D>, D>

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

Performs the `*` operation. Read more
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### impl<'a, 'b, T, C, const D: usize> Mul<&'b Rotation<T, D>> for &'a Transform<T, C, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

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

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField, const D: usize> Mul<&'b Rotation<T, D>> for &'a Translation<T, D>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Rotation<T, D>, D>

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

#### fn mul(self, right: &'b Rotation<T, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField, const D: usize> Mul<&'b Rotation<T, D>> for Isometry<T, Rotation<T, D>, D>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Rotation<T, D>, D>

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

#### fn mul(self, rhs: &'b Rotation<T, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T, const D: usize> Mul<&'b Rotation<T, D>> for Rotation<T, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,

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#### type Output = Rotation<T, D>

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

#### fn mul(self, right: &'b Rotation<T, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField, const D: usize> Mul<&'b Rotation<T, D>> for Similarity<T, Rotation<T, D>, D>where
T::Element: SimdRealField,

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#### type Output = Similarity<T, Rotation<T, D>, D>

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

#### fn mul(self, rhs: &'b Rotation<T, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T, C, const D: usize> Mul<&'b Rotation<T, D>> for Transform<T, C, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

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

#### fn mul(self, rhs: &'b Rotation<T, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField, const D: usize> Mul<&'b Rotation<T, D>> for Translation<T, D>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Rotation<T, D>, D>

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

#### fn mul(self, right: &'b Rotation<T, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T, R1, C1, SA, const D2: usize> Mul<&'b Rotation<T, D2>> for &'a Matrix<T, R1, C1, SA>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,
R1: Dim,
C1: Dim,
SA: Storage<T, R1, C1>,
DefaultAllocator: Allocator<T, R1, Const<D2>>,
ShapeConstraint: AreMultipliable<R1, C1, Const<D2>, Const<D2>>,

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#### type Output = Matrix<T, R1, Const<D2>, <DefaultAllocator as Allocator<T, R1, Const<D2>>>::Buffer>

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

#### fn mul(self, right: &'b Rotation<T, D2>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T, R1, C1, SA, const D2: usize> Mul<&'b Rotation<T, D2>> for Matrix<T, R1, C1, SA>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,
R1: Dim,
C1: Dim,
SA: Storage<T, R1, C1>,
DefaultAllocator: Allocator<T, R1, Const<D2>>,
ShapeConstraint: AreMultipliable<R1, C1, Const<D2>, Const<D2>>,

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#### type Output = Matrix<T, R1, Const<D2>, <DefaultAllocator as Allocator<T, R1, Const<D2>>>::Buffer>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: &'b Rotation<T, D2>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField, const D: usize> Mul<&'b Similarity<T, Rotation<T, D>, D>> for &'a Rotation<T, D>where
T::Element: SimdRealField,

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#### type Output = Similarity<T, Rotation<T, D>, D>

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

#### fn mul(self, right: &'b Similarity<T, Rotation<T, D>, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField, const D: usize> Mul<&'b Similarity<T, Rotation<T, D>, D>> for Rotation<T, D>where
T::Element: SimdRealField,

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#### type Output = Similarity<T, Rotation<T, D>, D>

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

#### fn mul(self, right: &'b Similarity<T, Rotation<T, D>, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T, C, const D: usize> Mul<&'b Transform<T, C, D>> for &'a Rotation<T, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

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

#### fn mul(self, rhs: &'b Transform<T, C, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T, C, const D: usize> Mul<&'b Transform<T, C, D>> for Rotation<T, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

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

#### fn mul(self, rhs: &'b Transform<T, C, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, 'b, T: SimdRealField, const D: usize> Mul<&'b Translation<T, D>> for &'a Rotation<T, D>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Rotation<T, D>, D>

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

#### fn mul(self, right: &'b Translation<T, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'b, T: SimdRealField, const D: usize> Mul<&'b Translation<T, D>> for Rotation<T, D>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Rotation<T, D>, D>

