Struct nalgebra::geometry::RotationBase

#[repr(C)]
pub struct RotationBase<N: Scalar, D: DimName, S> { /* fields omitted */ }

A rotation matrix.

Methods

impl<N: Scalar, D: DimName, S: Storage<N, D, D>> RotationBase<N, D, S> where
    N: Scalar,
    S: Storage<N, D, D>, 

fn matrix(&self) -> &SquareMatrix<N, D, S>

A reference to the underlying matrix representation of this rotation.

unsafe fn matrix_mut(&mut self) -> &mut SquareMatrix<N, D, S>

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) -> SquareMatrix<N, D, S>

Unwraps the underlying matrix.

fn to_homogeneous(&self) -> OwnedSquareMatrix<N, DimNameSum<D, U1>, S::Alloc> where
    N: Zero + One,
    D: DimNameAdd<U1>,
    S::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>, 

Converts this rotation into its equivalent homogeneous transformation matrix.

impl<N: Scalar, D: DimName, S: Storage<N, D, D>> RotationBase<N, D, S>

fn from_matrix_unchecked(matrix: SquareMatrix<N, D, S>) -> RotationBase<N, D, S>

Creates a new rotation from the given square matrix.

The matrix squareness is checked but not its orthonormality.

fn transpose(&self) -> OwnedRotation<N, D, S::Alloc>

Transposes self.

fn inverse(&self) -> OwnedRotation<N, D, S::Alloc>

Inverts self.

impl<N: Scalar, D: DimName, S: StorageMut<N, D, D>> RotationBase<N, D, S>

fn transpose_mut(&mut self)

Transposes self in-place.

fn inverse_mut(&mut self)

Inverts self in-place.

impl<N, D: DimName, S> RotationBase<N, D, S> where
    N: Scalar + Zero + One,
    S: OwnedStorage<N, D, D>,
    S::Alloc: OwnedAllocator<N, D, D, S>, 

fn identity() -> RotationBase<N, D, S>

Creates a new square identity rotation of the given dimension.

impl<N, S> RotationBase<N, U2, S> where
    N: Real,
    S: OwnedStorage<N, U2, U2>,
    S::Alloc: OwnedAllocator<N, U2, U2, S>, 

fn new(angle: N) -> Self

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

fn from_scaled_axis<SB: Storage<N, U1, U1>>(
    axisangle: ColumnVector<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]).

fn rotation_between<SB, SC>(
    a: &ColumnVector<N, U2, SB>,
    b: &ColumnVector<N, U2, SC>
) -> Self 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: &ColumnVector<N, U2, SB>,
    b: &ColumnVector<N, U2, SC>,
    s: N
) -> Self 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, S> RotationBase<N, U2, S> where
    N: Real,
    S: Storage<N, U2, U2>, 

fn angle(&self) -> N

The rotation angle.

fn angle_to<SB: Storage<N, U2, U2>>(&self, other: &RotationBase<N, U2, SB>) -> N

The rotation angle needed to make self and other coincide.

fn rotation_to<SB>(
    &self,
    other: &RotationBase<N, U2, SB>
) -> OwnedRotation<N, U2, SB::Alloc> where
    SB: Storage<N, U2, 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) -> OwnedRotation<N, U2, S::Alloc>

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) -> OwnedColumnVector<N, U1, S::Alloc> where
    S::Alloc: Allocator<N, U1, U1>, 

The rotation angle returned as a 1-dimensional vector.

impl<N, S> RotationBase<N, U3, S> where
    N: Real,
    S: OwnedStorage<N, U3, U3>,
    S::Alloc: OwnedAllocator<N, U3, U3, S>, 

fn new<SB: Storage<N, U3, U1>>(axisangle: ColumnVector<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.

fn from_scaled_axis<SB: Storage<N, U3, U1>>(
    axisangle: ColumnVector<N, U3, SB>
) -> Self

