Struct nalgebra::geometry::Rotation

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

A rotation matrix.

Implementations

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

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

A reference to the underlying matrix representation of this rotation.

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

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.

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

Unwraps the underlying matrix.

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

Converts this rotation into its equivalent homogeneous transformation matrix.

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

Creates a new rotation from the given square matrix.

The matrix squareness is checked but not its orthonormality.

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

Transposes self.

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

Inverts self.

pub fn transpose_mut(&mut self)

Transposes self in-place.

pub fn inverse_mut(&mut self)

Inverts self in-place.

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

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

Creates a new square identity rotation of the given dimension.

impl<N: Real> Rotation<N, U2>

pub fn new(angle: N) -> Self

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

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

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

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

pub fn rotation_between<SB, SC>(
    a: &Vector<N, U2, SB>,
    b: &Vector<N, U2, SC>
) -> Selfwhere
    SB: Storage<N, U2>,
    SC: Storage<N, U2>,

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

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

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

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

impl<N: Real> Rotation<N, U2>

pub fn angle(&self) -> N

The rotation angle.

pub fn angle_to(&self, other: &Rotation2<N>) -> N

The rotation angle needed to make self and other coincide.

pub fn rotation_to(&self, other: &Rotation2<N>) -> Rotation2<N>

The rotation matrix needed to make self and other coincide.

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

pub fn powf(&self, n: N) -> Rotation2<N>

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

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

The rotation angle returned as a 1-dimensional vector.

impl<N: Real> Rotation<N, U3>

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

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

Arguments

• axisangle - A vector representing the rotation. Its magnitude is the amount of rotation in radian. Its direction is the axis of rotation.

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

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

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

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

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

Creates a new rotation from Euler angles.

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

pub fn to_euler_angles(&self) -> (N, N, N)

Creates Euler angles from a rotation.

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

pub fn new_observer_frame<SB, SC>(
    dir: &Vector<N, U3, SB>,
    up: &Vector<N, U3, SC>
) -> Selfwhere
    SB: Storage<N, U3>,
    SC: Storage<N, U3>,

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

It maps the 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.

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

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.

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

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.

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

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

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

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

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

pub fn angle(&self) -> N

The rotation angle.

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

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

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

The rotation axis multiplied by the rotation angle.

pub fn angle_to(&self, other: &Rotation3<N>) -> N

The rotation angle needed to make self and other coincide.

pub fn rotation_to(&self, other: &Rotation3<N>) -> Rotation3<N>

The rotation matrix needed to make self and other coincide.

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

pub fn powf(&self, n: N) -> Rotation3<N>

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

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

Used for specifying relative comparisons.

fn default_epsilon() -> Self::Epsilon

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

fn abs_diff_eq(&self, other: &Self, epsilon: Self::Epsilon) -> bool

A test for equality that uses the absolute difference to compute the approximate equality of two numbers.

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

The inverse of ApproxEq::abs_diff_eq.

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

fn operate(&self, rhs: &Self) -> Self

Performs an operation.

fn op(&self, _: O, lhs: &Self) -> Self

Performs specific operation.

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

fn prop_operating_identity_element_is_noop_approx(args: (Self,)) -> boolwhere
    Self: RelativeEq<Self>,

Checks whether operating with the identity element is a no-op for the given argument. Approximate equality is used for verifications.

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

fn prop_inv_is_latin_square_approx(args: (Self, Self)) -> boolwhere
    Self: RelativeEq<Self>,

Returns true if latin squareness holds for the given arguments. Approximate equality is used for verifications.

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

fn prop_is_associative_approx(args: (Self, Self, Self)) -> boolwhere
    Self: RelativeEq<Self>,

Returns true if associativity holds for the given arguments. Approximate equality is used for verifications.

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

type Rotation = Rotation<N, D>

Type of the first rotation to be applied.

type NonUniformScaling = Id<Multiplicative>

Type of the non-uniform scaling to be applied.

type Translation = Id<Multiplicative>

The type of the pure translation part of this affine transformation.

fn decompose(&self) -> (Id, Self, Id, Self)

Decomposes this affine transformation into a rotation followed by a non-uniform scaling, followed by a rotation, followed by a translation.

fn append_translation(&self, _: &Self::Translation) -> Self

Appends a translation to this similarity.

fn prepend_translation(&self, _: &Self::Translation) -> Self

Prepends a translation to this similarity.

fn append_rotation(&self, r: &Self::Rotation) -> Self

Appends a rotation to this similarity.

fn prepend_rotation(&self, r: &Self::Rotation) -> Self

Prepends a rotation to this similarity.

fn append_scaling(&self, _: &Self::NonUniformScaling) -> Self

Appends a scaling factor to this similarity.

fn prepend_scaling(&self, _: &Self::NonUniformScaling) -> Self

Prepends a scaling factor to this similarity.

fn append_rotation_wrt_point(&self, r: &Self::Rotation, p: &E) -> Option<Self>

Appends to this similarity a rotation centered at the point p, i.e., this point is left invariant.

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

fn clone(&self) -> Self

Returns a copy of the value.

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

Performs copy-assignment from source.

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

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

Formats the value using the given formatter.

