Struct nalgebra::geometry::Rotation

#[repr(C)]
pub struct Rotation<N: Scalar, D: DimName> where
    DefaultAllocator: Allocator<N, D, D>,  { /* fields omitted */ }

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

impl<N: Scalar, D: DimName> Rotation<N, D> where
    DefaultAllocator: Allocator<N, D, D>, 

pub fn from_matrix_unchecked(matrix: MatrixN<N, D>) -> Self

Creates a new rotation from the given square matrix.

The matrix squareness is checked but not its orthonormality.

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);

impl<N: Scalar, D: DimName> Rotation<N, D> where
    DefaultAllocator: Allocator<N, D, D>, 

Conversion to a matrix

pub fn matrix(&self) -> &MatrixN<N, 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);

pub unsafe fn matrix_mut(&mut self) -> &mut MatrixN<N, D>

👎 Deprecated:

Use .matrix_mut_unchecked() instead.

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

pub fn matrix_mut_unchecked(&mut self) -> &mut MatrixN<N, 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-square, non-inversible, or non-orthonormal. If one of those properties is broken, subsequent method calls may be UB.

pub fn into_inner(self) -> MatrixN<N, 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);

pub fn unwrap(self) -> MatrixN<N, D>

👎 Deprecated:

use .into_inner() instead

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

pub fn to_homogeneous(&self) -> MatrixN<N, DimNameSum<D, U1>> where
    N: Zero + One,
    D: DimNameAdd<U1>,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<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);

impl<N: Scalar, D: DimName> Rotation<N, D> where
    DefaultAllocator: Allocator<N, D, D>, 

Transposition and inversion

#[must_use = "Did you mean to use transpose_mut()?"]

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);

#[must_use = "Did you mean to use inverse_mut()?"]

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);

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);

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);

impl<N: SimdRealField, D: DimName> Rotation<N, D> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D>, 

Transformation of a vector or a point

pub fn transform_point(&self, pt: &Point<N, D>) -> Point<N, 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);

pub fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, 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);

pub fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, 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);

pub fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, 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);

pub fn inverse_transform_unit_vector(
    &self,
    v: &Unit<VectorN<N, D>>
) -> Unit<VectorN<N, 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);

impl<N, D: DimName> Rotation<N, D> where
    N: Scalar + Zero + One,
    DefaultAllocator: Allocator<N, D, D>, 

Identity

pub fn identity() -> Rotation<N, D>

Creates a new square identity rotation of the given dimension.

Example

let rot1 = Quaternion::identity();
let rot2 = Quaternion::new(1.0, 2.0, 3.0, 4.0);

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

impl<N: SimdRealField> Rotation<N, U2>

Interpolation

pub fn slerp(&self, other: &Self, t: N) -> Self where
    N::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);

impl<N: SimdRealField> Rotation<N, U3>

pub fn slerp(&self, other: &Self, t: N) -> Self where
    N: 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));

pub fn try_slerp(&self, other: &Self, t: N, epsilon: N) -> Option<Self> where
    N: 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.

impl<N: SimdRealField> Rotation<N, U2>

Construction from a 2D rotation angle

pub fn new(angle: N) -> 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));

pub fn from_scaled_axis<SB: Storage<N, U1>>(
    axisangle: Vector<N, 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.

impl<N: SimdRealField> Rotation<N, U2>

Construction from an existing 2D matrix or rotations

pub fn from_matrix(m: &Matrix2<N>) -> Self where
    N: 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.

pub fn from_matrix_eps(
    m: &Matrix2<N>,
    eps: N,
    max_iter: usize,
    guess: Self
) -> Self where
    N: 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.

pub fn rotation_between<SB, SC>(
    a: &Vector<N, U2, SB>,
    b: &Vector<N, U2, SC>
) -> Self where
    N: RealField,
    SB: Storage<N, U2>,
    SC: Storage<N, 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);

pub fn scaled_rotation_between<SB, SC>(
    a: &Vector<N, U2, SB>,
    b: &Vector<N, U2, SC>,
    s: N
) -> Self where
    N: RealField,
    SB: Storage<N, U2>,
    SC: Storage<N, 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);

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);

pub fn renormalize(&mut self) where
    N: 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.

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

Raise the quaternion 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);

impl<N: SimdRealField> Rotation<N, U2>

2D angle extraction

pub fn angle(&self) -> N

The rotation angle.

Example

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

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

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);

pub fn scaled_axis(&self) -> VectorN<N, U1>

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.

impl<N: SimdRealField> Rotation<N, U3> where
    N::Element: SimdRealField, 

Construction from a 3D axis and/or angles

pub fn new<SB: Storage<N, U3>>(axisangle: Vector<N, 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());

pub fn from_scaled_axis<SB: Storage<N, U3>>(
    axisangle: Vector<N, 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());

pub fn from_axis_angle<SB>(axis: &Unit<Vector<N, U3, SB>>, angle: N) -> Self where
    SB: Storage<N, 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());

pub fn from_euler_angles(roll: N, pitch: N, yaw: N) -> 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);

impl<N: SimdRealField> Rotation<N, U3> where
    N::Element: SimdRealField, 

Construction from a 3D eye position and target point

pub fn face_towards<SB, SC>(
    dir: &Vector<N, U3, SB>,
    up: &Vector<N, U3, SC>
) -> Self where
    SB: Storage<N, U3>,
    SC: Storage<N, 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());

pub fn new_observer_frames<SB, SC>(
    dir: &Vector<N, U3, SB>,
    up: &Vector<N, U3, SC>
) -> Self where
    SB: Storage<N, U3>,
    SC: Storage<N, U3>, 

👎 Deprecated:

renamed to face_towards

Deprecated: Use [Rotation3::face_towards] instead.

pub fn look_at_rh<SB, SC>(
    dir: &Vector<N, U3, SB>,
    up: &Vector<N, U3, SC>
) -> Self where
    SB: Storage<N, U3>,
    SC: Storage<N, 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());

pub fn look_at_lh<SB, SC>(
    dir: &Vector<N, U3, SB>,
    up: &Vector<N, U3, SC>
) -> Self where
    SB: Storage<N, U3>,
    SC: Storage<N, 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());

impl<N: SimdRealField> Rotation<N, U3> where
    N::Element: SimdRealField, 

Construction from an existing 3D matrix or rotations

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

pub fn scaled_rotation_between<SB, SC>(
    a: &Vector<N, U3, SB>,
    b: &Vector<N, U3, SC>,
    n: N
) -> Option<Self> where
    N: RealField,
    SB: Storage<N, U3>,
    SC: Storage<N, 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);

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);

pub fn powf(&self, n: N) -> Self where
    N: RealField, 

Raise the quaternion 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);

pub fn from_matrix(m: &Matrix3<N>) -> Self where
    N: 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.

pub fn from_matrix_eps(
    m: &Matrix3<N>,
    eps: N,
    max_iter: usize,
    guess: Self
) -> Self where
    N: 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.

pub fn renormalize(&mut self) where
    N: 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.

impl<N: SimdRealField> Rotation<N, U3>

3D axis and angle extraction

pub fn angle(&self) -> N

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);

pub fn axis(&self) -> Option<Unit<Vector3<N>>> where
    N: 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());

pub fn scaled_axis(&self) -> Vector3<N> where
    N: 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);

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

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

Returns None if the angle is zero.

Example

let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
let angle = 1.2;
let rot = 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());

pub fn angle_to(&self, other: &Self) -> N where
    N::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);

pub fn to_euler_angles(&self) -> (N, N, N) where
    N: 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).

pub fn euler_angles(&self) -> (N, N, N) where
    N: 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

impl<N, D: DimName> AbsDiffEq<Rotation<N, D>> for Rotation<N, D> where
    N: Scalar + AbsDiffEq,
    DefaultAllocator: Allocator<N, D, D>,
    N::Epsilon: Copy, 

type Epsilon = N::Epsilon

Used for specifying relative comparisons.

fn default_epsilon() -> Self::Epsilon

The default tolerance to use when testing values that are close together.