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

fn from_axis_angle<SB>(axis: &Unit<ColumnVector<N, U3, SB>>, angle: N) -> Self 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) -> Self

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: &ColumnVector<N, U3, SB>,
    up: &ColumnVector<N, U3, SC>
) -> Self 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: &ColumnVector<N, U3, SB>,
    up: &ColumnVector<N, U3, SC>
) -> Self 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: &ColumnVector<N, U3, SB>,
    up: &ColumnVector<N, U3, SC>
) -> Self 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: &ColumnVector<N, U3, SB>,
    b: &ColumnVector<N, U3, SC>
) -> Option<Self> 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: &ColumnVector<N, U3, SB>,
    b: &ColumnVector<N, U3, SC>,
    n: N
) -> Option<Self> 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.

impl<N, S> RotationBase<N, U3, S> where
    N: Real,
    S: Storage<N, U3, U3>, 

fn angle(&self) -> N

The rotation angle.

impl<N, S> RotationBase<N, U3, S> where
    N: Real,
    S: Storage<N, U3, U3>,
    S::Alloc: Allocator<N, U3, U1>, 

fn axis(&self) -> Option<Unit<OwnedColumnVector<N, U3, S::Alloc>>>

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

fn scaled_axis(&self) -> OwnedColumnVector<N, U3, S::Alloc>

The rotation axis multiplied by the rotation angle.

fn angle_to<SB: Storage<N, U3, U3>>(&self, other: &RotationBase<N, U3, SB>) -> N

The rotation angle needed to make self and other coincide.

fn rotation_to<SB>(
    &self,
    other: &RotationBase<N, U3, SB>
) -> OwnedRotation<N, U3, SB::Alloc> where
    SB: Storage<N, U3, 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) -> OwnedRotation<N, U3, S::Alloc>

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: Hash + Scalar, D: Hash + DimName, S: Hash> Hash for RotationBase<N, D, S>

fn hash<__HNDS: Hasher>(&self, __arg_0: &mut __HNDS)

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: Debug + Scalar, D: Debug + DimName, S: Debug> Debug for RotationBase<N, D, S>

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

Formats the value using the given formatter.

impl<N: Clone + Scalar, D: Clone + DimName, S: Clone> Clone for RotationBase<N, D, S>

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

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<N: Copy + Scalar, D: Copy + DimName, S: Copy> Copy for RotationBase<N, D, S>

impl<N: Scalar + Eq, D: DimName, S: Storage<N, D, D>> Eq for RotationBase<N, D, S>

impl<N: Scalar + PartialEq, D: DimName, S: Storage<N, D, D>> PartialEq for RotationBase<N, D, S>

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

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

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

This method tests for !=.

impl<N, D: DimName, S> ApproxEq for RotationBase<N, D, S> where
    N: Scalar + ApproxEq,
    S: Storage<N, D, D>,
    N::Epsilon: Copy, 

type Epsilon = N::Epsilon

Used for specifying relative comparisons.

fn default_epsilon() -> Self::Epsilon

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

fn default_max_relative() -> Self::Epsilon

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

fn default_max_ulps() -> u32

The default ULPs to tolerate when 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 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 relative_ne(
    &self,
    other: &Self,
    epsilon: Self::Epsilon,
    max_relative: Self::Epsilon
) -> bool

The inverse of ApproxEq::relative_eq.

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

The inverse of ApproxEq::ulps_eq.

impl<N, D: DimName, S> Display for RotationBase<N, D, S> where
    N: Real + Display,
    S: Storage<N, D, D>,
    S::Alloc: Allocator<usize, D, D>, 

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

Formats the value using the given formatter.

impl<N, D: DimName, S> One for RotationBase<N, D, S> where
    N: Scalar + Zero + One + ClosedAdd + ClosedMul,
    S: OwnedStorage<N, D, D>,
    S::Alloc: OwnedAllocator<N, D, D, S>, 