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

#### fn mul(self, right: &'b Translation<T, D>) -> 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.
source§

#### 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.
source§

#### fn mul(self, rhs: &'b UnitComplex<T>) -> 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 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 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, T: SimdRealField, const D: usize> Mul<Isometry<T, Rotation<T, D>, D>> for &'a Rotation<T, D>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Rotation<T, D>, D>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: Isometry<T, Rotation<T, D>, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField, const D: usize> Mul<Isometry<T, Rotation<T, D>, D>> for Rotation<T, D>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Rotation<T, D>, D>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: Isometry<T, Rotation<T, D>, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T, R2, C2, SB, const D1: usize> Mul<Matrix<T, R2, C2, SB>> for &'a Rotation<T, D1>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,
R2: Dim,
C2: Dim,
SB: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, Const<D1>, C2>,
ShapeConstraint: AreMultipliable<Const<D1>, Const<D1>, R2, C2>,

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#### type Output = Matrix<T, Const<D1>, C2, <DefaultAllocator as Allocator<T, Const<D1>, C2>>::Buffer>

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

#### fn mul(self, right: Matrix<T, R2, C2, SB>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T, R2, C2, SB, const D1: usize> Mul<Matrix<T, R2, C2, SB>> for Rotation<T, D1>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,
R2: Dim,
C2: Dim,
SB: Storage<T, R2, C2>,
DefaultAllocator: Allocator<T, Const<D1>, C2>,
ShapeConstraint: AreMultipliable<Const<D1>, Const<D1>, R2, C2>,

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#### type Output = Matrix<T, Const<D1>, C2, <DefaultAllocator as Allocator<T, Const<D1>, C2>>::Buffer>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: Matrix<T, R2, C2, SB>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T, const D: usize> Mul<OPoint<T, Const<D>>> for &'a Rotation<T, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,
ShapeConstraint: AreMultipliable<Const<D>, Const<D>, Const<D>, U1>,

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#### type Output = OPoint<T, Const<D>>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: Point<T, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T, const D: usize> Mul<OPoint<T, Const<D>>> for Rotation<T, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,
ShapeConstraint: AreMultipliable<Const<D>, Const<D>, Const<D>, U1>,

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#### type Output = OPoint<T, Const<D>>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: Point<T, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField> Mul<Rotation<T, 2>> 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: Rotation<T, 2>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField> Mul<Rotation<T, 2>> 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: Rotation<T, 2>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField> Mul<Rotation<T, 3>> 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: Rotation<T, 3>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField> Mul<Rotation<T, 3>> 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: Rotation<T, 3>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField, const D: usize> Mul<Rotation<T, D>> for &'a Isometry<T, Rotation<T, D>, D>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Rotation<T, D>, D>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: Rotation<T, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T, const D: usize> Mul<Rotation<T, D>> for &'a Rotation<T, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,

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#### type Output = Rotation<T, D>

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

#### fn mul(self, right: Rotation<T, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField, const D: usize> Mul<Rotation<T, D>> for &'a Similarity<T, Rotation<T, D>, D>where
T::Element: SimdRealField,

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#### type Output = Similarity<T, Rotation<T, D>, D>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: Rotation<T, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T, C, const D: usize> Mul<Rotation<T, D>> for &'a Transform<T, C, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

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

#### fn mul(self, rhs: Rotation<T, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField, const D: usize> Mul<Rotation<T, D>> for &'a Translation<T, D>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Rotation<T, D>, D>

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

#### fn mul(self, right: Rotation<T, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField, const D: usize> Mul<Rotation<T, D>> for Isometry<T, Rotation<T, D>, D>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Rotation<T, D>, D>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: Rotation<T, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T, const D: usize> Mul<Rotation<T, D>> for Rotation<T, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,

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#### type Output = Rotation<T, D>

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

#### fn mul(self, right: Rotation<T, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField, const D: usize> Mul<Rotation<T, D>> for Similarity<T, Rotation<T, D>, D>where
T::Element: SimdRealField,

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#### type Output = Similarity<T, Rotation<T, D>, D>

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: Rotation<T, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T, C, const D: usize> Mul<Rotation<T, D>> for Transform<T, C, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

The resulting type after applying the `*` operator.
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#### fn mul(self, rhs: Rotation<T, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField, const D: usize> Mul<Rotation<T, D>> for Translation<T, D>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Rotation<T, D>, D>

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

#### fn mul(self, right: Rotation<T, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T, R1, C1, SA, const D2: usize> Mul<Rotation<T, D2>> for &'a Matrix<T, R1, C1, SA>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,
R1: Dim,
C1: Dim,
SA: Storage<T, R1, C1>,
DefaultAllocator: Allocator<T, R1, Const<D2>>,
ShapeConstraint: AreMultipliable<R1, C1, Const<D2>, Const<D2>>,