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.

pub fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of AbsDiffEq::abs_diff_eq.

impl<N: SimdRealField, D: DimName> AbstractRotation<N, D> for Rotation<N, D> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>, 

fn identity() -> Self

The rotation identity.

fn inverse(&self) -> Self

The rotation inverse.

fn inverse_mut(&mut self)

Change self to its inverse.

fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> where
    DefaultAllocator: Allocator<N, D>, 

Apply the rotation to the given vector.

fn transform_point(&self, p: &Point<N, D>) -> Point<N, D> where
    DefaultAllocator: Allocator<N, D>, 

Apply the rotation to the given point.

fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D> where
    DefaultAllocator: Allocator<N, D>, 

Apply the inverse rotation to the given vector.

fn inverse_transform_unit_vector(
    &self,
    v: &Unit<VectorN<N, D>>
) -> Unit<VectorN<N, D>> where
    DefaultAllocator: Allocator<N, D>, 

Apply the inverse rotation to the given unit vector.

fn inverse_transform_point(&self, p: &Point<N, D>) -> Point<N, D> where
    DefaultAllocator: Allocator<N, D>, 

Apply the inverse rotation to the given point.

impl<N: Scalar, D: DimName> Clone for Rotation<N, D> where
    DefaultAllocator: Allocator<N, D, D>,
    <DefaultAllocator as Allocator<N, D, D>>::Buffer: Clone, 

fn clone(&self) -> Self

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<N: Debug + Scalar, D: Debug + DimName> Debug for Rotation<N, D> where
    DefaultAllocator: Allocator<N, D, D>, 

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

Formats the value using the given formatter.

impl<'a, N: Scalar, D: DimName> Deserialize<'a> for Rotation<N, D> where
    DefaultAllocator: Allocator<N, D, D>,
    Owned<N, D, D>: Deserialize<'a>, 

fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error> where
    Des: Deserializer<'a>, 

Deserialize this value from the given Serde deserializer.

impl<N, D: DimName> Display for Rotation<N, D> where
    N: RealField + Display,
    DefaultAllocator: Allocator<N, D, D> + Allocator<usize, D, D>, 

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

Formats the value using the given formatter.

impl<N: SimdRealField> Distribution<Rotation<N, U2>> for Standard where
    N::Element: SimdRealField,
    OpenClosed01: Distribution<N>, 

fn sample<'a, R: Rng + ?Sized>(&self, rng: &'a mut R) -> Rotation2<N>

Generate a uniformly distributed random rotation.

pub fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T> where
    R: Rng, 

Create an iterator that generates random values of T, using rng as the source of randomness.

impl<N: SimdRealField> Distribution<Rotation<N, U3>> for Standard where
    N::Element: SimdRealField,
    OpenClosed01: Distribution<N>, 

fn sample<'a, R: Rng + ?Sized>(&self, rng: &mut R) -> Rotation3<N>

Generate a uniformly distributed random rotation.

pub fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T> where
    R: Rng, 

Create an iterator that generates random values of T, using rng as the source of randomness.

impl<'b, N: SimdRealField, D: DimName> Div<&'b Isometry<N, D, Rotation<N, D>>> for Rotation<N, D> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Isometry<N, D, Rotation<N, D>>

The resulting type after applying the / operator.

fn div(self, right: &'b Isometry<N, D, Rotation<N, D>>) -> Self::Output

Performs the / operation.

impl<'a, 'b, N: SimdRealField, D: DimName> Div<&'b Isometry<N, D, Rotation<N, D>>> for &'a Rotation<N, D> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Isometry<N, D, Rotation<N, D>>

The resulting type after applying the / operator.

fn div(self, right: &'b Isometry<N, D, Rotation<N, D>>) -> Self::Output

Performs the / operation.

impl<'b, N, D: DimName> Div<&'b Rotation<N, D>> for Rotation<N, D> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D, D>, 

type Output = Rotation<N, D>

The resulting type after applying the / operator.

fn div(self, right: &'b Rotation<N, D>) -> Self::Output

Performs the / operation.

impl<'a, 'b, N, D: DimName> Div<&'b Rotation<N, D>> for &'a Rotation<N, D> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D, D>, 

type Output = Rotation<N, D>

The resulting type after applying the / operator.

fn div(self, right: &'b Rotation<N, D>) -> Self::Output

Performs the / operation.

impl<'b, N: SimdRealField, D: DimName> Div<&'b Rotation<N, D>> for Isometry<N, D, Rotation<N, D>> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Isometry<N, D, Rotation<N, D>>

The resulting type after applying the / operator.

fn div(self, rhs: &'b Rotation<N, D>) -> Self::Output

Performs the / operation.

impl<'a, 'b, N: SimdRealField, D: DimName> Div<&'b Rotation<N, D>> for &'a Isometry<N, D, Rotation<N, D>> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Isometry<N, D, Rotation<N, D>>

The resulting type after applying the / operator.

fn div(self, rhs: &'b Rotation<N, D>) -> Self::Output

Performs the / operation.

impl<'b, N: SimdRealField, D: DimName> Div<&'b Rotation<N, D>> for Similarity<N, D, Rotation<N, D>> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Similarity<N, D, Rotation<N, D>>

The resulting type after applying the / operator.

fn div(self, rhs: &'b Rotation<N, D>) -> Self::Output

Performs the / operation.

impl<'a, 'b, N: SimdRealField, D: DimName> Div<&'b Rotation<N, D>> for &'a Similarity<N, D, Rotation<N, D>> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Similarity<N, D, Rotation<N, D>>

The resulting type after applying the / operator.

fn div(self, rhs: &'b Rotation<N, D>) -> Self::Output

Performs the / operation.

impl<'b, N, D: DimNameAdd<U1>, C: TCategoryMul<TAffine>> Div<&'b Rotation<N, D>> for Transform<N, D, C> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, D> + Allocator<N, DimNameSum<D, U1>, D>, 

type Output = Transform<N, D, C::Representative>

The resulting type after applying the / operator.

fn div(self, rhs: &'b Rotation<N, D>) -> Self::Output

Performs the / operation.

impl<'a, 'b, N, D: DimNameAdd<U1>, C: TCategoryMul<TAffine>> Div<&'b Rotation<N, D>> for &'a Transform<N, D, C> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, D> + Allocator<N, DimNameSum<D, U1>, D>, 

type Output = Transform<N, D, C::Representative>

The resulting type after applying the / operator.

fn div(self, rhs: &'b Rotation<N, D>) -> Self::Output

Performs the / operation.

impl<'b, N, R1: Dim, C1: Dim, D2: DimName, SA: Storage<N, R1, C1>> Div<&'b Rotation<N, D2>> for Matrix<N, R1, C1, SA> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, R1, C1> + Allocator<N, D2, D2> + Allocator<N, R1, D2>,
    DefaultAllocator: Allocator<N, R1, D2>,
    ShapeConstraint: AreMultipliable<R1, C1, D2, D2>, 

type Output = MatrixMN<N, R1, D2>

The resulting type after applying the / operator.

fn div(self, right: &'b Rotation<N, D2>) -> Self::Output

Performs the / operation.

impl<'a, 'b, N, R1: Dim, C1: Dim, D2: DimName, SA: Storage<N, R1, C1>> Div<&'b Rotation<N, D2>> for &'a Matrix<N, R1, C1, SA> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, R1, C1> + Allocator<N, D2, D2> + Allocator<N, R1, D2>,
    DefaultAllocator: Allocator<N, R1, D2>,
    ShapeConstraint: AreMultipliable<R1, C1, D2, D2>, 

type Output = MatrixMN<N, R1, D2>

The resulting type after applying the / operator.

fn div(self, right: &'b Rotation<N, D2>) -> Self::Output

Performs the / operation.

impl<'b, N: SimdRealField> Div<&'b Rotation<N, U2>> for UnitComplex<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

type Output = UnitComplex<N>

The resulting type after applying the / operator.