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

impl<N: Scalar, D: DimName, S: Storage<N, D, D>> Index<(usize, usize)> for RotationBase<N, D, S>

type Output = N

The returned type after indexing

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

The method for the indexing (container[index]) operation

impl<N, D: DimName, SA, SB> Mul<RotationBase<N, D, SB>> for RotationBase<N, D, SA> where
    N: Scalar + Zero + ClosedAdd + ClosedMul,
    SA: Storage<N, D, D>,
    SB: Storage<N, D, D>, 

type Output = OwnedRotation<N, D, SA::Alloc>

The resulting type after applying the * operator

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

The method for the * operator

impl<'a, N, D: DimName, SA, SB> Mul<RotationBase<N, D, SB>> for &'a RotationBase<N, D, SA> where
    N: Scalar + Zero + ClosedAdd + ClosedMul,
    SA: Storage<N, D, D>,
    SB: Storage<N, D, D>, 

type Output = OwnedRotation<N, D, SA::Alloc>

The resulting type after applying the * operator

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

The method for the * operator

impl<'b, N, D: DimName, SA, SB> Mul<&'b RotationBase<N, D, SB>> for RotationBase<N, D, SA> where
    N: Scalar + Zero + ClosedAdd + ClosedMul,
    SA: Storage<N, D, D>,
    SB: Storage<N, D, D>, 

type Output = OwnedRotation<N, D, SA::Alloc>

The resulting type after applying the * operator

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

The method for the * operator

impl<'a, 'b, N, D: DimName, SA, SB> Mul<&'b RotationBase<N, D, SB>> for &'a RotationBase<N, D, SA> where
    N: Scalar + Zero + ClosedAdd + ClosedMul,
    SA: Storage<N, D, D>,
    SB: Storage<N, D, D>, 

type Output = OwnedRotation<N, D, SA::Alloc>

The resulting type after applying the * operator

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

The method for the * operator

impl<N, D: DimName, SA, SB> Div<RotationBase<N, D, SB>> for RotationBase<N, D, SA> where
    N: Scalar + Zero + ClosedAdd + ClosedMul,
    SA: Storage<N, D, D>,
    SB: Storage<N, D, D>, 

type Output = OwnedRotation<N, D, SA::Alloc>

The resulting type after applying the / operator

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

The method for the / operator

impl<'a, N, D: DimName, SA, SB> Div<RotationBase<N, D, SB>> for &'a RotationBase<N, D, SA> where
    N: Scalar + Zero + ClosedAdd + ClosedMul,
    SA: Storage<N, D, D>,
    SB: Storage<N, D, D>, 

type Output = OwnedRotation<N, D, SA::Alloc>

The resulting type after applying the / operator

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

The method for the / operator

impl<'b, N, D: DimName, SA, SB> Div<&'b RotationBase<N, D, SB>> for RotationBase<N, D, SA> where
    N: Scalar + Zero + ClosedAdd + ClosedMul,
    SA: Storage<N, D, D>,
    SB: Storage<N, D, D>, 

type Output = OwnedRotation<N, D, SA::Alloc>

The resulting type after applying the / operator

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

The method for the / operator

impl<'a, 'b, N, D: DimName, SA, SB> Div<&'b RotationBase<N, D, SB>> for &'a RotationBase<N, D, SA> where
    N: Scalar + Zero + ClosedAdd + ClosedMul,
    SA: Storage<N, D, D>,
    SB: Storage<N, D, D>, 

