Struct na::Rotation[][src]

#[repr(C)]
pub struct Rotation<N, D> where
    D: DimName,
    N: Scalar,
    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

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.

Conversion

Implementations

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

pub fn from_matrix_unchecked(
    matrix: Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>
) -> Rotation<N, D>
[src]

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

pub fn matrix(
    &self
) -> &Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>
[src]

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 Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>
[src]

👎 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 Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>
[src]

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
) -> Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>
[src]

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
) -> Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>
[src]

👎 Deprecated:

use .into_inner() instead

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

pub fn to_homogeneous(
    &self
) -> Matrix<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer> where
    D: DimNameAdd<U1>,
    N: Zero + One,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 
[src]

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

#[must_use = "Did you mean to use transpose_mut()?"]
pub fn transpose(&self) -> Rotation<N, D>
[src]

Transposes self.

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

Example

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

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

#[must_use = "Did you mean to use inverse_mut()?"]
pub fn inverse(&self) -> Rotation<N, D>
[src]

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)[src]

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)[src]

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, D> Rotation<N, D> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

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: &Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>
) -> Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>
[src]

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>[src]

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: &Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>
) -> Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>
[src]

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<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>
) -> Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>
[src]

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> Rotation<N, D> where
    D: DimName,
    N: Scalar + Zero + One,
    DefaultAllocator: Allocator<N, D, D>, 
[src]

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

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> Rotation<N, U2> where
    N: SimdRealField
[src]

pub fn slerp(&self, other: &Rotation<N, U2>, t: N) -> Rotation<N, U2> where
    <N as SimdValue>::Element: SimdRealField
[src]

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> Rotation<N, U3> where
    N: SimdRealField
[src]

pub fn slerp(&self, other: &Rotation<N, U3>, t: N) -> Rotation<N, U3> where
    N: RealField
[src]

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: &Rotation<N, U3>,
    t: N,
    epsilon: N
) -> Option<Rotation<N, U3>> where
    N: RealField
[src]

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> Rotation<N, U2> where
    N: SimdRealField
[src]

pub fn new(angle: N) -> Rotation<N, U2>[src]

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>(axisangle: Matrix<N, U1, U1, SB>) -> Rotation<N, U2> where
    SB: Storage<N, U1, U1>, 
[src]

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> Rotation<N, U2> where
    N: SimdRealField
[src]

pub fn from_matrix(
    m: &Matrix<N, U2, U2, <DefaultAllocator as Allocator<N, U2, U2>>::Buffer>
) -> Rotation<N, U2> where
    N: RealField
[src]

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: &Matrix<N, U2, U2, <DefaultAllocator as Allocator<N, U2, U2>>::Buffer>,
    eps: N,
    max_iter: usize,
    guess: Rotation<N, U2>
) -> Rotation<N, U2> where
    N: RealField
[src]

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: &Matrix<N, U2, U1, SB>,
    b: &Matrix<N, U2, U1, SC>
) -> Rotation<N, U2> where
    N: RealField,
    SB: Storage<N, U2, U1>,
    SC: Storage<N, U2, U1>, 
[src]

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: &Matrix<N, U2, U1, SB>,
    b: &Matrix<N, U2, U1, SC>,
    s: N
) -> Rotation<N, U2> where
    N: RealField,
    SB: Storage<N, U2, U1>,
    SC: Storage<N, U2, U1>, 
[src]

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: &Rotation<N, U2>) -> Rotation<N, U2>[src]

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
[src]

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) -> Rotation<N, U2>[src]

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> Rotation<N, U2> where
    N: SimdRealField
[src]

pub fn angle(&self) -> N[src]

The rotation angle.

Example

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

pub fn angle_to(&self, other: &Rotation<N, U2>) -> N[src]

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
) -> Matrix<N, U1, U1, <DefaultAllocator as Allocator<N, U1, U1>>::Buffer>
[src]

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> Rotation<N, U3> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField
[src]

pub fn new<SB>(axisangle: Matrix<N, U3, U1, SB>) -> Rotation<N, U3> where
    SB: Storage<N, U3, U1>, 
[src]

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>(axisangle: Matrix<N, U3, U1, SB>) -> Rotation<N, U3> where
    SB: Storage<N, U3, U1>, 
[src]

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<Matrix<N, U3, U1, SB>>,
    angle: N
) -> Rotation<N, U3> where
    SB: Storage<N, U3, U1>, 
[src]

