Struct ggez::graphics::na::Rotation

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

A rotation matrix.

Methods

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

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

A reference to the underlying matrix representation of this rotation.

unsafe fn matrix_mut(
    &mut self
) -> &mut Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>

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

This is unsafe 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.

fn unwrap(
    self
) -> Matrix<N, D, D, <DefaultAllocator as Allocator<N, D, D>>::Buffer>

Unwraps the underlying matrix.

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>, 

Converts this rotation into its equivalent homogeneous transformation matrix.

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

Creates a new rotation from the given square matrix.

The matrix squareness is checked but not its orthonormality.

fn transpose(&self) -> Rotation<N, D>

Transposes self.

fn inverse(&self) -> Rotation<N, D>

Inverts self.

fn transpose_mut(&mut self)

Transposes self in-place.

fn inverse_mut(&mut self)

Inverts self in-place.

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

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

Creates a new square identity rotation of the given dimension.

impl<N> Rotation<N, U2> where
    N: Real, 

fn new(angle: N) -> Rotation<N, U2>

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

fn from_scaled_axis<SB>(axisangle: Matrix<N, U1, U1, SB>) -> Rotation<N, U2> where
    SB: Storage<N, U1, U1>, 

Builds a 2 dimensional rotation matrix from an angle in radian wrapped in a 1-dimensional vector.

Equivalent to Self::new(axisangle[0]).

fn rotation_between<SB, SC>(
    a: &Matrix<N, U2, U1, SB>,
    b: &Matrix<N, U2, U1, SC>
) -> Rotation<N, U2> where
    SB: Storage<N, U2, U1>,
    SC: Storage<N, U2, U1>, 

The rotation matrix required to align a and b but with its angl.

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

fn scaled_rotation_between<SB, SC>(
    a: &Matrix<N, U2, U1, SB>,
    b: &Matrix<N, U2, U1, SC>,
    s: N
) -> Rotation<N, U2> where
    SB: Storage<N, U2, U1>,
    SC: Storage<N, U2, U1>, 

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

impl<N> Rotation<N, U2> where
    N: Real, 

fn angle(&self) -> N

The rotation angle.

fn angle_to(&self, other: &Rotation<N, U2>) -> N

The rotation angle needed to make self and other coincide.

fn rotation_to(&self, other: &Rotation<N, U2>) -> Rotation<N, U2>

The rotation matrix needed to make self and other coincide.

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

fn powf(&self, n: N) -> Rotation<N, U2>

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

fn scaled_axis(
    &self
) -> Matrix<N, U1, U1, <DefaultAllocator as Allocator<N, U1, U1>>::Buffer>

The rotation angle returned as a 1-dimensional vector.

impl<N> Rotation<N, U3> where
    N: Real, 

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

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.

fn from_scaled_axis<SB>(axisangle: Matrix<N, U3, U1, SB>) -> Rotation<N, U3> where
    SB: Storage<N, U3, U1>, 

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

fn from_axis_angle<SB>(
    axis: &Unit<Matrix<N, U3, U1, SB>>,
    angle: N
) -> Rotation<N, U3> where
    SB: Storage<N, U3, U1>, 

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

fn from_euler_angles(roll: N, pitch: N, yaw: N) -> Rotation<N, U3>

Creates a new rotation from Euler angles.

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

fn new_observer_frame<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>, 

Creates a rotation that corresponds to the local frame of an observer standing at the origin and looking toward dir.

It maps the view direction dir to the positive z axis.

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.

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>, 

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

This conforms to the common notion of right handed look-at matrix from the computer graphics community.

Arguments

• eye - The eye position.
• target - The target position.
• up - A vector approximately aligned with required the vertical axis. The only requirement of this parameter is to not be collinear to target - eye.

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>, 

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

This conforms to the common notion of left handed look-at matrix from the computer graphics community.

Arguments

• eye - The eye position.
• target - The target position.
• up - A vector approximately aligned with required the vertical axis. The only requirement of this parameter is to not be collinear to target - eye.

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

The rotation matrix required to align a and b but with its angl.