type Output = OwnedRotation<N, D, SA::Alloc>

The resulting type after applying the / operator

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

The method for the / operator

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

type Output = MatrixMul<N, D1, D1, C2, SA>

The resulting type after applying the * operator

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

The method for the * operator

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

type Output = MatrixMul<N, D1, D1, C2, SA>

The resulting type after applying the * operator

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

The method for the * operator

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

type Output = MatrixMul<N, D1, D1, C2, SA>

The resulting type after applying the * operator

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

The method for the * operator

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

type Output = MatrixMul<N, D1, D1, C2, SA>

The resulting type after applying the * operator

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

The method for the * operator

impl<N, D: DimName, SA, SB> Mul<PointBase<N, D, SB>> for RotationBase<N, D, SA> where
    N: Scalar + Zero + ClosedAdd + ClosedMul,
    SA: Storage<N, D, D>,
    SB: Storage<N, D, U1>,
    SA::Alloc: Allocator<N, D, U1>,
    ShapeConstraint: AreMultipliable<D, D, D, U1>, 

type Output = PointMul<N, D, D, SA>

The resulting type after applying the * operator

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

The method for the * operator

impl<'a, N, D: DimName, SA, SB> Mul<PointBase<N, D, SB>> for &'a RotationBase<N, D, SA> where
    N: Scalar + Zero + ClosedAdd + ClosedMul,
    SA: Storage<N, D, D>,
    SB: Storage<N, D, U1>,
    SA::Alloc: Allocator<N, D, U1>,
    ShapeConstraint: AreMultipliable<D, D, D, U1>, 

type Output = PointMul<N, D, D, SA>

The resulting type after applying the * operator

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

The method for the * operator

impl<'b, N, D: DimName, SA, SB> Mul<&'b PointBase<N, D, SB>> for RotationBase<N, D, SA> where
    N: Scalar + Zero + ClosedAdd + ClosedMul,
    SA: Storage<N, D, D>,
    SB: Storage<N, D, U1>,
    SA::Alloc: Allocator<N, D, U1>,
    ShapeConstraint: AreMultipliable<D, D, D, U1>, 

type Output = PointMul<N, D, D, SA>

The resulting type after applying the * operator

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

The method for the * operator

impl<'a, 'b, N, D: DimName, SA, SB> Mul<&'b PointBase<N, D, SB>> for &'a RotationBase<N, D, SA> where
    N: Scalar + Zero + ClosedAdd + ClosedMul,
    SA: Storage<N, D, D>,
    SB: Storage<N, D, U1>,
    SA::Alloc: Allocator<N, D, U1>,
    ShapeConstraint: AreMultipliable<D, D, D, U1>, 

type Output = PointMul<N, D, D, SA>

The resulting type after applying the * operator

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

The method for the * operator

impl<N, D: DimName, SA, SB> MulAssign<RotationBase<N, D, SB>> for RotationBase<N, D, SA> where
    N: Scalar + Zero + ClosedAdd + ClosedMul,
    SA: OwnedStorage<N, D, D>,
    SB: Storage<N, D, D>,
    SA::Alloc: OwnedAllocator<N, D, D, SA>, 

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

The method for the *= operator

impl<'b, N, D: DimName, SA, SB> MulAssign<&'b RotationBase<N, D, SB>> for RotationBase<N, D, SA> where
    N: Scalar + Zero + ClosedAdd + ClosedMul,
    SA: OwnedStorage<N, D, D>,
    SB: Storage<N, D, D>,
    SA::Alloc: OwnedAllocator<N, D, D, SA>, 

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

The method for the *= operator

impl<N, D: DimName, SA, SB> DivAssign<RotationBase<N, D, SB>> for RotationBase<N, D, SA> where
    N: Scalar + Zero + ClosedAdd + ClosedMul,
    SA: OwnedStorage<N, D, D>,
    SB: Storage<N, D, D>,
    SA::Alloc: OwnedAllocator<N, D, D, SA>, 

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

The method for the /= operator

impl<'b, N, D: DimName, SA, SB> DivAssign<&'b RotationBase<N, D, SB>> for RotationBase<N, D, SA> where
    N: Scalar + Zero + ClosedAdd + ClosedMul,
    SA: OwnedStorage<N, D, D>,
    SB: Storage<N, D, D>,
    SA::Alloc: OwnedAllocator<N, D, D, SA>, 

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

The method for the /= operator

impl<N, D: DimName, S> Identity<Multiplicative> for RotationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, D>,
    S::Alloc: OwnedAllocator<N, D, D, S>, 

fn identity() -> Self

The identity element.

impl<N, D: DimName, S> Inverse<Multiplicative> for RotationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, D>,
    S::Alloc: OwnedAllocator<N, D, D, S>, 

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<N, D: DimName, S> AbstractMagma<Multiplicative> for RotationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, D>,
    S::Alloc: OwnedAllocator<N, D, D, S>, 

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

Performs an operation.