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) -> Rotation<N, U3>[src]

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> Rotation<N, U3> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField
[src]

pub fn face_towards<SB, SC>(
    dir: &Matrix<N, U3, U1, SB>,
    up: &Matrix<N, U3, U1, SC>
) -> Rotation<N, U3> where
    SB: Storage<N, U3, U1>,
    SC: Storage<N, U3, U1>, 
[src]

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: &Matrix<N, U3, U1, SB>,
    up: &Matrix<N, U3, U1, SC>
) -> Rotation<N, U3> where
    SB: Storage<N, U3, U1>,
    SC: Storage<N, U3, U1>, 
[src]

👎 Deprecated:

renamed to face_towards

Deprecated: Use [Rotation3::face_towards] instead.

pub fn look_at_rh<SB, SC>(
    dir: &Matrix<N, U3, U1, SB>,
    up: &Matrix<N, U3, U1, SC>
) -> Rotation<N, U3> where
    SB: Storage<N, U3, U1>,
    SC: Storage<N, U3, U1>, 
[src]

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: &Matrix<N, U3, U1, SB>,
    up: &Matrix<N, U3, U1, SC>
) -> Rotation<N, U3> where
    SB: Storage<N, U3, U1>,
    SC: Storage<N, U3, U1>, 
[src]

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> Rotation<N, U3> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField
[src]

pub fn rotation_between<SB, SC>(
    a: &Matrix<N, U3, U1, SB>,
    b: &Matrix<N, U3, U1, SC>
) -> Option<Rotation<N, U3>> where
    N: RealField,
    SB: Storage<N, U3, U1>,
    SC: Storage<N, U3, U1>, 
[src]

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: &Matrix<N, U3, U1, SB>,
    b: &Matrix<N, U3, U1, SC>,
    n: N
) -> Option<Rotation<N, U3>> where
    N: RealField,
    SB: Storage<N, U3, U1>,
    SC: Storage<N, U3, U1>, 
[src]

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: &Rotation<N, U3>) -> Rotation<N, U3>[src]

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) -> Rotation<N, U3> where
    N: RealField
[src]

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

Example

let axis = Unit::new_normalize(Vector3::new(1.0, 2.0, 3.0));
let angle = 1.2;
let rot = Rotation3::from_axis_angle(&axis, angle);
let pow = rot.powf(2.0);
assert_relative_eq!(pow.axis().unwrap(), axis, epsilon = 1.0e-6);
assert_eq!(pow.angle(), 2.4);

pub fn from_matrix(
    m: &Matrix<N, U3, U3, <DefaultAllocator as Allocator<N, U3, U3>>::Buffer>
) -> Rotation<N, U3> where
    N: RealField
[src]

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: &Matrix<N, U3, U3, <DefaultAllocator as Allocator<N, U3, U3>>::Buffer>,
    eps: N,
    max_iter: usize,
    guess: Rotation<N, U3>
) -> Rotation<N, U3> where
    N: RealField
[src]

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
[src]

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> Rotation<N, U3> where
    N: SimdRealField
[src]

pub fn angle(&self) -> N[src]

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<Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>>> where
    N: RealField
[src]

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
) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer> where
    N: RealField
[src]

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<Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>>, N)> where
    N: RealField
[src]

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: &Rotation<N, U3>) -> N where
    <N as SimdValue>::Element: SimdRealField
[src]

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
[src]

👎 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
[src]

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> AbsDiffEq<Rotation<N, D>> for Rotation<N, D> where
    D: DimName,
    N: Scalar + AbsDiffEq<N>,
    DefaultAllocator: Allocator<N, D, D>,
    <N as AbsDiffEq<N>>::Epsilon: Copy
[src]

type Epsilon = <N as AbsDiffEq<N>>::Epsilon

Used for specifying relative comparisons.

impl<N, D> AbstractRotation<N, D> for Rotation<N, D> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>, 
[src]

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

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

impl<'a, N, D> Deserialize<'a> for Rotation<N, D> where
    D: DimName,
    N: Scalar,
    DefaultAllocator: Allocator<N, D, D>,
    <DefaultAllocator as Allocator<N, D, D>>::Buffer: Deserialize<'a>, 
[src]

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

impl<'a, 'b, N, D> Div<&'b Isometry<N, D, Rotation<N, D>>> for &'a Rotation<N, D> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the / operator.

impl<'b, N, D> Div<&'b Isometry<N, D, Rotation<N, D>>> for Rotation<N, D> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the / operator.

impl<'a, 'b, N, D> Div<&'b Rotation<N, D>> for &'a Isometry<N, D, Rotation<N, D>> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the / operator.