fn div(self, rhs: &'b Rotation<N, U2>) -> Self::Output

Performs the / operation.

impl<'a, 'b, N: SimdRealField> Div<&'b Rotation<N, U2>> for &'a UnitComplex<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

type Output = UnitComplex<N>

The resulting type after applying the / operator.

fn div(self, rhs: &'b Rotation<N, U2>) -> Self::Output

Performs the / operation.

impl<'a, 'b, N: SimdRealField> Div<&'b Rotation<N, U3>> for &'a UnitQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U3>, 

type Output = UnitQuaternion<N>

The resulting type after applying the / operator.

fn div(self, rhs: &'b Rotation<N, U3>) -> Self::Output

Performs the / operation.

impl<'b, N: SimdRealField> Div<&'b Rotation<N, U3>> for UnitQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U3>, 

type Output = UnitQuaternion<N>

The resulting type after applying the / operator.

fn div(self, rhs: &'b Rotation<N, U3>) -> Self::Output

Performs the / operation.

impl<'b, N: SimdRealField, D: DimName> Div<&'b Similarity<N, D, Rotation<N, D>>> for Rotation<N, D> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Similarity<N, D, Rotation<N, D>>

The resulting type after applying the / operator.

fn div(self, right: &'b Similarity<N, D, Rotation<N, D>>) -> Self::Output

Performs the / operation.

impl<'a, 'b, N: SimdRealField, D: DimName> Div<&'b Similarity<N, D, Rotation<N, D>>> for &'a Rotation<N, D> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Similarity<N, D, Rotation<N, D>>

The resulting type after applying the / operator.

fn div(self, right: &'b Similarity<N, D, Rotation<N, D>>) -> Self::Output

Performs the / operation.

impl<'b, N, D: DimNameAdd<U1>, C: TCategoryMul<TAffine>> Div<&'b Transform<N, D, C>> for Rotation<N, D> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, DimNameSum<D, U1>>, 

type Output = Transform<N, D, C::Representative>

The resulting type after applying the / operator.

fn div(self, rhs: &'b Transform<N, D, C>) -> Self::Output

Performs the / operation.

impl<'a, 'b, N, D: DimNameAdd<U1>, C: TCategoryMul<TAffine>> Div<&'b Transform<N, D, C>> for &'a Rotation<N, D> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, DimNameSum<D, U1>>, 

type Output = Transform<N, D, C::Representative>

The resulting type after applying the / operator.

fn div(self, rhs: &'b Transform<N, D, C>) -> Self::Output

Performs the / operation.

impl<'b, N: SimdRealField> Div<&'b Unit<Complex<N>>> for Rotation<N, U2> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

type Output = UnitComplex<N>

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitComplex<N>) -> Self::Output

Performs the / operation.

impl<'a, 'b, N: SimdRealField> Div<&'b Unit<Complex<N>>> for &'a Rotation<N, U2> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

type Output = UnitComplex<N>

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitComplex<N>) -> Self::Output

Performs the / operation.

impl<'a, 'b, N: SimdRealField> Div<&'b Unit<Quaternion<N>>> for &'a Rotation<N, U3> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3> + Allocator<N, U4, U1>, 

type Output = UnitQuaternion<N>

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitQuaternion<N>) -> Self::Output

Performs the / operation.

impl<'b, N: SimdRealField> Div<&'b Unit<Quaternion<N>>> for Rotation<N, U3> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3> + Allocator<N, U4, U1>, 

type Output = UnitQuaternion<N>

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitQuaternion<N>) -> Self::Output

Performs the / operation.

impl<N: SimdRealField, D: DimName> Div<Isometry<N, D, Rotation<N, D>>> for Rotation<N, D> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Isometry<N, D, Rotation<N, D>>

The resulting type after applying the / operator.

fn div(self, right: Isometry<N, D, Rotation<N, D>>) -> Self::Output

Performs the / operation.

impl<'a, N: SimdRealField, D: DimName> Div<Isometry<N, D, Rotation<N, D>>> for &'a Rotation<N, D> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Isometry<N, D, Rotation<N, D>>

The resulting type after applying the / operator.

fn div(self, right: Isometry<N, D, Rotation<N, D>>) -> Self::Output

Performs the / operation.

impl<N, D: DimName> Div<Rotation<N, D>> for Rotation<N, D> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D, D>, 

type Output = Rotation<N, D>

The resulting type after applying the / operator.

fn div(self, right: Rotation<N, D>) -> Self::Output

Performs the / operation.

impl<'a, N, D: DimName> Div<Rotation<N, D>> for &'a Rotation<N, D> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D, D>, 

type Output = Rotation<N, D>

The resulting type after applying the / operator.

fn div(self, right: Rotation<N, D>) -> Self::Output

Performs the / operation.

impl<N: SimdRealField, D: DimName> Div<Rotation<N, D>> for Isometry<N, D, Rotation<N, D>> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Isometry<N, D, Rotation<N, D>>

The resulting type after applying the / operator.

fn div(self, rhs: Rotation<N, D>) -> Self::Output

Performs the / operation.

impl<'a, N: SimdRealField, D: DimName> Div<Rotation<N, D>> for &'a Isometry<N, D, Rotation<N, D>> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Isometry<N, D, Rotation<N, D>>

The resulting type after applying the / operator.

fn div(self, rhs: Rotation<N, D>) -> Self::Output

Performs the / operation.

impl<N: SimdRealField, D: DimName> Div<Rotation<N, D>> for Similarity<N, D, Rotation<N, D>> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Similarity<N, D, Rotation<N, D>>

The resulting type after applying the / operator.

fn div(self, rhs: Rotation<N, D>) -> Self::Output

Performs the / operation.

impl<'a, N: SimdRealField, D: DimName> Div<Rotation<N, D>> for &'a Similarity<N, D, Rotation<N, D>> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Similarity<N, D, Rotation<N, D>>

The resulting type after applying the / operator.

fn div(self, rhs: Rotation<N, D>) -> Self::Output

Performs the / operation.

impl<N, D: DimNameAdd<U1>, C: TCategoryMul<TAffine>> Div<Rotation<N, D>> for Transform<N, D, C> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, D> + Allocator<N, DimNameSum<D, U1>, D>, 

type Output = Transform<N, D, C::Representative>

The resulting type after applying the / operator.

fn div(self, rhs: Rotation<N, D>) -> Self::Output

Performs the / operation.

impl<'a, N, D: DimNameAdd<U1>, C: TCategoryMul<TAffine>> Div<Rotation<N, D>> for &'a Transform<N, D, C> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, D> + Allocator<N, DimNameSum<D, U1>, D>, 

type Output = Transform<N, D, C::Representative>

The resulting type after applying the / operator.

fn div(self, rhs: Rotation<N, D>) -> Self::Output

Performs the / operation.

impl<N, R1: Dim, C1: Dim, D2: DimName, SA: Storage<N, R1, C1>> Div<Rotation<N, D2>> for Matrix<N, R1, C1, SA> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, R1, C1> + Allocator<N, D2, D2> + Allocator<N, R1, D2>,
    DefaultAllocator: Allocator<N, R1, D2>,
    ShapeConstraint: AreMultipliable<R1, C1, D2, D2>, 

type Output = MatrixMN<N, R1, D2>

The resulting type after applying the / operator.

fn div(self, right: Rotation<N, D2>) -> Self::Output

Performs the / operation.

impl<'a, N, R1: Dim, C1: Dim, D2: DimName, SA: Storage<N, R1, C1>> Div<Rotation<N, D2>> for &'a Matrix<N, R1, C1, SA> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, R1, C1> + Allocator<N, D2, D2> + Allocator<N, R1, D2>,
    DefaultAllocator: Allocator<N, R1, D2>,
    ShapeConstraint: AreMultipliable<R1, C1, D2, D2>, 

type Output = MatrixMN<N, R1, D2>

The resulting type after applying the / operator.

fn div(self, right: Rotation<N, D2>) -> Self::Output

Performs the / operation.