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

Performs specific operation.

impl<N, D: DimName, S> AbstractSemigroup<Multiplicative> for RotationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, D>,
    S::Alloc: OwnedAllocator<N, D, D, S>, 

fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
    Self: ApproxEq, 

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

fn prop_is_associative(args: (Self, Self, Self)) -> bool where
    Self: Eq, 

Returns true if associativity holds for the given arguments.

impl<N, D: DimName, S> AbstractMonoid<Multiplicative> for RotationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, D>,
    S::Alloc: OwnedAllocator<N, D, D, S>, 

fn prop_operating_identity_element_is_noop_approx(a: Self) -> bool where
    Self: ApproxEq, 

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

fn prop_operating_identity_element_is_noop(a: Self) -> bool where
    Self: Eq, 

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

impl<N, D: DimName, S> AbstractQuasigroup<Multiplicative> for RotationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, D>,
    S::Alloc: OwnedAllocator<N, D, D, S>, 

fn prop_inv_is_latin_square_approx(args: (Self, Self)) -> bool where
    Self: ApproxEq, 

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

fn prop_inv_is_latin_square(args: (Self, Self)) -> bool where
    Self: Eq, 

Returns true if latin squareness holds for the given arguments.

impl<N, D: DimName, S> AbstractLoop<Multiplicative> for RotationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, D>,
    S::Alloc: OwnedAllocator<N, D, D, S>, 

impl<N, D: DimName, S> AbstractGroup<Multiplicative> for RotationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, D>,
    S::Alloc: OwnedAllocator<N, D, D, S>, 

impl<N, D: DimName, SA, SB> Transformation<PointBase<N, D, SB>> for RotationBase<N, D, SA> where
    N: Real,
    SA: OwnedStorage<N, D, D>,
    SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
    SA::Alloc: OwnedAllocator<N, D, D, SA>,
    SB::Alloc: OwnedAllocator<N, D, U1, SB>, 

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

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

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

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

impl<N, D: DimName, SA, SB> ProjectiveTransformation<PointBase<N, D, SB>> for RotationBase<N, D, SA> where
    N: Real,
    SA: OwnedStorage<N, D, D>,
    SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
    SA::Alloc: OwnedAllocator<N, D, D, SA>,
    SB::Alloc: OwnedAllocator<N, D, U1, SB>, 

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

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

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

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

impl<N, D: DimName, SA, SB> AffineTransformation<PointBase<N, D, SB>> for RotationBase<N, D, SA> where
    N: Real,
    SA: OwnedStorage<N, D, D>,
    SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
    SA::Alloc: OwnedAllocator<N, D, D, SA>,
    SB::Alloc: OwnedAllocator<N, D, U1, SB>, 

type Rotation = Self

Type of the first rotation to be applied.

type NonUniformScaling = Id

Type of the non-uniform scaling to be applied.