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

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
    SB: Storage<N, U3, U1>,
    SC: Storage<N, U3, U1>, 

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

fn angle(&self) -> N

The rotation angle.

fn axis(
    &self
) -> Option<Unit<Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>>>

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

fn scaled_axis(
    &self
) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>

The rotation axis multiplied by the rotation angle.

fn angle_to(&self, other: &Rotation<N, U3>) -> N

The rotation angle needed to make self and other coincide.

fn rotation_to(&self, other: &Rotation<N, U3>) -> Rotation<N, U3>

The rotation matrix needed to make self and other coincide.

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

fn powf(&self, n: N) -> Rotation<N, U3>

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.

Trait Implementations

impl<N> Rand for Rotation<N, U2> where
    N: Rand + Real, 

fn rand<R>(rng: &mut R) -> Rotation<N, U2> where
    R: Rng, 

impl<N> Rand for Rotation<N, U3> where
    N: Rand + Real, 

fn rand<R>(rng: &mut R) -> Rotation<N, U3> where
    R: Rng, 

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

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, 

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

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<N, D> AbstractMonoid<Multiplicative> for Rotation<N, D> where
    D: DimName,
    N: Real,
    DefaultAllocator: Allocator<N, D, D>, 

impl<N1, N2, D, R> SubsetOf<Isometry<N2, D, R>> for Rotation<N1, D> where
    D: DimName,
    N1: Real,
    N2: Real + SupersetOf<N1>,
    R: Rotation<Point<N2, D>> + SupersetOf<Rotation<N1, D>>,
    DefaultAllocator: Allocator<N1, D, D>,
    DefaultAllocator: Allocator<N2, D, U1>, 

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

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

unsafe fn from_superset_unchecked(iso: &Isometry<N2, D, R>) -> Rotation<N1, D>

impl<N1, N2> SubsetOf<Unit<Complex<N2>>> for Rotation<N1, U2> where
    N1: Real,
    N2: Real + SupersetOf<N1>, 

fn to_superset(&self) -> Unit<Complex<N2>>

fn is_in_subset(q: &Unit<Complex<N2>>) -> bool

unsafe fn from_superset_unchecked(q: &Unit<Complex<N2>>) -> Rotation<N1, U2>

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: Real,
    N2: Real + 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>, 

fn to_superset(
    &self
) -> 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>

fn is_in_subset(
    m: &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>
) -> bool

unsafe fn from_superset_unchecked(
    m: &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>
) -> Rotation<N1, D>

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: Real,
    N2: Real + 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>, 

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

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

unsafe fn from_superset_unchecked(t: &Transform<N2, D, C>) -> Rotation<N1, D>

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

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

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

unsafe fn from_superset_unchecked(rot: &Rotation<N2, D>) -> Rotation<N1, D>

impl<N1, N2> SubsetOf<Unit<Quaternion<N2>>> for Rotation<N1, U3> where
    N1: Real,
    N2: Real + SupersetOf<N1>, 

fn to_superset(&self) -> Unit<Quaternion<N2>>

fn is_in_subset(q: &Unit<Quaternion<N2>>) -> bool

unsafe fn from_superset_unchecked(q: &Unit<Quaternion<N2>>) -> Rotation<N1, U3>

impl<N1, N2, D, R> SubsetOf<Similarity<N2, D, R>> for Rotation<N1, D> where
    D: DimName,
    N1: Real,
    N2: Real + SupersetOf<N1>,
    R: Rotation<Point<N2, D>> + SupersetOf<Rotation<N1, D>>,
    DefaultAllocator: Allocator<N1, D, D>,
    DefaultAllocator: Allocator<N2, D, U1>, 

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

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

unsafe fn from_superset_unchecked(sim: &Similarity<N2, D, R>) -> Rotation<N1, D>

impl<N, D> Inverse<Multiplicative> for Rotation<N, D> where
    D: DimName,
    N: Real,
    DefaultAllocator: Allocator<N, D, D>, 

fn inverse(&self) -> Rotation<N, D>

fn inverse_mut(&mut self)

impl<N, D> ProjectiveTransformation<Point<N, D>> for Rotation<N, D> where
    D: DimName,
    N: Real,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