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

type Output = Rotation<N, D>

The resulting type after applying the / operator.

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

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

The resulting type after applying the / operator.

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

type Output = Rotation<N, D>

The resulting type after applying the / operator.

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

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

The resulting type after applying the / operator.

impl<'a, 'b, N, D> Div<&'b Rotation<N, D>> for &'a Similarity<N, D, Rotation<N, D>> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the / operator.

impl<'b, N, D> Div<&'b Rotation<N, D>> for Similarity<N, D, Rotation<N, D>> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the / operator.

impl<'b, N, D> Div<&'b Rotation<N, D>> for Isometry<N, D, Rotation<N, D>> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the / operator.

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

type Output = Matrix<N, R1, D2, <DefaultAllocator as Allocator<N, R1, D2>>::Buffer>

The resulting type after applying the / operator.

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

type Output = Matrix<N, R1, D2, <DefaultAllocator as Allocator<N, R1, D2>>::Buffer>

The resulting type after applying the / operator.

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

type Output = Unit<Complex<N>>

The resulting type after applying the / operator.

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

type Output = Unit<Complex<N>>

The resulting type after applying the / operator.

impl<'a, 'b, N> Div<&'b Rotation<N, U3>> for &'a Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U3>, 
[src]

type Output = Unit<Quaternion<N>>

The resulting type after applying the / operator.

impl<'b, N> Div<&'b Rotation<N, U3>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U3>, 
[src]

type Output = Unit<Quaternion<N>>

The resulting type after applying the / operator.

impl<'b, N, D> Div<&'b Similarity<N, D, Rotation<N, D>>> for Rotation<N, D> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the / operator.

impl<'a, 'b, N, D> Div<&'b Similarity<N, D, Rotation<N, D>>> for &'a Rotation<N, D> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the / operator.

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

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

The resulting type after applying the / operator.

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

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

The resulting type after applying the / operator.

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

type Output = Unit<Complex<N>>

The resulting type after applying the / operator.

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

type Output = Unit<Complex<N>>

The resulting type after applying the / operator.

impl<'b, N> Div<&'b Unit<Quaternion<N>>> for Rotation<N, U3> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3>,
    DefaultAllocator: Allocator<N, U4, U1>, 
[src]

type Output = Unit<Quaternion<N>>

The resulting type after applying the / operator.

impl<'a, 'b, N> Div<&'b Unit<Quaternion<N>>> for &'a Rotation<N, U3> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3>,
    DefaultAllocator: Allocator<N, U4, U1>, 
[src]

type Output = Unit<Quaternion<N>>

The resulting type after applying the / operator.

impl<N, D> Div<Isometry<N, D, Rotation<N, D>>> for Rotation<N, D> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the / operator.

impl<'a, N, D> Div<Isometry<N, D, Rotation<N, D>>> for &'a Rotation<N, D> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the / operator.

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

type Output = Rotation<N, D>

The resulting type after applying the / operator.

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

type Output = Rotation<N, D>

The resulting type after applying the / operator.

impl<N, D> Div<Rotation<N, D>> for Isometry<N, D, Rotation<N, D>> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the / operator.

impl<'a, N, D> Div<Rotation<N, D>> for &'a Isometry<N, D, Rotation<N, D>> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the / operator.

impl<'a, N, D> Div<Rotation<N, D>> for &'a Similarity<N, D, Rotation<N, D>> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the / operator.

impl<N, D> Div<Rotation<N, D>> for Similarity<N, D, Rotation<N, D>> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the / operator.

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

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

The resulting type after applying the / operator.

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

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

The resulting type after applying the / operator.

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

type Output = Matrix<N, R1, D2, <DefaultAllocator as Allocator<N, R1, D2>>::Buffer>

The resulting type after applying the / operator.

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

type Output = Matrix<N, R1, D2, <DefaultAllocator as Allocator<N, R1, D2>>::Buffer>

The resulting type after applying the / operator.

impl<N> Div<Rotation<N, U2>> for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 
[src]

type Output = Unit<Complex<N>>

The resulting type after applying the / operator.