type Translation = Id

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, D: DimName, SA, SB> Similarity<PointBase<N, D, SB>> for RotationBase<N, D, SA> where
    N: Real,
    SA: OwnedStorage<N, D, D>,
    SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
    SA::Alloc: OwnedAllocator<N, D, D, SA>,
    SB::Alloc: OwnedAllocator<N, D, U1, SB>, 

type Scaling = Id

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<N, D: DimName, SA, SB> Isometry<PointBase<N, D, SB>> for RotationBase<N, D, SA> where
    N: Real,
    SA: OwnedStorage<N, D, D>,
    SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
    SA::Alloc: OwnedAllocator<N, D, D, SA>,
    SB::Alloc: OwnedAllocator<N, D, U1, SB>, 

impl<N, D: DimName, SA, SB> DirectIsometry<PointBase<N, D, SB>> for RotationBase<N, D, SA> where
    N: Real,
    SA: OwnedStorage<N, D, D>,
    SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
    SA::Alloc: OwnedAllocator<N, D, D, SA>,
    SB::Alloc: OwnedAllocator<N, D, U1, SB>, 

impl<N, D: DimName, SA, SB> OrthogonalTransformation<PointBase<N, D, SB>> for RotationBase<N, D, SA> where
    N: Real,
    SA: OwnedStorage<N, D, D>,
    SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
    SA::Alloc: OwnedAllocator<N, D, D, SA>,
    SB::Alloc: OwnedAllocator<N, D, U1, SB>, 

impl<N, D: DimName, SA, SB> Rotation<PointBase<N, D, SB>> for RotationBase<N, D, SA> where
    N: Real,
    SA: OwnedStorage<N, D, D>,
    SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
    SA::Alloc: OwnedAllocator<N, D, D, SA>,
    SB::Alloc: OwnedAllocator<N, D, U1, SB>, 

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(
    _: &ColumnVector<N, D, SB>,
    _: &ColumnVector<N, D, SB>
) -> 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(
    _: &ColumnVector<N, D, SB>,
    _: &ColumnVector<N, D, SB>,
    _: N
) -> Option<Self>

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

impl<N1, N2, D: DimName, SA, SB> SubsetOf<RotationBase<N2, D, SB>> for RotationBase<N1, D, SA> where
    N1: Real,
    N2: Real + SupersetOf<N1>,
    SA: OwnedStorage<N1, D, D>,
    SB: OwnedStorage<N2, D, D>,
    SA::Alloc: OwnedAllocator<N1, D, D, SA>,
    SB::Alloc: OwnedAllocator<N2, D, D, SB>, 

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

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

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

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

unsafe fn from_superset_unchecked(rot: &RotationBase<N2, D, SB>) -> 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, SA, SB> SubsetOf<UnitQuaternionBase<N2, SB>> for RotationBase<N1, U3, SA> where
    N1: Real,
    N2: Real + SupersetOf<N1>,
    SA: OwnedStorage<N1, U3, U3>,
    SB: OwnedStorage<N2, U4, U1>,
    SA::Alloc: OwnedAllocator<N1, U3, U3, SA> + Allocator<N1, U4, U1> + Allocator<N1, U3, U1>,
    SB::Alloc: OwnedAllocator<N2, U4, U1, SB> + Allocator<N2, U3, U3>, 

fn to_superset(&self) -> UnitQuaternionBase<N2, SB>

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

fn is_in_subset(q: &UnitQuaternionBase<N2, SB>) -> bool

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

unsafe fn from_superset_unchecked(q: &UnitQuaternionBase<N2, SB>) -> 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, SA, SB, R> SubsetOf<IsometryBase<N2, D, SB, R>> for RotationBase<N1, D, SA> where
    N1: Real,
    N2: Real + SupersetOf<N1>,
    SA: OwnedStorage<N1, D, D>,
    SB: OwnedStorage<N2, D, U1>,
    R: AlgaRotation<PointBase<N2, D, SB>> + SupersetOf<RotationBase<N1, D, SA>>,
    SA::Alloc: OwnedAllocator<N1, D, D, SA>,
    SB::Alloc: OwnedAllocator<N2, D, U1, SB>, 