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>

impl<N, D> Isometry<Point<N, D>> for Rotation<N, D> where
    D: DimName,
    N: Real,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 

impl<N, D> AffineTransformation<Point<N, D>> for Rotation<N, D> where
    D: DimName,
    N: Real,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Rotation = Rotation<N, D>

type NonUniformScaling = Id<Multiplicative>

type Translation = Id<Multiplicative>

fn decompose(
    &self
) -> (Id<Multiplicative>, Rotation<N, D>, Id<Multiplicative>, Rotation<N, D>)

fn append_translation(
    &self,
    &<Rotation<N, D> as AffineTransformation<Point<N, D>>>::Translation
) -> Rotation<N, D>

fn prepend_translation(
    &self,
    &<Rotation<N, D> as AffineTransformation<Point<N, D>>>::Translation
) -> Rotation<N, D>

fn append_rotation(
    &self,
    r: &<Rotation<N, D> as AffineTransformation<Point<N, D>>>::Rotation
) -> Rotation<N, D>

fn prepend_rotation(
    &self,
    r: &<Rotation<N, D> as AffineTransformation<Point<N, D>>>::Rotation
) -> Rotation<N, D>

fn append_scaling(
    &self,
    &<Rotation<N, D> as AffineTransformation<Point<N, D>>>::NonUniformScaling
) -> Rotation<N, D>

fn prepend_scaling(
    &self,
    &<Rotation<N, D> as AffineTransformation<Point<N, D>>>::NonUniformScaling
) -> Rotation<N, D>

impl<N, D> Transformation<Point<N, D>> for Rotation<N, D> where
    D: DimName,
    N: Real,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

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>

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>, 

type Output = Rotation<N, D>

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

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

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

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

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> + Real,
    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>, 

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

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

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

type Output = Unit<Quaternion<N>>

fn div(
    self,
    rhs: Unit<Quaternion<N>>
) -> <Rotation<N, U3> as Div<Unit<Quaternion<N>>>>::Output

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>, 

type Output = Rotation<N, D>

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

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

type Output = Unit<Quaternion<N>>

fn div(
    self,
    rhs: Unit<Quaternion<N>>
) -> <&'a Rotation<N, U3> as Div<Unit<Quaternion<N>>>>::Output

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

type Output = Unit<Complex<N>>

fn div(
    self,
    rhs: &'b Unit<Complex<N>>
) -> <Rotation<N, U2> as Div<&'b Unit<Complex<N>>>>::Output

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

type Output = Unit<Complex<N>>

fn div(
    self,
    rhs: Unit<Complex<N>>
) -> <Rotation<N, U2> as Div<Unit<Complex<N>>>>::Output

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

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

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

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> + Real,
    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>, 

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

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

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

type Output = Unit<Complex<N>>

fn div(
    self,
    rhs: Unit<Complex<N>>
) -> <&'a Rotation<N, U2> as Div<Unit<Complex<N>>>>::Output

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

type Output = Unit<Complex<N>>

fn div(
    self,
    rhs: &'b Unit<Complex<N>>
) -> <&'a Rotation<N, U2> as Div<&'b Unit<Complex<N>>>>::Output

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

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

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

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>, 

type Output = Rotation<N, D>

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

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

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

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

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

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

fn div(
    self,
    right: Similarity<N, D, Rotation<N, D>>
) -> <&'a Rotation<N, D> as Div<Similarity<N, D, Rotation<N, D>>>>::Output

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> + Real,
    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>, 

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

fn div(
    self,
    rhs: &'b Transform<N, D, C>
) -> <&'a Rotation<N, D> as Div<&'b Transform<N, D, C>>>::Output

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

type Output = Unit<Quaternion<N>>

fn div(
    self,
    rhs: &'b Unit<Quaternion<N>>
) -> <Rotation<N, U3> as Div<&'b Unit<Quaternion<N>>>>::Output

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

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

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

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

type Output = Unit<Quaternion<N>>

fn div(
    self,
    rhs: &'b Unit<Quaternion<N>>
) -> <&'a Rotation<N, U3> as Div<&'b Unit<Quaternion<N>>>>::Output

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

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

fn div(
    self,
    right: Isometry<N, D, Rotation<N, D>>
) -> <&'a Rotation<N, D> as Div<Isometry<N, D, Rotation<N, D>>>>::Output

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> + Real,
    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>, 

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

fn div(
    self,
    rhs: Transform<N, D, C>
) -> <&'a Rotation<N, D> as Div<Transform<N, D, C>>>::Output