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

type Output = Unit<Complex<N>>

The resulting type after applying the / operator.

impl<'a, N> Div<Rotation<N, U3>> for &'a Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U3>, 
[src]

type Output = Unit<Quaternion<N>>

The resulting type after applying the / operator.

impl<N> Div<Rotation<N, U3>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U3>, 
[src]

type Output = Unit<Quaternion<N>>

The resulting type after applying the / operator.

impl<'a, N, D> Div<Similarity<N, D, Rotation<N, D>>> for &'a Rotation<N, D> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the / operator.

impl<N, D> Div<Similarity<N, D, Rotation<N, D>>> for Rotation<N, D> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the / operator.

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

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

The resulting type after applying the / operator.

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

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

The resulting type after applying the / operator.

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

type Output = Unit<Complex<N>>

The resulting type after applying the / operator.

impl<N> Div<Unit<Complex<N>>> for Rotation<N, U2> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 
[src]

type Output = Unit<Complex<N>>

The resulting type after applying the / operator.

impl<N> Div<Unit<Quaternion<N>>> for Rotation<N, U3> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3>,
    DefaultAllocator: Allocator<N, U4, U1>, 
[src]

type Output = Unit<Quaternion<N>>

The resulting type after applying the / operator.

impl<'a, N> Div<Unit<Quaternion<N>>> for &'a Rotation<N, U3> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3>,
    DefaultAllocator: Allocator<N, U4, U1>, 
[src]

type Output = Unit<Quaternion<N>>

The resulting type after applying the / operator.

impl<'b, N, R1, C1> DivAssign<&'b Rotation<N, C1>> for Matrix<N, R1, C1, <DefaultAllocator as Allocator<N, R1, C1>>::Buffer> where
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N>,
    R1: DimName,
    C1: DimName,
    DefaultAllocator: Allocator<N, R1, C1>,
    DefaultAllocator: Allocator<N, C1, C1>, 
[src]

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

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

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

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

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

impl<'b, N> DivAssign<&'b Rotation<N, U3>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U3>, 
[src]

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

impl<N, R1, C1> DivAssign<Rotation<N, C1>> for Matrix<N, R1, C1, <DefaultAllocator as Allocator<N, R1, C1>>::Buffer> where
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N>,
    R1: DimName,
    C1: DimName,
    DefaultAllocator: Allocator<N, R1, C1>,
    DefaultAllocator: Allocator<N, C1, C1>, 
[src]

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

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

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

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

impl<N> DivAssign<Rotation<N, U2>> for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 
[src]

impl<N> DivAssign<Rotation<N, U3>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U3>, 
[src]

impl<N> DivAssign<Unit<Complex<N>>> for Rotation<N, U2> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 
[src]

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

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

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

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

impl<N> From<Rotation<N, U2>> for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField
[src]

impl<N> From<Rotation<N, U2>> for Matrix<N, U2, U2, <DefaultAllocator as Allocator<N, U2, U2>>::Buffer> where
    N: RealField
[src]

impl<N> From<Rotation<N, U2>> for Matrix<N, U3, U3, <DefaultAllocator as Allocator<N, U3, U3>>::Buffer> where
    N: RealField
[src]

impl<N> From<Rotation<N, U3>> for Matrix<N, U3, U3, <DefaultAllocator as Allocator<N, U3, U3>>::Buffer> where
    N: RealField
[src]

impl<N> From<Rotation<N, U3>> for Matrix<N, U4, U4, <DefaultAllocator as Allocator<N, U4, U4>>::Buffer> where
    N: RealField
[src]

impl<N> From<Rotation<N, U3>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField
[src]

impl<N> From<Unit<Complex<N>>> for Rotation<N, U2> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField
[src]

impl<N> From<Unit<Quaternion<N>>> for Rotation<N, U3> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField
[src]

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

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

type Output = N

The returned type after indexing.

impl<'b, N, D> Mul<&'b Isometry<N, D, Rotation<N, D>>> for Rotation<N, D> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the * operator.

impl<'a, 'b, N, D> Mul<&'b Isometry<N, D, Rotation<N, D>>> for &'a Rotation<N, D> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the * operator.

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

type Output = Matrix<N, D1, C2, <DefaultAllocator as Allocator<N, D1, C2>>::Buffer>

The resulting type after applying the * operator.