impl<N: SimdRealField> Div<Rotation<N, U2>> for UnitComplex<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

type Output = UnitComplex<N>

The resulting type after applying the / operator.

fn div(self, rhs: Rotation<N, U2>) -> Self::Output

Performs the / operation.

impl<'a, N: SimdRealField> Div<Rotation<N, U2>> for &'a UnitComplex<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

type Output = UnitComplex<N>

The resulting type after applying the / operator.

fn div(self, rhs: Rotation<N, U2>) -> Self::Output

Performs the / operation.

impl<'a, N: SimdRealField> Div<Rotation<N, U3>> for &'a UnitQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U3>, 

type Output = UnitQuaternion<N>

The resulting type after applying the / operator.

fn div(self, rhs: Rotation<N, U3>) -> Self::Output

Performs the / operation.

impl<N: SimdRealField> Div<Rotation<N, U3>> for UnitQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U3>, 

type Output = UnitQuaternion<N>

The resulting type after applying the / operator.

fn div(self, rhs: Rotation<N, U3>) -> Self::Output

Performs the / operation.

impl<N: SimdRealField, D: DimName> Div<Similarity<N, D, Rotation<N, D>>> for Rotation<N, D> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Similarity<N, D, Rotation<N, D>>

The resulting type after applying the / operator.

fn div(self, right: Similarity<N, D, Rotation<N, D>>) -> Self::Output

Performs the / operation.

impl<'a, N: SimdRealField, D: DimName> Div<Similarity<N, D, Rotation<N, D>>> for &'a Rotation<N, D> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Similarity<N, D, Rotation<N, D>>

The resulting type after applying the / operator.

fn div(self, right: Similarity<N, D, Rotation<N, D>>) -> Self::Output

Performs the / operation.

impl<N, D: DimNameAdd<U1>, C: TCategoryMul<TAffine>> Div<Transform<N, D, C>> for Rotation<N, D> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, DimNameSum<D, U1>>, 

type Output = Transform<N, D, C::Representative>

The resulting type after applying the / operator.

fn div(self, rhs: Transform<N, D, C>) -> Self::Output

Performs the / operation.

impl<'a, N, D: DimNameAdd<U1>, C: TCategoryMul<TAffine>> Div<Transform<N, D, C>> for &'a Rotation<N, D> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, DimNameSum<D, U1>>, 

type Output = Transform<N, D, C::Representative>

The resulting type after applying the / operator.

fn div(self, rhs: Transform<N, D, C>) -> Self::Output

Performs the / operation.

impl<N: SimdRealField> Div<Unit<Complex<N>>> for Rotation<N, U2> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

type Output = UnitComplex<N>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, N: SimdRealField> Div<Unit<Complex<N>>> for &'a Rotation<N, U2> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

type Output = UnitComplex<N>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, N: SimdRealField> Div<Unit<Quaternion<N>>> for &'a Rotation<N, U3> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3> + Allocator<N, U4, U1>, 

type Output = UnitQuaternion<N>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<N: SimdRealField> Div<Unit<Quaternion<N>>> for Rotation<N, U3> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3> + Allocator<N, U4, U1>, 

type Output = UnitQuaternion<N>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'b, N, R1: DimName, C1: DimName> DivAssign<&'b Rotation<N, C1>> for MatrixMN<N, R1, C1> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, R1, C1> + Allocator<N, C1, C1>, 

fn div_assign(&mut self, right: &'b Rotation<N, C1>)

Performs the /= operation.

impl<'b, N, D: DimName> DivAssign<&'b Rotation<N, D>> for Rotation<N, D> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D, D>, 

fn div_assign(&mut self, right: &'b Rotation<N, D>)

Performs the /= operation.

impl<'b, N, D: DimName> DivAssign<&'b Rotation<N, D>> for Isometry<N, D, Rotation<N, D>> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1> + Allocator<N, D, D>, 

fn div_assign(&mut self, rhs: &'b Rotation<N, D>)

Performs the /= operation.

impl<'b, N, D: DimName> DivAssign<&'b Rotation<N, D>> for Similarity<N, D, Rotation<N, D>> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1> + Allocator<N, D, D>, 

fn div_assign(&mut self, rhs: &'b Rotation<N, D>)

Performs the /= operation.

impl<'b, N, D: DimNameAdd<U1>, C: TCategory> DivAssign<&'b Rotation<N, D>> for Transform<N, D, C> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, D>, 

fn div_assign(&mut self, rhs: &'b Rotation<N, D>)

Performs the /= operation.

impl<'b, N: SimdRealField> DivAssign<&'b Rotation<N, U2>> for UnitComplex<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

fn div_assign(&mut self, rhs: &'b Rotation<N, U2>)

Performs the /= operation.

impl<'b, N: SimdRealField> DivAssign<&'b Rotation<N, U3>> for UnitQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U3>, 

fn div_assign(&mut self, rhs: &'b Rotation<N, U3>)

Performs the /= operation.

impl<'b, N: SimdRealField> DivAssign<&'b Unit<Complex<N>>> for Rotation<N, U2> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

fn div_assign(&mut self, rhs: &'b UnitComplex<N>)

Performs the /= operation.

impl<N, R1: DimName, C1: DimName> DivAssign<Rotation<N, C1>> for MatrixMN<N, R1, C1> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, R1, C1> + Allocator<N, C1, C1>, 

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

Performs the /= operation.

impl<N, D: DimName> DivAssign<Rotation<N, D>> for Rotation<N, D> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D, D>, 

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

Performs the /= operation.

impl<N, D: DimName> DivAssign<Rotation<N, D>> for Isometry<N, D, Rotation<N, D>> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1> + Allocator<N, D, D>, 

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

Performs the /= operation.

impl<N, D: DimName> DivAssign<Rotation<N, D>> for Similarity<N, D, Rotation<N, D>> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1> + Allocator<N, D, D>, 

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

Performs the /= operation.

impl<N, D: DimNameAdd<U1>, C: TCategory> DivAssign<Rotation<N, D>> for Transform<N, D, C> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, D>, 

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

Performs the /= operation.

impl<N: SimdRealField> DivAssign<Rotation<N, U2>> for UnitComplex<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

fn div_assign(&mut self, rhs: Rotation<N, U2>)

Performs the /= operation.

impl<N: SimdRealField> DivAssign<Rotation<N, U3>> for UnitQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U3>, 

fn div_assign(&mut self, rhs: Rotation<N, U3>)

Performs the /= operation.

impl<N: SimdRealField> DivAssign<Unit<Complex<N>>> for Rotation<N, U2> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

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

Performs the /= operation.

impl<N: Scalar + PrimitiveSimdValue, D: DimName> From<[Rotation<<N as SimdValue>::Element, D>; 16]> for Rotation<N, D> where
    N: From<[<N as SimdValue>::Element; 16]>,
    N::Element: Scalar + Copy,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N::Element, D, D>, 

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

Performs the conversion.

impl<N: Scalar + PrimitiveSimdValue, D: DimName> From<[Rotation<<N as SimdValue>::Element, D>; 2]> for Rotation<N, D> where
    N: From<[<N as SimdValue>::Element; 2]>,
    N::Element: Scalar + Copy,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N::Element, D, D>, 

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

Performs the conversion.

impl<N: Scalar + PrimitiveSimdValue, D: DimName> From<[Rotation<<N as SimdValue>::Element, D>; 4]> for Rotation<N, D> where
    N: From<[<N as SimdValue>::Element; 4]>,
    N::Element: Scalar + Copy,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N::Element, D, D>, 

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

Performs the conversion.

impl<N: Scalar + PrimitiveSimdValue, D: DimName> From<[Rotation<<N as SimdValue>::Element, D>; 8]> for Rotation<N, D> where
    N: From<[<N as SimdValue>::Element; 8]>,
    N::Element: Scalar + Copy,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N::Element, D, D>, 

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

Performs the conversion.