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

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

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

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

unsafe fn from_superset_unchecked(iso: &IsometryBase<N2, D, SB, 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: DimName, SA, SB, R> SubsetOf<SimilarityBase<N2, D, SB, R>> for RotationBase<N1, D, SA> where
    N1: Real,
    N2: Real + SupersetOf<N1>,
    SA: OwnedStorage<N1, D, D>,
    SB: OwnedStorage<N2, D, U1>,
    R: AlgaRotation<PointBase<N2, D, SB>> + SupersetOf<RotationBase<N1, D, SA>>,
    SA::Alloc: OwnedAllocator<N1, D, D, SA>,
    SB::Alloc: OwnedAllocator<N2, D, U1, SB>, 

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

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

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

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

unsafe fn from_superset_unchecked(sim: &SimilarityBase<N2, D, SB, 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, SA, SB, C> SubsetOf<TransformBase<N2, D, SB, C>> for RotationBase<N1, D, SA> where
    N1: Real,
    N2: Real + SupersetOf<N1>,
    SA: OwnedStorage<N1, D, D>,
    SB: OwnedStorage<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>,
    C: SuperTCategoryOf<TAffine>,
    D: DimNameAdd<U1>,
    SA::Alloc: OwnedAllocator<N1, D, D, SA> + Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>>,
    SB::Alloc: OwnedAllocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>, SB> + Allocator<N2, D, D> + Allocator<N2, U1, D>, 

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

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

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

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

unsafe fn from_superset_unchecked(t: &TransformBase<N2, D, SB, 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<N1, N2, D, SA, SB> SubsetOf<SquareMatrix<N2, DimNameSum<D, U1>, SB>> for RotationBase<N1, D, SA> where
    N1: Real,
    N2: Real + SupersetOf<N1>,
    SA: OwnedStorage<N1, D, D>,
    SB: OwnedStorage<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>,
    D: DimNameAdd<U1>,
    SA::Alloc: OwnedAllocator<N1, D, D, SA> + Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>>,
    SB::Alloc: OwnedAllocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>, SB> + Allocator<N2, D, D> + Allocator<N2, U1, D>, 

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

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

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

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

unsafe fn from_superset_unchecked(
    m: &SquareMatrix<N2, DimNameSum<D, U1>, SB>
) -> 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, S> Rand for RotationBase<N, U2, S> where
    N: Real + Rand,
    S: OwnedStorage<N, U2, U2>,
    S::Alloc: OwnedAllocator<N, U2, U2, S>, 

fn rand<R: Rng>(rng: &mut R) -> Self

Generates a random instance of this type using the specified source of randomness.

impl<N, S> Rand for RotationBase<N, U3, S> where
    N: Real + Rand,
    S: OwnedStorage<N, U3, U3>,
    S::Alloc: OwnedAllocator<N, U3, U3, S> + Allocator<N, U3, U1>, 

fn rand<R: Rng>(rng: &mut R) -> Self

Generates a random instance of this type using the specified source of randomness.

impl<'a, 'b, N, SA, SB> Mul<&'b UnitQuaternionBase<N, SB>> for &'a RotationBase<N, U3, SA> where
    N: Real,
    SA: Storage<N, U3, U3>,
    SB: Storage<N, U4, U1>,
    SA::Alloc: Allocator<N, U3, U1>,
    SB::Alloc: Allocator<N, U3, U1>, 

type Output = OwnedUnitQuaternionBase<N, SB::Alloc>

The resulting type after applying the * operator

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

The method for the * operator

impl<'a, N, SA, SB> Mul<UnitQuaternionBase<N, SB>> for &'a RotationBase<N, U3, SA> where
    N: Real,
    SA: Storage<N, U3, U3>,
    SB: Storage<N, U4, U1>,
    SA::Alloc: Allocator<N, U3, U1>,
    SB::Alloc: Allocator<N, U3, U1>, 

type Output = OwnedUnitQuaternionBase<N, SB::Alloc>

The resulting type after applying the * operator

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

The method for the * operator

impl<'b, N, SA, SB> Mul<&'b UnitQuaternionBase<N, SB>> for RotationBase<N, U3, SA> where
    N: Real,
    SA: Storage<N, U3, U3>,
    SB: Storage<N, U4, U1>,
    SA::Alloc: Allocator<N, U3, U1>,
    SB::Alloc: Allocator<N, U3, U1>, 