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

type Output = Matrix<N, D1, C2, <DefaultAllocator as Allocator<N, D1, C2>>::Buffer>

The resulting type after applying the * operator.

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

type Output = Point<N, D>

The resulting type after applying the * operator.

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

type Output = Point<N, D>

The resulting type after applying the * operator.

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

type Output = Rotation<N, D>

The resulting type after applying the * operator.

impl<'b, N, D> Mul<&'b Rotation<N, D>> for Isometry<N, D, Rotation<N, D>> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the * operator.

impl<'a, 'b, N, D> Mul<&'b Rotation<N, D>> for &'a Similarity<N, D, Rotation<N, D>> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the * operator.

impl<'b, N, D> Mul<&'b Rotation<N, D>> for Translation<N, D> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the * operator.

impl<'a, 'b, N, D> Mul<&'b Rotation<N, D>> for &'a Isometry<N, D, Rotation<N, D>> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the * operator.

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

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

The resulting type after applying the * operator.

impl<'b, N, D> Mul<&'b Rotation<N, D>> for Similarity<N, D, Rotation<N, D>> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the * operator.

impl<'a, 'b, N, D> Mul<&'b Rotation<N, D>> for &'a Translation<N, D> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the * operator.

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

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

The resulting type after applying the * operator.

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

type Output = Rotation<N, D>

The resulting type after applying the * operator.

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

type Output = Matrix<N, R1, D2, <DefaultAllocator as Allocator<N, R1, D2>>::Buffer>

The resulting type after applying the * operator.

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

type Output = Matrix<N, R1, D2, <DefaultAllocator as Allocator<N, R1, D2>>::Buffer>

The resulting type after applying the * operator.

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

type Output = Unit<Complex<N>>

The resulting type after applying the * operator.

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

type Output = Unit<Complex<N>>

The resulting type after applying the * operator.

impl<'b, N> Mul<&'b Rotation<N, U3>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U3>, 
[src]

type Output = Unit<Quaternion<N>>

The resulting type after applying the * operator.

impl<'a, 'b, N> Mul<&'b Rotation<N, U3>> for &'a Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U3>, 
[src]

type Output = Unit<Quaternion<N>>

The resulting type after applying the * operator.

impl<'b, N, D> Mul<&'b Similarity<N, D, Rotation<N, D>>> for Rotation<N, D> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the * operator.

impl<'a, 'b, N, D> Mul<&'b Similarity<N, D, Rotation<N, D>>> for &'a Rotation<N, D> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the * operator.

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

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

The resulting type after applying the * operator.

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

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

The resulting type after applying the * operator.

impl<'b, N, D> Mul<&'b Translation<N, D>> for Rotation<N, D> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the * operator.

impl<'a, 'b, N, D> Mul<&'b Translation<N, D>> for &'a Rotation<N, D> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the * operator.

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

type Output = Unit<Complex<N>>

The resulting type after applying the * operator.

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

type Output = Unit<Complex<N>>

The resulting type after applying the * operator.

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

type Output = Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>

The resulting type after applying the * operator.

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

type Output = Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>

The resulting type after applying the * operator.

impl<'b, N> Mul<&'b Unit<Quaternion<N>>> for Rotation<N, U3> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3>,
    DefaultAllocator: Allocator<N, U4, U1>, 
[src]

type Output = Unit<Quaternion<N>>

The resulting type after applying the * operator.

impl<'a, 'b, N> Mul<&'b Unit<Quaternion<N>>> for &'a Rotation<N, U3> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3>,
    DefaultAllocator: Allocator<N, U4, U1>, 
[src]

type Output = Unit<Quaternion<N>>

The resulting type after applying the * operator.

impl<N, D> Mul<Isometry<N, D, Rotation<N, D>>> for Rotation<N, D> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the * operator.

impl<'a, N, D> Mul<Isometry<N, D, Rotation<N, D>>> for &'a Rotation<N, D> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the * operator.

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

type Output = Matrix<N, D1, C2, <DefaultAllocator as Allocator<N, D1, C2>>::Buffer>

The resulting type after applying the * operator.

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

type Output = Matrix<N, D1, C2, <DefaultAllocator as Allocator<N, D1, C2>>::Buffer>

The resulting type after applying the * operator.

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

type Output = Point<N, D>

The resulting type after applying the * operator.

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

type Output = Point<N, D>

The resulting type after applying the * operator.

impl<'a, N, D> Mul<Rotation<N, D>> for &'a Similarity<N, D, Rotation<N, D>> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the * operator.