impl<N: RealField> From<Rotation<N, U2>> for Matrix3<N>

fn from(q: Rotation2<N>) -> Self

Performs the conversion.

impl<N: RealField> From<Rotation<N, U2>> for Matrix2<N>

fn from(q: Rotation2<N>) -> Self

Performs the conversion.

impl<N: SimdRealField> From<Rotation<N, U2>> for UnitComplex<N> where
    N::Element: SimdRealField, 

fn from(q: Rotation2<N>) -> Self

Performs the conversion.

impl<N: RealField> From<Rotation<N, U3>> for Matrix4<N>

fn from(q: Rotation3<N>) -> Self

Performs the conversion.

impl<N: RealField> From<Rotation<N, U3>> for Matrix3<N>

fn from(q: Rotation3<N>) -> Self

Performs the conversion.

impl<N: SimdRealField> From<Rotation<N, U3>> for UnitQuaternion<N> where
    N::Element: SimdRealField, 

fn from(q: Rotation3<N>) -> Self

Performs the conversion.

impl<N: Scalar + Hash, D: DimName + Hash> Hash for Rotation<N, D> where
    DefaultAllocator: Allocator<N, D, D>,
    <DefaultAllocator as Allocator<N, D, D>>::Buffer: Hash, 

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

Feeds this value into the given Hasher.

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

Feeds a slice of this type into the given Hasher.

impl<N: Scalar, D: DimName> Index<(usize, usize)> for Rotation<N, D> where
    DefaultAllocator: Allocator<N, D, D>, 

type Output = N

The returned type after indexing.

fn index(&self, row_col: (usize, usize)) -> &N

Performs the indexing (container[index]) operation.

impl<'b, N: SimdRealField, D: DimName> Mul<&'b Isometry<N, D, Rotation<N, D>>> for Rotation<N, D> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Isometry<N, D, Rotation<N, D>>

The resulting type after applying the * operator.

fn mul(self, right: &'b Isometry<N, D, Rotation<N, D>>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N: SimdRealField, D: DimName> Mul<&'b Isometry<N, D, Rotation<N, D>>> for &'a Rotation<N, D> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Isometry<N, D, Rotation<N, D>>

The resulting type after applying the * operator.

fn mul(self, right: &'b Isometry<N, D, Rotation<N, D>>) -> Self::Output

Performs the * operation.

impl<'b, N, D1: DimName, R2: Dim, C2: Dim, SB: Storage<N, R2, C2>> Mul<&'b Matrix<N, R2, C2, SB>> for Rotation<N, D1> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D1, D1> + Allocator<N, R2, C2> + Allocator<N, D1, C2>,
    DefaultAllocator: Allocator<N, D1, C2>,
    ShapeConstraint: AreMultipliable<D1, D1, R2, C2>, 

type Output = MatrixMN<N, D1, C2>

The resulting type after applying the * operator.

fn mul(self, right: &'b Matrix<N, R2, C2, SB>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N, D1: DimName, R2: Dim, C2: Dim, SB: Storage<N, R2, C2>> Mul<&'b Matrix<N, R2, C2, SB>> for &'a Rotation<N, D1> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D1, D1> + Allocator<N, R2, C2> + Allocator<N, D1, C2>,
    DefaultAllocator: Allocator<N, D1, C2>,
    ShapeConstraint: AreMultipliable<D1, D1, R2, C2>, 

type Output = MatrixMN<N, D1, C2>

The resulting type after applying the * operator.

fn mul(self, right: &'b Matrix<N, R2, C2, SB>) -> Self::Output

Performs the * operation.

impl<'b, N, D: DimName> Mul<&'b Point<N, D>> for Rotation<N, D> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, D>,
    ShapeConstraint: AreMultipliable<D, D, D, U1>, 

type Output = Point<N, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<N, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N, D: DimName> Mul<&'b Point<N, D>> for &'a Rotation<N, D> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, D>,
    ShapeConstraint: AreMultipliable<D, D, D, U1>, 

type Output = Point<N, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<N, D>) -> Self::Output

Performs the * operation.

impl<'b, N, D: DimName> Mul<&'b Rotation<N, D>> for Rotation<N, D> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D, D>, 

type Output = Rotation<N, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Rotation<N, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N, D: DimName> Mul<&'b Rotation<N, D>> for &'a Rotation<N, D> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D, D>, 

type Output = Rotation<N, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Rotation<N, D>) -> Self::Output

Performs the * operation.

impl<'b, N: SimdRealField, D: DimName> Mul<&'b Rotation<N, D>> for Isometry<N, D, Rotation<N, D>> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Isometry<N, D, Rotation<N, D>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Rotation<N, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N: SimdRealField, D: DimName> Mul<&'b Rotation<N, D>> for &'a Isometry<N, D, Rotation<N, D>> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Isometry<N, D, Rotation<N, D>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Rotation<N, D>) -> Self::Output

Performs the * operation.

impl<'b, N: SimdRealField, D: DimName> Mul<&'b Rotation<N, D>> for Translation<N, D> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Isometry<N, D, Rotation<N, D>>

The resulting type after applying the * operator.

fn mul(self, right: &'b Rotation<N, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N: SimdRealField, D: DimName> Mul<&'b Rotation<N, D>> for &'a Translation<N, D> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Isometry<N, D, Rotation<N, D>>

The resulting type after applying the * operator.

fn mul(self, right: &'b Rotation<N, D>) -> Self::Output

Performs the * operation.

impl<'b, N: SimdRealField, D: DimName> Mul<&'b Rotation<N, D>> for Similarity<N, D, Rotation<N, D>> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Similarity<N, D, Rotation<N, D>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Rotation<N, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N: SimdRealField, D: DimName> Mul<&'b Rotation<N, D>> for &'a Similarity<N, D, Rotation<N, D>> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Similarity<N, D, Rotation<N, D>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Rotation<N, D>) -> Self::Output

Performs the * operation.

impl<'b, N, D: DimNameAdd<U1>, C: TCategoryMul<TAffine>> Mul<&'b Rotation<N, D>> for Transform<N, D, C> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, D> + Allocator<N, DimNameSum<D, U1>, D>, 

type Output = Transform<N, D, C::Representative>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Rotation<N, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N, D: DimNameAdd<U1>, C: TCategoryMul<TAffine>> Mul<&'b Rotation<N, D>> for &'a Transform<N, D, C> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, D> + Allocator<N, DimNameSum<D, U1>, D>, 

type Output = Transform<N, D, C::Representative>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Rotation<N, D>) -> Self::Output

Performs the * operation.

impl<'b, N, R1: Dim, C1: Dim, D2: DimName, SA: Storage<N, R1, C1>> Mul<&'b Rotation<N, D2>> for Matrix<N, R1, C1, SA> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, R1, C1> + Allocator<N, D2, D2> + Allocator<N, R1, D2>,
    DefaultAllocator: Allocator<N, R1, D2>,
    ShapeConstraint: AreMultipliable<R1, C1, D2, D2>, 

type Output = MatrixMN<N, R1, D2>

The resulting type after applying the * operator.

fn mul(self, right: &'b Rotation<N, D2>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N, R1: Dim, C1: Dim, D2: DimName, SA: Storage<N, R1, C1>> Mul<&'b Rotation<N, D2>> for &'a Matrix<N, R1, C1, SA> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, R1, C1> + Allocator<N, D2, D2> + Allocator<N, R1, D2>,
    DefaultAllocator: Allocator<N, R1, D2>,
    ShapeConstraint: AreMultipliable<R1, C1, D2, D2>, 

type Output = MatrixMN<N, R1, D2>

The resulting type after applying the * operator.

fn mul(self, right: &'b Rotation<N, D2>) -> Self::Output

Performs the * operation.

impl<'b, N: SimdRealField> Mul<&'b Rotation<N, U2>> for UnitComplex<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

type Output = UnitComplex<N>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Rotation<N, U2>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N: SimdRealField> Mul<&'b Rotation<N, U2>> for &'a UnitComplex<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

type Output = UnitComplex<N>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Rotation<N, U2>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N: SimdRealField> Mul<&'b Rotation<N, U3>> for &'a UnitQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U3>, 

type Output = UnitQuaternion<N>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Rotation<N, U3>) -> Self::Output