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#### type Output = Matrix<T, R1, Const<D2>, <DefaultAllocator as Allocator<T, R1, Const<D2>>>::Buffer>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: Rotation<T, D2>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T, R1, C1, SA, const D2: usize> Mul<Rotation<T, D2>> for Matrix<T, R1, C1, SA>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,
R1: Dim,
C1: Dim,
SA: Storage<T, R1, C1>,
DefaultAllocator: Allocator<T, R1, Const<D2>>,
ShapeConstraint: AreMultipliable<R1, C1, Const<D2>, Const<D2>>,

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#### type Output = Matrix<T, R1, Const<D2>, <DefaultAllocator as Allocator<T, R1, Const<D2>>>::Buffer>

The resulting type after applying the `*` operator.
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#### fn mul(self, right: Rotation<T, D2>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField, const D: usize> Mul<Similarity<T, Rotation<T, D>, D>> for &'a Rotation<T, D>where
T::Element: SimdRealField,

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#### type Output = Similarity<T, Rotation<T, D>, D>

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

#### fn mul(self, right: Similarity<T, Rotation<T, D>, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField, const D: usize> Mul<Similarity<T, Rotation<T, D>, D>> for Rotation<T, D>where
T::Element: SimdRealField,

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#### type Output = Similarity<T, Rotation<T, D>, D>

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

#### fn mul(self, right: Similarity<T, Rotation<T, D>, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T, C, const D: usize> Mul<Transform<T, C, D>> for &'a Rotation<T, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

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

#### fn mul(self, rhs: Transform<T, C, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T, C, const D: usize> Mul<Transform<T, C, D>> for Rotation<T, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

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

#### fn mul(self, rhs: Transform<T, C, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<'a, T: SimdRealField, const D: usize> Mul<Translation<T, D>> for &'a Rotation<T, D>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Rotation<T, D>, D>

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

#### fn mul(self, right: Translation<T, D>) -> Self::Output

Performs the `*` operation. Read more
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### impl<T: SimdRealField, const D: usize> Mul<Translation<T, D>> for Rotation<T, D>where
T::Element: SimdRealField,

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#### type Output = Isometry<T, Rotation<T, D>, D>

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

#### fn mul(self, right: Translation<T, D>) -> 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.
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
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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.
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#### 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 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: 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.
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#### fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

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

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#### fn mul_assign(&mut self, rhs: &'b Rotation<T, 2>)

Performs the `*=` operation. Read more
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### impl<'b, T: SimdRealField> MulAssign<&'b Rotation<T, 3>> for UnitQuaternion<T>where
T::Element: SimdRealField,

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#### fn mul_assign(&mut self, rhs: &'b Rotation<T, 3>)

Performs the `*=` operation. Read more
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### impl<'b, T, const R1: usize, const C1: usize> MulAssign<&'b Rotation<T, C1>> for SMatrix<T, R1, C1>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,

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#### fn mul_assign(&mut self, right: &'b Rotation<T, C1>)

Performs the `*=` operation. Read more
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### impl<'b, T, const D: usize> MulAssign<&'b Rotation<T, D>> for Isometry<T, Rotation<T, D>, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

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#### fn mul_assign(&mut self, rhs: &'b Rotation<T, D>)

Performs the `*=` operation. Read more
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### impl<'b, T, const D: usize> MulAssign<&'b Rotation<T, D>> for Rotation<T, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,

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#### fn mul_assign(&mut self, right: &'b Rotation<T, D>)

Performs the `*=` operation. Read more
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### impl<'b, T, const D: usize> MulAssign<&'b Rotation<T, D>> for Similarity<T, Rotation<T, D>, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

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#### fn mul_assign(&mut self, rhs: &'b Rotation<T, D>)

Performs the `*=` operation. Read more
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### impl<'b, T, C, const D: usize> MulAssign<&'b Rotation<T, D>> for Transform<T, C, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategory,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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#### fn mul_assign(&mut self, rhs: &'b Rotation<T, D>)

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,

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

Performs the `*=` operation. Read more
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### impl<T: SimdRealField> MulAssign<Rotation<T, 2>> for UnitComplex<T>where
T::Element: SimdRealField,