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

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

The resulting type after applying the * operator.

impl<'a, N, D> Mul<Rotation<N, D>> for &'a Translation<N, D> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the * operator.

impl<N, D> Mul<Rotation<N, D>> for Translation<N, D> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the * operator.

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

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

The resulting type after applying the * operator.

impl<N, D> Mul<Rotation<N, D>> for Similarity<N, D, Rotation<N, D>> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the * operator.

impl<N, D> Mul<Rotation<N, D>> for Isometry<N, D, Rotation<N, D>> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the * operator.

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

type Output = Rotation<N, D>

The resulting type after applying the * operator.

impl<'a, N, D> Mul<Rotation<N, D>> for &'a Isometry<N, D, Rotation<N, D>> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the * operator.

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

type Output = Rotation<N, D>

The resulting type after applying the * operator.

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

type Output = Matrix<N, R1, D2, <DefaultAllocator as Allocator<N, R1, D2>>::Buffer>

The resulting type after applying the * operator.

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

type Output = Matrix<N, R1, D2, <DefaultAllocator as Allocator<N, R1, D2>>::Buffer>

The resulting type after applying the * operator.

impl<N> Mul<Rotation<N, U2>> for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 
[src]

type Output = Unit<Complex<N>>

The resulting type after applying the * operator.

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

type Output = Unit<Complex<N>>

The resulting type after applying the * operator.

impl<'a, N> Mul<Rotation<N, U3>> for &'a Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U3>, 
[src]

type Output = Unit<Quaternion<N>>

The resulting type after applying the * operator.

impl<N> Mul<Rotation<N, U3>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U3>, 
[src]

type Output = Unit<Quaternion<N>>

The resulting type after applying the * operator.

impl<'a, N, D> Mul<Similarity<N, D, Rotation<N, D>>> for &'a Rotation<N, D> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the * operator.

impl<N, D> Mul<Similarity<N, D, Rotation<N, D>>> for Rotation<N, D> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the * operator.

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

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

The resulting type after applying the * operator.

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

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

The resulting type after applying the * operator.

impl<N, D> Mul<Translation<N, D>> for Rotation<N, D> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the * operator.

impl<'a, N, D> Mul<Translation<N, D>> for &'a Rotation<N, D> where
    D: DimName,
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 
[src]

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

The resulting type after applying the * operator.

impl<N> Mul<Unit<Complex<N>>> for Rotation<N, U2> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 
[src]

type Output = Unit<Complex<N>>

The resulting type after applying the * operator.

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

type Output = Unit<Complex<N>>

The resulting type after applying the * operator.

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

type Output = Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>

The resulting type after applying the * operator.

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

type Output = Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>

The resulting type after applying the * operator.

impl<'a, N> Mul<Unit<Quaternion<N>>> for &'a Rotation<N, U3> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3>,
    DefaultAllocator: Allocator<N, U4, U1>, 
[src]

type Output = Unit<Quaternion<N>>

The resulting type after applying the * operator.

impl<N> Mul<Unit<Quaternion<N>>> for Rotation<N, U3> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3>,
    DefaultAllocator: Allocator<N, U4, U1>, 
[src]

type Output = Unit<Quaternion<N>>

The resulting type after applying the * operator.

impl<'b, N, R1, C1> MulAssign<&'b Rotation<N, C1>> for Matrix<N, R1, C1, <DefaultAllocator as Allocator<N, R1, C1>>::Buffer> where
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N>,
    R1: DimName,
    C1: DimName,
    DefaultAllocator: Allocator<N, R1, C1>,
    DefaultAllocator: Allocator<N, C1, C1>, 
[src]

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

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

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

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

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

impl<'b, N> MulAssign<&'b Rotation<N, U3>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U3>, 
[src]

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

impl<N, R1, C1> MulAssign<Rotation<N, C1>> for Matrix<N, R1, C1, <DefaultAllocator as Allocator<N, R1, C1>>::Buffer> where
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N>,
    R1: DimName,
    C1: DimName,
    DefaultAllocator: Allocator<N, R1, C1>,
    DefaultAllocator: Allocator<N, C1, C1>, 
[src]

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

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

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

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

impl<N> MulAssign<Rotation<N, U2>> for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 
[src]

impl<N> MulAssign<Rotation<N, U3>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U3>, 
[src]

impl<N> MulAssign<Unit<Complex<N>>> for Rotation<N, U2> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>, 
[src]