Performs the * operation.

impl<'b, N: SimdRealField> Mul<&'b Rotation<N, U3>> for UnitQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U3>, 

type Output = UnitQuaternion<N>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Rotation<N, U3>) -> Self::Output

Performs the * operation.

impl<'b, N: SimdRealField, D: DimName> Mul<&'b Similarity<N, D, Rotation<N, D>>> for Rotation<N, D> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Similarity<N, D, Rotation<N, D>>

The resulting type after applying the * operator.

fn mul(self, right: &'b Similarity<N, D, Rotation<N, D>>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N: SimdRealField, D: DimName> Mul<&'b Similarity<N, D, Rotation<N, D>>> for &'a Rotation<N, D> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Similarity<N, D, Rotation<N, D>>

The resulting type after applying the * operator.

fn mul(self, right: &'b Similarity<N, D, Rotation<N, D>>) -> Self::Output

Performs the * operation.

impl<'b, N, D: DimNameAdd<U1>, C: TCategoryMul<TAffine>> Mul<&'b Transform<N, D, C>> for Rotation<N, D> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, DimNameSum<D, U1>>, 

type Output = Transform<N, D, C::Representative>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Transform<N, D, C>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N, D: DimNameAdd<U1>, C: TCategoryMul<TAffine>> Mul<&'b Transform<N, D, C>> for &'a Rotation<N, D> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, DimNameSum<D, U1>>, 

type Output = Transform<N, D, C::Representative>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Transform<N, D, C>) -> Self::Output

Performs the * operation.

impl<'b, N: SimdRealField, D: DimName> Mul<&'b Translation<N, D>> for Rotation<N, D> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Isometry<N, D, Rotation<N, D>>

The resulting type after applying the * operator.

fn mul(self, right: &'b Translation<N, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N: SimdRealField, D: DimName> Mul<&'b Translation<N, D>> for &'a Rotation<N, D> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Isometry<N, D, Rotation<N, D>>

The resulting type after applying the * operator.

fn mul(self, right: &'b Translation<N, D>) -> Self::Output

Performs the * operation.

impl<'b, N: SimdRealField> Mul<&'b Unit<Complex<N>>> for Rotation<N, U2> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

type Output = UnitComplex<N>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitComplex<N>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N: SimdRealField> Mul<&'b Unit<Complex<N>>> for &'a Rotation<N, U2> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

type Output = UnitComplex<N>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitComplex<N>) -> Self::Output

Performs the * operation.

impl<'b, N, D: DimName, S: Storage<N, D>> Mul<&'b Unit<Matrix<N, D, U1, S>>> for Rotation<N, D> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, D>,
    ShapeConstraint: AreMultipliable<D, D, D, U1>, 

type Output = Unit<VectorN<N, D>>

The resulting type after applying the * operator.

fn mul(self, right: &'b Unit<Vector<N, D, S>>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N, D: DimName, S: Storage<N, D>> Mul<&'b Unit<Matrix<N, D, U1, S>>> for &'a Rotation<N, D> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, D>,
    ShapeConstraint: AreMultipliable<D, D, D, U1>, 

type Output = Unit<VectorN<N, D>>

The resulting type after applying the * operator.

fn mul(self, right: &'b Unit<Vector<N, D, S>>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N: SimdRealField> Mul<&'b Unit<Quaternion<N>>> for &'a Rotation<N, U3> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3> + Allocator<N, U4, U1>, 

type Output = UnitQuaternion<N>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitQuaternion<N>) -> Self::Output

Performs the * operation.

impl<'b, N: SimdRealField> Mul<&'b Unit<Quaternion<N>>> for Rotation<N, U3> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3> + Allocator<N, U4, U1>, 

type Output = UnitQuaternion<N>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitQuaternion<N>) -> Self::Output

Performs the * operation.

impl<N: SimdRealField, D: DimName> Mul<Isometry<N, D, Rotation<N, D>>> for Rotation<N, D> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Isometry<N, D, Rotation<N, D>>

The resulting type after applying the * operator.

fn mul(self, right: Isometry<N, D, Rotation<N, D>>) -> Self::Output

Performs the * operation.

impl<'a, N: SimdRealField, D: DimName> Mul<Isometry<N, D, Rotation<N, D>>> for &'a Rotation<N, D> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Isometry<N, D, Rotation<N, D>>

The resulting type after applying the * operator.

fn mul(self, right: Isometry<N, D, Rotation<N, D>>) -> Self::Output

Performs the * operation.

impl<N, D1: DimName, R2: Dim, C2: Dim, SB: Storage<N, R2, C2>> Mul<Matrix<N, R2, C2, SB>> for Rotation<N, D1> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D1, D1> + Allocator<N, R2, C2> + Allocator<N, D1, C2>,
    DefaultAllocator: Allocator<N, D1, C2>,
    ShapeConstraint: AreMultipliable<D1, D1, R2, C2>, 

type Output = MatrixMN<N, D1, C2>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N, D1: DimName, R2: Dim, C2: Dim, SB: Storage<N, R2, C2>> Mul<Matrix<N, R2, C2, SB>> for &'a Rotation<N, D1> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D1, D1> + Allocator<N, R2, C2> + Allocator<N, D1, C2>,
    DefaultAllocator: Allocator<N, D1, C2>,
    ShapeConstraint: AreMultipliable<D1, D1, R2, C2>, 

type Output = MatrixMN<N, D1, C2>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N, D: DimName> Mul<Point<N, D>> for Rotation<N, D> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, D>,
    ShapeConstraint: AreMultipliable<D, D, D, U1>, 

type Output = Point<N, D>

The resulting type after applying the * operator.

fn mul(self, right: Point<N, D>) -> Self::Output

Performs the * operation.

impl<'a, N, D: DimName> Mul<Point<N, D>> for &'a Rotation<N, D> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, D>,
    ShapeConstraint: AreMultipliable<D, D, D, U1>, 

type Output = Point<N, D>

The resulting type after applying the * operator.

fn mul(self, right: Point<N, D>) -> Self::Output

Performs the * operation.

impl<N, D: DimName> Mul<Rotation<N, D>> for Rotation<N, D> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D, D>, 

type Output = Rotation<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N, D: DimName> Mul<Rotation<N, D>> for &'a Rotation<N, D> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D, D>, 

type Output = Rotation<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N: SimdRealField, D: DimName> Mul<Rotation<N, D>> for Isometry<N, D, Rotation<N, D>> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Isometry<N, D, Rotation<N, D>>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N: SimdRealField, D: DimName> Mul<Rotation<N, D>> for &'a Isometry<N, D, Rotation<N, D>> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Isometry<N, D, Rotation<N, D>>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N: SimdRealField, D: DimName> Mul<Rotation<N, D>> for Translation<N, D> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Isometry<N, D, Rotation<N, D>>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N: SimdRealField, D: DimName> Mul<Rotation<N, D>> for &'a Translation<N, D> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Isometry<N, D, Rotation<N, D>>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N: SimdRealField, D: DimName> Mul<Rotation<N, D>> for Similarity<N, D, Rotation<N, D>> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Similarity<N, D, Rotation<N, D>>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N: SimdRealField, D: DimName> Mul<Rotation<N, D>> for &'a Similarity<N, D, Rotation<N, D>> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Similarity<N, D, Rotation<N, D>>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N, D: DimNameAdd<U1>, C: TCategoryMul<TAffine>> Mul<Rotation<N, D>> for Transform<N, D, C> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, D> + Allocator<N, DimNameSum<D, U1>, D>, 

type Output = Transform<N, D, C::Representative>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N, D: DimNameAdd<U1>, C: TCategoryMul<TAffine>> Mul<Rotation<N, D>> for &'a Transform<N, D, C> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, D> + Allocator<N, DimNameSum<D, U1>, D>, 

type Output = Transform<N, D, C::Representative>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N, R1: Dim, C1: Dim, D2: DimName, SA: Storage<N, R1, C1>> Mul<Rotation<N, D2>> for Matrix<N, R1, C1, SA> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, R1, C1> + Allocator<N, D2, D2> + Allocator<N, R1, D2>,
    DefaultAllocator: Allocator<N, R1, D2>,
    ShapeConstraint: AreMultipliable<R1, C1, D2, D2>, 

type Output = MatrixMN<N, R1, D2>

The resulting type after applying the * operator.