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#### fn mul_assign(&mut self, rhs: Rotation<T, 2>)

Performs the `*=` operation. Read more
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### impl<T: SimdRealField> MulAssign<Rotation<T, 3>> for UnitQuaternion<T>where
T::Element: SimdRealField,

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#### fn mul_assign(&mut self, rhs: Rotation<T, 3>)

Performs the `*=` operation. Read more
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### impl<T, const R1: usize, const C1: usize> MulAssign<Rotation<T, C1>> for SMatrix<T, R1, C1>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,

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#### fn mul_assign(&mut self, right: Rotation<T, C1>)

Performs the `*=` operation. Read more
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### impl<T, const D: usize> MulAssign<Rotation<T, D>> for Isometry<T, Rotation<T, D>, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

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#### fn mul_assign(&mut self, rhs: Rotation<T, D>)

Performs the `*=` operation. Read more
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### impl<T, const D: usize> MulAssign<Rotation<T, D>> for Rotation<T, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,

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#### fn mul_assign(&mut self, right: Rotation<T, D>)

Performs the `*=` operation. Read more
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### impl<T, const D: usize> MulAssign<Rotation<T, D>> for Similarity<T, Rotation<T, D>, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

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#### fn mul_assign(&mut self, rhs: Rotation<T, D>)

Performs the `*=` operation. Read more
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### impl<T, C, const D: usize> MulAssign<Rotation<T, D>> for Transform<T, C, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategory,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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#### fn mul_assign(&mut self, rhs: Rotation<T, D>)

Performs the `*=` operation. Read more
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### impl<T: SimdRealField> MulAssign<Unit<Complex<T>>> for Rotation<T, 2>where
T::Element: SimdRealField,

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

Performs the `*=` operation. Read more
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### impl<T, const D: usize> One for Rotation<T, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul,

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#### fn one() -> Self

Returns the multiplicative identity element of `Self`, `1`. Read more
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#### fn set_one(&mut self)

Sets `self` to the multiplicative identity element of `Self`, `1`.
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#### fn is_one(&self) -> bool where
Self: PartialEq<Self>,

Returns `true` if `self` is equal to the multiplicative identity. Read more
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### impl<T: Scalar + PartialEq, const D: usize> PartialEq<Rotation<T, D>> for Rotation<T, D>

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#### fn eq(&self, right: &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, const D: usize> RelativeEq<Rotation<T, D>> for Rotation<T, D>where
T: Scalar + RelativeEq,
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, const D: usize> SimdValue for Rotation<T, D>where
T: Scalar + SimdValue,
T::Element: Scalar,

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#### type Element = Rotation<<T as SimdValue>::Element, D>

The type of the elements of each lane of this SIMD value.
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#### type SimdBool = <T as SimdValue>::SimdBool

Type of the result of comparing two SIMD values like `self`.
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#### fn lanes() -> usize

The number of lanes of this SIMD value.
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#### fn splat(val: Self::Element) -> Self

Initializes an SIMD value with each lanes set to `val`.
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#### fn extract(&self, i: usize) -> Self::Element

Extracts the i-th lane of `self`. Read more
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#### unsafe fn extract_unchecked(&self, i: usize) -> Self::Element

Extracts the i-th lane of `self` without bound-checking.
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#### fn replace(&mut self, i: usize, val: Self::Element)

Replaces the i-th lane of `self` by `val`. Read more
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#### unsafe fn replace_unchecked(&mut self, i: usize, val: Self::Element)

Replaces the i-th lane of `self` by `val` without bound-checking.
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#### fn select(self, cond: Self::SimdBool, other: Self) -> Self

Merges `self` and `other` depending on the lanes of `cond`. Read more
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#### fn map_lanes(self, f: impl Fn(Self::Element) -> Self::Element) -> Selfwhere
Self: Clone,

Applies a function to each lane of `self`. Read more
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#### fn zip_map_lanes(
self,
b: Self,
f: impl Fn(Self::Element, Self::Element) -> Self::Element
) -> Selfwhere
Self: Clone,

Applies a function to each lane of `self` paired with the corresponding lane of `b`. Read more
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### impl<T1, T2, R, const D: usize> SubsetOf<Isometry<T2, R, D>> for Rotation<T1, D>where
T1: RealField,
T2: RealField + SupersetOf<T1>,
R: AbstractRotation<T2, D> + SupersetOf<Self>,