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

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

impl<N, D> RelativeEq<Rotation<N, D>> for Rotation<N, D> where
    D: DimName,
    N: Scalar + RelativeEq<N>,
    DefaultAllocator: Allocator<N, D, D>,
    <N as AbsDiffEq<N>>::Epsilon: Copy
[src]

impl<N, D> Serialize for Rotation<N, D> where
    D: DimName,
    N: Scalar,
    DefaultAllocator: Allocator<N, D, D>,
    <DefaultAllocator as Allocator<N, D, D>>::Buffer: Serialize
[src]

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

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

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

type SimdBool = <N as SimdValue>::SimdBool

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

impl<N1, N2, D, R> SubsetOf<Isometry<N2, D, R>> for Rotation<N1, D> where
    D: DimName,
    R: AbstractRotation<N2, D> + SupersetOf<Rotation<N1, D>>,
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    DefaultAllocator: Allocator<N1, D, D>,
    DefaultAllocator: Allocator<N2, D, U1>, 
[src]

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
    D: DimNameAdd<U1> + DimMin<D, Output = D>,
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    DefaultAllocator: Allocator<N1, D, D>,
    DefaultAllocator: Allocator<N2, D, D>,
    DefaultAllocator: Allocator<N1, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<(usize, usize), D, U1>, 
[src]

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

impl<N1, N2> SubsetOf<Rotation<N2, U2>> for Unit<Complex<N1>> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>, 
[src]

impl<N1, N2> SubsetOf<Rotation<N2, U3>> for Unit<Quaternion<N1>> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>, 
[src]

impl<N1, N2, D, R> SubsetOf<Similarity<N2, D, R>> for Rotation<N1, D> where
    D: DimName,
    R: AbstractRotation<N2, D> + SupersetOf<Rotation<N1, D>>,
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    DefaultAllocator: Allocator<N1, D, D>,
    DefaultAllocator: Allocator<N2, D, U1>, 
[src]

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

impl<N1, N2> SubsetOf<Unit<Complex<N2>>> for Rotation<N1, U2> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>, 
[src]

impl<N1, N2> SubsetOf<Unit<Quaternion<N2>>> for Rotation<N1, U3> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>, 
[src]

impl<N, D> UlpsEq<Rotation<N, D>> for Rotation<N, D> where
    D: DimName,
    N: Scalar + UlpsEq<N>,
    DefaultAllocator: Allocator<N, D, D>,
    <N as AbsDiffEq<N>>::Epsilon: Copy
[src]

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

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

Auto Trait Implementations

impl<N, D> !RefUnwindSafe for Rotation<N, D>

impl<N, D> !Send for Rotation<N, D>

impl<N, D> !Sync for Rotation<N, D>

impl<N, D> !Unpin for Rotation<N, D>

impl<N, D> !UnwindSafe for Rotation<N, D>

Blanket Implementations

impl<T> Any for T where
    T: 'static + ?Sized
[src]

impl<T> Borrow<T> for T where
    T: ?Sized
[src]

impl<T> BorrowMut<T> for T where
    T: ?Sized
[src]

impl<T> From<T> for T[src]

impl<T, U> Into<U> for T where
    U: From<T>, 
[src]

impl<V> IntoPnt<V> for V[src]

impl<V> IntoVec<V> for V[src]

impl<T> Same<T> for T[src]

type Output = T

Should always be Self

impl<SS, SP> SupersetOf<SS> for SP where
    SS: SubsetOf<SP>, 
[src]

impl<T> ToOwned for T where
    T: Clone
[src]

type Owned = T

The resulting type after obtaining ownership.

impl<T> ToString for T where
    T: Display + ?Sized
[src]

impl<T, U> TryFrom<U> for T where
    U: Into<T>, 
[src]

type Error = Infallible

The type returned in the event of a conversion error.

impl<T, U> TryInto<U> for T where
    U: TryFrom<T>, 
[src]

type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.

impl<V, T> VZip<V> for T where
    V: MultiLane<T>, 
[src]

impl<T, Right> ClosedDiv<Right> for T where
    T: Div<Right, Output = T> + DivAssign<Right>, 
[src]

impl<T, Right> ClosedMul<Right> for T where
    T: Mul<Right, Output = T> + MulAssign<Right>, 
[src]