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

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);

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

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

Cast the components of self to another type.

Example

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

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_basis_unchecked(basis: &[Vector2<N>; 2]) -> Self

Builds a rotation from a basis assumed to be orthonormal.

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

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_basis_unchecked(basis: &[Vector3<N>; 3]) -> Self

Builds a rotation from a basis assumed to be orthonormal.

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

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.

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.

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<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<'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.

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.

fn set_one(&mut self)

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

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 ==.

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.

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

The inverse of RelativeEq::relative_eq.

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.

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

Applies a function to each lane of self.

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.

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.

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.

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.

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.

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.

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.

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.

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>,