fn mul(self, right: Rotation<N, D2>) -> Self::Output

Performs the * operation.

impl<'a, N, R1: Dim, C1: Dim, D2: DimName, SA: Storage<N, R1, C1>> Mul<Rotation<N, D2>> for &'a Matrix<N, R1, C1, SA> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, R1, C1> + Allocator<N, D2, D2> + Allocator<N, R1, D2>,
    DefaultAllocator: Allocator<N, R1, D2>,
    ShapeConstraint: AreMultipliable<R1, C1, D2, D2>, 

type Output = MatrixMN<N, R1, D2>

The resulting type after applying the * operator.

fn mul(self, right: Rotation<N, D2>) -> Self::Output

Performs the * operation.

impl<N: SimdRealField> Mul<Rotation<N, U2>> for UnitComplex<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

type Output = UnitComplex<N>

The resulting type after applying the * operator.

fn mul(self, rhs: Rotation<N, U2>) -> Self::Output

Performs the * operation.

impl<'a, N: SimdRealField> Mul<Rotation<N, U2>> for &'a UnitComplex<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

type Output = UnitComplex<N>

The resulting type after applying the * operator.

fn mul(self, rhs: Rotation<N, U2>) -> Self::Output

Performs the * operation.

impl<'a, N: SimdRealField> Mul<Rotation<N, U3>> for &'a UnitQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U3>, 

type Output = UnitQuaternion<N>

The resulting type after applying the * operator.

fn mul(self, rhs: Rotation<N, U3>) -> Self::Output

Performs the * operation.

impl<N: SimdRealField> Mul<Rotation<N, U3>> for UnitQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U3>, 

type Output = UnitQuaternion<N>

The resulting type after applying the * operator.

fn mul(self, rhs: Rotation<N, U3>) -> Self::Output

Performs the * operation.

impl<N: SimdRealField, D: DimName> Mul<Similarity<N, D, Rotation<N, D>>> for Rotation<N, D> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Similarity<N, D, Rotation<N, D>>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N: SimdRealField, D: DimName> Mul<Similarity<N, D, Rotation<N, D>>> for &'a Rotation<N, D> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Similarity<N, D, Rotation<N, D>>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N, D: DimNameAdd<U1>, C: TCategoryMul<TAffine>> Mul<Transform<N, D, C>> for Rotation<N, D> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, DimNameSum<D, U1>>, 

type Output = Transform<N, D, C::Representative>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N, D: DimNameAdd<U1>, C: TCategoryMul<TAffine>> Mul<Transform<N, D, C>> for &'a Rotation<N, D> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, DimNameSum<D, U1>>, 

type Output = Transform<N, D, C::Representative>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N: SimdRealField, D: DimName> Mul<Translation<N, D>> for Rotation<N, D> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Isometry<N, D, Rotation<N, D>>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N: SimdRealField, D: DimName> Mul<Translation<N, D>> for &'a Rotation<N, D> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

type Output = Isometry<N, D, Rotation<N, D>>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N: SimdRealField> Mul<Unit<Complex<N>>> for Rotation<N, U2> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

type Output = UnitComplex<N>

The resulting type after applying the * operator.

fn mul(self, rhs: UnitComplex<N>) -> Self::Output

Performs the * operation.

impl<'a, N: SimdRealField> Mul<Unit<Complex<N>>> for &'a Rotation<N, U2> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

type Output = UnitComplex<N>

The resulting type after applying the * operator.

fn mul(self, rhs: UnitComplex<N>) -> Self::Output

Performs the * operation.

impl<N, D: DimName, S: Storage<N, D>> Mul<Unit<Matrix<N, D, U1, S>>> for Rotation<N, D> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, D>,
    ShapeConstraint: AreMultipliable<D, D, D, U1>, 

type Output = Unit<VectorN<N, D>>

The resulting type after applying the * operator.

fn mul(self, right: Unit<Vector<N, D, S>>) -> Self::Output

Performs the * operation.

impl<'a, N, D: DimName, S: Storage<N, D>> Mul<Unit<Matrix<N, D, U1, S>>> for &'a Rotation<N, D> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, D>,
    ShapeConstraint: AreMultipliable<D, D, D, U1>, 

type Output = Unit<VectorN<N, D>>

The resulting type after applying the * operator.

fn mul(self, right: Unit<Vector<N, D, S>>) -> Self::Output

Performs the * operation.

impl<'a, N: SimdRealField> Mul<Unit<Quaternion<N>>> for &'a Rotation<N, U3> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3> + Allocator<N, U4, U1>, 

type Output = UnitQuaternion<N>

The resulting type after applying the * operator.

fn mul(self, rhs: UnitQuaternion<N>) -> Self::Output

Performs the * operation.

impl<N: SimdRealField> Mul<Unit<Quaternion<N>>> for Rotation<N, U3> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3> + Allocator<N, U4, U1>, 

type Output = UnitQuaternion<N>

The resulting type after applying the * operator.

fn mul(self, rhs: UnitQuaternion<N>) -> Self::Output

Performs the * operation.

impl<'b, N, R1: DimName, C1: DimName> MulAssign<&'b Rotation<N, C1>> for MatrixMN<N, R1, C1> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, R1, C1> + Allocator<N, C1, C1>, 

fn mul_assign(&mut self, right: &'b Rotation<N, C1>)

Performs the *= operation.

impl<'b, N, D: DimName> MulAssign<&'b Rotation<N, D>> for Rotation<N, D> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D, D>, 

fn mul_assign(&mut self, right: &'b Rotation<N, D>)

Performs the *= operation.

impl<'b, N, D: DimName> MulAssign<&'b Rotation<N, D>> for Isometry<N, D, Rotation<N, D>> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1> + Allocator<N, D, D>, 

fn mul_assign(&mut self, rhs: &'b Rotation<N, D>)

Performs the *= operation.

impl<'b, N, D: DimName> MulAssign<&'b Rotation<N, D>> for Similarity<N, D, Rotation<N, D>> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1> + Allocator<N, D, D>, 

fn mul_assign(&mut self, rhs: &'b Rotation<N, D>)

Performs the *= operation.

impl<'b, N, D: DimNameAdd<U1>, C: TCategory> MulAssign<&'b Rotation<N, D>> for Transform<N, D, C> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, D>, 

fn mul_assign(&mut self, rhs: &'b Rotation<N, D>)

Performs the *= operation.

impl<'b, N: SimdRealField> MulAssign<&'b Rotation<N, U2>> for UnitComplex<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

fn mul_assign(&mut self, rhs: &'b Rotation<N, U2>)

Performs the *= operation.

impl<'b, N: SimdRealField> MulAssign<&'b Rotation<N, U3>> for UnitQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U3>, 

fn mul_assign(&mut self, rhs: &'b Rotation<N, U3>)

Performs the *= operation.

impl<'b, N: SimdRealField> MulAssign<&'b Unit<Complex<N>>> for Rotation<N, U2> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

fn mul_assign(&mut self, rhs: &'b UnitComplex<N>)

Performs the *= operation.

impl<N, R1: DimName, C1: DimName> MulAssign<Rotation<N, C1>> for MatrixMN<N, R1, C1> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, R1, C1> + Allocator<N, C1, C1>, 

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

Performs the *= operation.

impl<N, D: DimName> MulAssign<Rotation<N, D>> for Rotation<N, D> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D, D>, 