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

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

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

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>, 

type Output = Rotation<N, D>

fn div(
    self,
    right: Rotation<N, D>
) -> <&'a Rotation<N, D> as Div<Rotation<N, D>>>::Output

impl<N, D> AbstractSemigroup<Multiplicative> for Rotation<N, D> where
    D: DimName,
    N: Real,
    DefaultAllocator: Allocator<N, D, D>, 

impl<N, D> AbstractLoop<Multiplicative> for Rotation<N, D> where
    D: DimName,
    N: Real,
    DefaultAllocator: Allocator<N, D, D>, 

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>, 

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

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

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

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>, 

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

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

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

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

type Epsilon = <N as ApproxEq>::Epsilon

fn default_epsilon() -> <Rotation<N, D> as ApproxEq>::Epsilon

fn default_max_relative() -> <Rotation<N, D> as ApproxEq>::Epsilon

fn default_max_ulps() -> u32

fn relative_eq(
    &self,
    other: &Rotation<N, D>,
    epsilon: <Rotation<N, D> as ApproxEq>::Epsilon,
    max_relative: <Rotation<N, D> as ApproxEq>::Epsilon
) -> bool

fn ulps_eq(
    &self,
    other: &Rotation<N, D>,
    epsilon: <Rotation<N, D> as ApproxEq>::Epsilon,
    max_ulps: u32
) -> bool

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, 

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

Feeds this value into the given [Hasher].

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

Feeds a slice of this type into the given [Hasher].

impl<N, D> Similarity<Point<N, D>> for Rotation<N, D> where
    D: DimName,
    N: Real,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Scaling = Id<Multiplicative>

fn translation(&self) -> Id<Multiplicative>

fn rotation(&self) -> Rotation<N, D>

fn scaling(&self) -> Id<Multiplicative>

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

fn eq(&self, right: &Rotation<N, D>) -> bool

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

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

This method tests for !=.

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

fn fmt(&self, __arg_0: &mut Formatter) -> Result<(), Error>

Formats the value using the given formatter.

impl<N, D> Rotation<Point<N, D>> for Rotation<N, D> where
    D: DimName,
    N: Real,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 

Subgroups of the n-dimensional rotation group SO(n).

fn powf(&self, N) -> Option<Rotation<N, D>>

fn rotation_between(
    &Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>,
    &Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>
) -> Option<Rotation<N, D>>

fn scaled_rotation_between(
    &Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>,
    &Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>,
    N
) -> Option<Rotation<N, D>>

impl<N, D> DirectIsometry<Point<N, D>> for Rotation<N, D> where
    D: DimName,
    N: Real,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 

impl<N, D> AbstractQuasigroup<Multiplicative> for Rotation<N, D> where
    D: DimName,
    N: Real,
    DefaultAllocator: Allocator<N, D, D>, 

impl<N, D> AbstractGroup<Multiplicative> for Rotation<N, D> where
    D: DimName,
    N: Real,
    DefaultAllocator: Allocator<N, D, D>, 

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

fn one() -> Rotation<N, D>

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

type Output = N

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

impl<N, D> Identity<Multiplicative> for Rotation<N, D> where
    D: DimName,
    N: Real,
    DefaultAllocator: Allocator<N, D, D>, 

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

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

impl<N, D> OrthogonalTransformation<Point<N, D>> for Rotation<N, D> where
    D: DimName,
    N: Real,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

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

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>, 

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

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

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

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>, 

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

impl<N, D> AbstractMagma<Multiplicative> for Rotation<N, D> where
    D: DimName,
    N: Real,
    DefaultAllocator: Allocator<N, D, D>, 

fn operate(&self, rhs: &Rotation<N, D>) -> Rotation<N, D>

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

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

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

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

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

fn mul(
    self,
    right: Similarity<N, D, Rotation<N, D>>
) -> <&'a Rotation<N, D> as Mul<Similarity<N, D, Rotation<N, D>>>>::Output

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

type Output = Unit<Quaternion<N>>

fn mul(
    self,
    rhs: Unit<Quaternion<N>>
) -> <Rotation<N, U3> as Mul<Unit<Quaternion<N>>>>::Output

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> + Real,
    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>, 

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

fn mul(
    self,
    rhs: Transform<N, D, C>
) -> <&'a Rotation<N, D> as Mul<Transform<N, D, C>>>::Output