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

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

Formats the value using the given formatter.

impl<N: Real> Distribution<Rotation<N, U2>> for Standardwhere
    OpenClosed01: Distribution<N>,

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

Generate a uniformly distributed random rotation.

fn sample_iter<R, 'a>(&'a self, rng: &'a mut R) -> DistIter<'a, Self, R, T>where
    Self: Sized,
    R: Rng,

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

impl<N: Real> Distribution<Rotation<N, U3>> for Standardwhere
    OpenClosed01: Distribution<N>,

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

Generate a uniformly distributed random rotation.

fn sample_iter<R, 'a>(&'a self, rng: &'a mut R) -> DistIter<'a, Self, R, T>where
    Self: Sized,
    R: Rng,

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

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Rotation<N, D>

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Rotation<N, D>

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Unit<Complex<N>>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Unit<Complex<N>>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Unit<Quaternion<N>>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Unit<Quaternion<N>>

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Unit<Complex<N>>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Unit<Complex<N>>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Unit<Quaternion<N>>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Unit<Quaternion<N>>

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Rotation<N, D>

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Rotation<N, D>

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Unit<Complex<N>>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Unit<Complex<N>>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Unit<Quaternion<N>>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Unit<Quaternion<N>>

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Unit<Complex<N>>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Unit<Complex<N>>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Unit<Quaternion<N>>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Unit<Quaternion<N>>

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

fn from(q: Rotation2<N>) -> Matrix2<N>

Converts to this type from the input type.

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

fn from(q: Rotation2<N>) -> Matrix3<N>

Converts to this type from the input type.

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

fn from(q: Rotation3<N>) -> Matrix3<N>

Converts to this type from the input type.

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

fn from(q: Rotation3<N>) -> Matrix4<N>

Converts to this type from the input type.

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

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

Feeds this value into the given Hasher.

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

Feeds a slice of this type into the given Hasher.

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

fn identity() -> Self

The identity element.

fn id(_: O) -> Selfwhere
    Self: Sized,

Specific identity.

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

type Output = N

The returned type after indexing.

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

Performs the indexing (container[index]) operation.

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

fn inverse(&self) -> Self

Returns the inverse of self, relative to the operator O.

fn inverse_mut(&mut self)

In-place inversin of self.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Point<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Point<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Rotation<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Rotation<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Unit<Complex<N>>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Unit<Complex<N>>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Unit<Quaternion<N>>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Unit<Quaternion<N>>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Unit<Complex<N>>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Unit<Complex<N>>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Unit<Quaternion<N>>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Unit<Quaternion<N>>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Point<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Point<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Rotation<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Rotation<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Unit<Complex<N>>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Unit<Complex<N>>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Unit<Quaternion<N>>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Unit<Quaternion<N>>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Unit<Complex<N>>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Unit<Complex<N>>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Unit<Quaternion<N>>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Unit<Quaternion<N>>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

fn set_one(&mut self)

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

fn is_one(&self) -> boolwhere
    Self: PartialEq<Self>,

Returns true if self is equal to the multiplicative identity.

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

fn eq(&self, right: &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 !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

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

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

Applies this group’s inverse action on a point from the euclidean space.

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

Applies this group’s inverse action on a vector from the euclidean space.

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

fn default_max_relative() -> Self::Epsilon

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

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

A test for equality that uses a relative comparison if the values are far apart.

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

The inverse of ApproxEq::relative_eq.

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

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

fn powf(&self, _: N) -> Option<Self>

Raises this rotation to a power. If this is a simple rotation, the result must be equivalent to multiplying the rotation angle by n.

fn rotation_between(_: &VectorN<N, D>, _: &VectorN<N, D>) -> Option<Self>

Computes a simple rotation that makes the angle between a and b equal to zero, i.e., b.angle(a * delta_rotation(a, b)) = 0. If a and b are collinear, the computed rotation may not be unique. Returns None if no such simple rotation exists in the subgroup represented by Self.

fn scaled_rotation_between(
    _: &VectorN<N, D>,
    _: &VectorN<N, D>,
    _: N
) -> Option<Self>

Computes the rotation between a and b and raises it to the power n.

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

type Scaling = Id<Multiplicative>

The type of the pure (uniform) scaling part of this similarity transformation.

fn translation(&self) -> Id

The pure translational component of this similarity transformation.

fn rotation(&self) -> Self

The pure rotational component of this similarity transformation.

fn scaling(&self) -> Id

The pure scaling component of this similarity transformation.

fn translate_point(&self, pt: &E) -> E

Applies this transformation’s pure translational part to a point.

fn rotate_point(&self, pt: &E) -> E

Applies this transformation’s pure rotational part to a point.

fn scale_point(&self, pt: &E) -> E

Applies this transformation’s pure scaling part to a point.

fn rotate_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation’s pure rotational part to a vector.

fn scale_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation’s pure scaling part to a vector.

fn inverse_translate_point(&self, pt: &E) -> E

Applies this transformation inverse’s pure translational part to a point.

fn inverse_rotate_point(&self, pt: &E) -> E

Applies this transformation inverse’s pure rotational part to a point.

fn inverse_scale_point(&self, pt: &E) -> E

Applies this transformation inverse’s pure scaling part to a point.

fn inverse_rotate_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation inverse’s pure rotational part to a vector.

fn inverse_scale_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation inverse’s pure scaling part to a vector.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Applies this group’s action on a point from the euclidean space.

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

Applies this group’s action on a vector from the euclidean space.

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

fn default_max_ulps() -> u32

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

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

A test for equality that uses units in the last place (ULP) if the values are far apart.

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

The inverse of ApproxEq::ulps_eq.

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

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

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

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

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

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

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