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

Performs the *= operation.

impl<N, D: DimName> MulAssign<Rotation<N, D>> for Isometry<N, D, Rotation<N, D>> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1> + Allocator<N, D, D>, 

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

Performs the *= operation.

impl<N, D: DimName> MulAssign<Rotation<N, D>> for Similarity<N, D, Rotation<N, D>> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1> + Allocator<N, D, D>, 

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

Performs the *= operation.

impl<N, D: DimNameAdd<U1>, C: TCategory> MulAssign<Rotation<N, D>> for Transform<N, D, C> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, D>, 

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

Performs the *= operation.

impl<N: SimdRealField> MulAssign<Rotation<N, U2>> for UnitComplex<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

fn mul_assign(&mut self, rhs: Rotation<N, U2>)

Performs the *= operation.

impl<N: SimdRealField> MulAssign<Rotation<N, U3>> for UnitQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U3>, 

fn mul_assign(&mut self, rhs: Rotation<N, U3>)

Performs the *= operation.

impl<N: SimdRealField> MulAssign<Unit<Complex<N>>> for Rotation<N, U2> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 

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

Performs the *= operation.

impl<N, D: DimName> One for Rotation<N, D> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    DefaultAllocator: Allocator<N, D, D>, 

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

pub fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

pub fn is_one(&self) -> bool where
    Self: PartialEq<Self>, 

Returns true if self is equal to the multiplicative identity.

impl<N: Scalar + PartialEq, D: DimName> PartialEq<Rotation<N, D>> for Rotation<N, D> where
    DefaultAllocator: Allocator<N, D, D>, 

fn eq(&self, right: &Self) -> bool

This method tests for self and other values to be equal, and is used by ==.

#[must_use]

pub fn ne(&self, other: &Rhs) -> bool

This method tests for !=.

impl<N, D: DimName> RelativeEq<Rotation<N, D>> for Rotation<N, D> where
    N: Scalar + RelativeEq,
    DefaultAllocator: Allocator<N, D, D>,
    N::Epsilon: Copy, 

fn default_max_relative() -> Self::Epsilon

The default relative tolerance for testing values that are far-apart.

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.

pub fn relative_ne(
    &self,
    other: &Rhs,
    epsilon: Self::Epsilon,
    max_relative: Self::Epsilon
) -> bool

The inverse of RelativeEq::relative_eq.

impl<N: Scalar, D: DimName> Serialize for Rotation<N, D> where
    DefaultAllocator: Allocator<N, D, D>,
    Owned<N, D, D>: Serialize, 

fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error> where
    S: Serializer, 

Serialize this value into the given Serde serializer.

impl<N, D> SimdValue for Rotation<N, D> where
    N: Scalar + SimdValue,
    D: DimName,
    N::Element: Scalar,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N::Element, D, D>, 

type Element = Rotation<N::Element, D>

The type of the elements of each lane of this SIMD value.

type SimdBool = N::SimdBool

Type of the result of comparing two SIMD values like self.

fn lanes() -> usize

The number of lanes of this SIMD value.

fn splat(val: Self::Element) -> Self

Initializes an SIMD value with each lanes set to val.

fn extract(&self, i: usize) -> Self::Element

Extracts the i-th lane of self.

unsafe fn extract_unchecked(&self, i: usize) -> Self::Element

Extracts the i-th lane of self without bound-checking.

fn replace(&mut self, i: usize, val: Self::Element)

Replaces the i-th lane of self by val.

unsafe fn replace_unchecked(&mut self, i: usize, val: Self::Element)

Replaces the i-th lane of self by val without bound-checking.

fn select(self, cond: Self::SimdBool, other: Self) -> Self

Merges self and other depending on the lanes of cond.

pub fn map_lanes(self, f: impl Fn(Self::Element) -> Self::Element) -> Self where
    Self: Clone, 

Applies a function to each lane of self.

pub fn zip_map_lanes(
    self,
    b: Self,
    f: impl Fn(Self::Element, Self::Element) -> Self::Element
) -> Self where
    Self: Clone, 

Applies a function to each lane of self paired with the corresponding lane of b.

impl<N1, N2, D: DimName, R> SubsetOf<Isometry<N2, D, R>> for Rotation<N1, D> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    R: AbstractRotation<N2, D> + SupersetOf<Self>,
    DefaultAllocator: Allocator<N1, D, D> + Allocator<N2, D>, 

fn to_superset(&self) -> Isometry<N2, D, R>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(iso: &Isometry<N2, D, R>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

fn from_superset_unchecked(iso: &Isometry<N2, D, R>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

pub fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<N1, N2, D> SubsetOf<Matrix<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>> for Rotation<N1, D> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    D: DimNameAdd<U1> + DimMin<D, Output = D>,
    DefaultAllocator: Allocator<N1, D, D> + Allocator<N2, D, D> + Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<(usize, usize), D>, 

fn to_superset(&self) -> MatrixN<N2, DimNameSum<D, U1>>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(m: &MatrixN<N2, DimNameSum<D, U1>>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<D, U1>>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

pub fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<N1, N2, D: DimName> SubsetOf<Rotation<N2, D>> for Rotation<N1, D> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    DefaultAllocator: Allocator<N1, D, D> + Allocator<N2, D, D>, 

fn to_superset(&self) -> Rotation<N2, D>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(rot: &Rotation<N2, D>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

fn from_superset_unchecked(rot: &Rotation<N2, D>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

pub fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<N1, N2> SubsetOf<Rotation<N2, U2>> for UnitComplex<N1> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>, 

fn to_superset(&self) -> Rotation2<N2>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(rot: &Rotation2<N2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

fn from_superset_unchecked(rot: &Rotation2<N2>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

pub fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<N1, N2> SubsetOf<Rotation<N2, U3>> for UnitQuaternion<N1> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>, 

fn to_superset(&self) -> Rotation3<N2>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(rot: &Rotation3<N2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

fn from_superset_unchecked(rot: &Rotation3<N2>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

pub fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<N1, N2, D: DimName, R> SubsetOf<Similarity<N2, D, R>> for Rotation<N1, D> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    R: AbstractRotation<N2, D> + SupersetOf<Self>,
    DefaultAllocator: Allocator<N1, D, D> + Allocator<N2, D>, 

fn to_superset(&self) -> Similarity<N2, D, R>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(sim: &Similarity<N2, D, R>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

fn from_superset_unchecked(sim: &Similarity<N2, D, R>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

pub fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<N1, N2, D, C> SubsetOf<Transform<N2, D, C>> for Rotation<N1, D> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    C: SuperTCategoryOf<TAffine>,
    D: DimNameAdd<U1> + DimMin<D, Output = D>,
    DefaultAllocator: Allocator<N1, D, D> + Allocator<N2, D, D> + Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<(usize, usize), D>, 

fn to_superset(&self) -> Transform<N2, D, C>

The inclusion map: converts self to the equivalent element of its superset.

fn is_in_subset(t: &Transform<N2, D, C>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).

fn from_superset_unchecked(t: &Transform<N2, D, C>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.

pub fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset.

impl<N, D: DimName> UlpsEq<Rotation<N, D>> for Rotation<N, D> where
    N: Scalar + UlpsEq,
    DefaultAllocator: Allocator<N, D, D>,
    N::Epsilon: Copy, 

fn default_max_ulps() -> u32

The default ULPs to tolerate when testing values that are far-apart.

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.

pub fn ulps_ne(
    &self,
    other: &Rhs,
    epsilon: Self::Epsilon,
    max_ulps: u32
) -> bool

The inverse of UlpsEq::ulps_eq.

impl<N: Scalar + Copy, D: DimName> Copy for Rotation<N, D> where
    DefaultAllocator: Allocator<N, D, D>,
    <DefaultAllocator as Allocator<N, D, D>>::Buffer: Copy, 

impl<N: Scalar + Eq, D: DimName> Eq for Rotation<N, D> where
    DefaultAllocator: Allocator<N, D, D>,