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>, 

type Output = Point<N, D>

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

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

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

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

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

type Output = Unit<Complex<N>>

fn mul(
    self,
    rhs: Unit<Complex<N>>
) -> <Rotation<N, U2> as Mul<Unit<Complex<N>>>>::Output

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

type Output = Unit<Quaternion<N>>

fn mul(
    self,
    rhs: &'b Unit<Quaternion<N>>
) -> <Rotation<N, U3> as Mul<&'b Unit<Quaternion<N>>>>::Output

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>, 

type Output = Rotation<N, D>

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

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

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

fn mul(
    self,
    right: Translation<N, D>
) -> <&'a Rotation<N, D> as Mul<Translation<N, D>>>::Output

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

type Output = Unit<Complex<N>>

fn mul(
    self,
    rhs: &'b Unit<Complex<N>>
) -> <Rotation<N, U2> as Mul<&'b Unit<Complex<N>>>>::Output

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

type Output = Unit<Complex<N>>

fn mul(
    self,
    rhs: &'b Unit<Complex<N>>
) -> <&'a Rotation<N, U2> as Mul<&'b Unit<Complex<N>>>>::Output

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>, 

type Output = Rotation<N, D>

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

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

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

fn mul(
    self,
    right: &'b Matrix<N, R2, C2, SB>
) -> <Rotation<N, D1> as Mul<&'b Matrix<N, R2, C2, SB>>>::Output

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>, 

type Output = Rotation<N, D>

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

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>, 

type Output = Rotation<N, D>

fn mul(
    self,
    right: Rotation<N, D>
) -> <&'a Rotation<N, D> as Mul<Rotation<N, D>>>::Output

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

type Output = Unit<Complex<N>>

fn mul(
    self,
    rhs: Unit<Complex<N>>
) -> <&'a Rotation<N, U2> as Mul<Unit<Complex<N>>>>::Output

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

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

fn mul(
    self,
    right: Matrix<N, R2, C2, SB>
) -> <&'a Rotation<N, D1> as Mul<Matrix<N, R2, C2, SB>>>::Output

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

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

fn mul(
    self,
    right: Matrix<N, R2, C2, SB>
) -> <Rotation<N, D1> as Mul<Matrix<N, R2, C2, SB>>>::Output

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

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

fn mul(
    self,
    right: &'b Translation<N, D>
) -> <&'a Rotation<N, D> as Mul<&'b Translation<N, D>>>::Output

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

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

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

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

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

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

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

type Output = Unit<Quaternion<N>>

fn mul(
    self,
    rhs: Unit<Quaternion<N>>
) -> <&'a Rotation<N, U3> as Mul<Unit<Quaternion<N>>>>::Output

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>, 

type Output = Point<N, D>

fn mul(
    self,
    right: &'b Point<N, D>
) -> <&'a Rotation<N, D> as Mul<&'b Point<N, D>>>::Output

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

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

fn mul(
    self,
    right: &'b Matrix<N, R2, C2, SB>
) -> <&'a Rotation<N, D1> as Mul<&'b Matrix<N, R2, C2, SB>>>::Output

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

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

fn mul(
    self,
    right: Translation<N, D>
) -> <Rotation<N, D> as Mul<Translation<N, D>>>::Output

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> + Real,
    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>, 

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

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

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> + Real,
    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>, 

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

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

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

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

fn mul(
    self,
    right: Isometry<N, D, Rotation<N, D>>
) -> <&'a Rotation<N, D> as Mul<Isometry<N, D, Rotation<N, D>>>>::Output

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

type Output = Unit<Quaternion<N>>

fn mul(
    self,
    rhs: &'b Unit<Quaternion<N>>
) -> <&'a Rotation<N, U3> as Mul<&'b Unit<Quaternion<N>>>>::Output

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> + Real,
    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>, 

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

fn mul(
    self,
    rhs: &'b Transform<N, D, C>
) -> <&'a Rotation<N, D> as Mul<&'b Transform<N, D, C>>>::Output

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

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

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

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

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

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

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>, 

type Output = Point<N, D>

fn mul(self, right: Point<N, D>) -> <Rotation<N, D> as Mul<Point<N, D>>>::Output

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

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

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

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>, 

type Output = Point<N, D>

fn mul(
    self,
    right: Point<N, D>
) -> <&'a Rotation<N, D> as Mul<Point<N, D>>>::Output

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

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

Formats the value using the given formatter.