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#### fn to_superset(&self) -> Isometry<T2, R, D>

The inclusion map: converts `self` to the equivalent element of its superset.
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#### fn is_in_subset(iso: &Isometry<T2, R, D>) -> 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(iso: &Isometry<T2, R, D>) -> 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, const D: usize> SubsetOf<Matrix<T2, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output, <DefaultAllocator as Allocator<T2, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>>::Buffer>> for Rotation<T1, D>where
T1: RealField,
T2: RealField + SupersetOf<T1>,
Const<D>: DimNameAdd<U1> + DimMin<Const<D>, Output = Const<D>>,
DefaultAllocator: Allocator<T1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> + Allocator<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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#### fn to_superset(
&self
) -> OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>

The inclusion map: converts `self` to the equivalent element of its superset.
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#### fn is_in_subset(
m: &OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
) -> 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(
m: &OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
) -> 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<Rotation<T2, 2>> for UnitComplex<T1>where
T1: RealField,
T2: RealField + SupersetOf<T1>,

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#### fn to_superset(&self) -> Rotation2<T2>

The inclusion map: converts `self` to the equivalent element of its superset.
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#### fn is_in_subset(rot: &Rotation2<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(rot: &Rotation2<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<Rotation<T2, 3>> for UnitQuaternion<T1>where
T1: RealField,
T2: RealField + SupersetOf<T1>,

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#### fn to_superset(&self) -> Rotation3<T2>

The inclusion map: converts `self` to the equivalent element of its superset.
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#### fn is_in_subset(rot: &Rotation3<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(rot: &Rotation3<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, const D: usize> SubsetOf<Rotation<T2, D>> for Rotation<T1, D>where
T1: RealField,
T2: RealField + SupersetOf<T1>,

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#### fn to_superset(&self) -> Rotation<T2, D>

The inclusion map: converts `self` to the equivalent element of its superset.
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#### fn is_in_subset(rot: &Rotation<T2, D>) -> 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(rot: &Rotation<T2, D>) -> 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, R, const D: usize> SubsetOf<Similarity<T2, R, D>> for Rotation<T1, D>where
T1: RealField,
T2: RealField + SupersetOf<T1>,
R: AbstractRotation<T2, D> + SupersetOf<Self>,

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#### fn to_superset(&self) -> Similarity<T2, R, D>

The inclusion map: converts `self` to the equivalent element of its superset.
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#### fn is_in_subset(sim: &Similarity<T2, R, D>) -> 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(sim: &Similarity<T2, R, D>) -> 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, C, const D: usize> SubsetOf<Transform<T2, C, D>> for Rotation<T1, D>where
T1: RealField,
T2: RealField + SupersetOf<T1>,
C: SuperTCategoryOf<TAffine>,
Const<D>: DimNameAdd<U1> + DimMin<Const<D>, Output = Const<D>>,
DefaultAllocator: Allocator<T1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> + Allocator<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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#### fn to_superset(&self) -> Transform<T2, C, D>

The inclusion map: converts `self` to the equivalent element of its superset.
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#### fn is_in_subset(t: &Transform<T2, C, D>) -> 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(t: &Transform<T2, C, D>) -> 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, const D: usize> UlpsEq<Rotation<T, D>> for Rotation<T, D>where
T: Scalar + UlpsEq,
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
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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: Copy, const D: usize> Copy for Rotation<T, D>

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### impl<T: Scalar + Eq, const D: usize> Eq for Rotation<T, D>

## Auto Trait Implementations§

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### impl<T, const D: usize> RefUnwindSafe for Rotation<T, D>where
T: RefUnwindSafe,

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### impl<T, const D: usize> Send for Rotation<T, D>where
T: Send,

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### impl<T, const D: usize> Sync for Rotation<T, D>where
T: Sync,

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### impl<T, const D: usize> Unpin for Rotation<T, D>where
T: Unpin,

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### impl<T, const D: usize> UnwindSafe for Rotation<T, D>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
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### impl<T> Borrow<T> for Twhere
T: ?Sized,

const: unstable · source§

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

Immutably borrows from an owned value. Read more
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### 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
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### 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,

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#### type Owned = T

The resulting type after obtaining ownership.
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#### 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>,

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#### 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.
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### 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>,