type Output = OwnedUnitQuaternionBase<N, SB::Alloc>

The resulting type after applying the * operator

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

The method for the * operator

impl<N, SA, SB> Mul<UnitQuaternionBase<N, SB>> for RotationBase<N, U3, SA> where
    N: Real,
    SA: Storage<N, U3, U3>,
    SB: Storage<N, U4, U1>,
    SA::Alloc: Allocator<N, U3, U1>,
    SB::Alloc: Allocator<N, U3, U1>, 

type Output = OwnedUnitQuaternionBase<N, SB::Alloc>

The resulting type after applying the * operator

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

The method for the * operator

impl<'a, 'b, N, SA, SB> Div<&'b UnitQuaternionBase<N, SB>> for &'a RotationBase<N, U3, SA> where
    N: Real,
    SA: Storage<N, U3, U3>,
    SB: Storage<N, U4, U1>,
    SA::Alloc: Allocator<N, U3, U1>,
    SB::Alloc: Allocator<N, U3, U1>, 

type Output = OwnedUnitQuaternionBase<N, SB::Alloc>

The resulting type after applying the / operator

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

The method for the / operator

impl<'a, N, SA, SB> Div<UnitQuaternionBase<N, SB>> for &'a RotationBase<N, U3, SA> where
    N: Real,
    SA: Storage<N, U3, U3>,
    SB: Storage<N, U4, U1>,
    SA::Alloc: Allocator<N, U3, U1>,
    SB::Alloc: Allocator<N, U3, U1>, 

type Output = OwnedUnitQuaternionBase<N, SB::Alloc>

The resulting type after applying the / operator

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

The method for the / operator

impl<'b, N, SA, SB> Div<&'b UnitQuaternionBase<N, SB>> for RotationBase<N, U3, SA> where
    N: Real,
    SA: Storage<N, U3, U3>,
    SB: Storage<N, U4, U1>,
    SA::Alloc: Allocator<N, U3, U1>,
    SB::Alloc: Allocator<N, U3, U1>, 

type Output = OwnedUnitQuaternionBase<N, SB::Alloc>

The resulting type after applying the / operator

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

The method for the / operator

impl<N, SA, SB> Div<UnitQuaternionBase<N, SB>> for RotationBase<N, U3, SA> where
    N: Real,
    SA: Storage<N, U3, U3>,
    SB: Storage<N, U4, U1>,
    SA::Alloc: Allocator<N, U3, U1>,
    SB::Alloc: Allocator<N, U3, U1>, 

type Output = OwnedUnitQuaternionBase<N, SB::Alloc>

The resulting type after applying the / operator

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

The method for the / operator

impl<N, S> Mul<UnitComplex<N>> for RotationBase<N, U2, S> where
    N: Real,
    S: Storage<N, U2, U2>, 

type Output = UnitComplex<N>

The resulting type after applying the * operator

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

The method for the * operator

impl<'a, N, S> Mul<UnitComplex<N>> for &'a RotationBase<N, U2, S> where
    N: Real,
    S: Storage<N, U2, U2>, 

type Output = UnitComplex<N>

The resulting type after applying the * operator

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

The method for the * operator

impl<'b, N, S> Mul<&'b UnitComplex<N>> for RotationBase<N, U2, S> where
    N: Real,
    S: Storage<N, U2, U2>, 

type Output = UnitComplex<N>

The resulting type after applying the * operator

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

The method for the * operator

impl<'a, 'b, N, S> Mul<&'b UnitComplex<N>> for &'a RotationBase<N, U2, S> where
    N: Real,
    S: Storage<N, U2, U2>, 

type Output = UnitComplex<N>

The resulting type after applying the * operator

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

The method for the * operator

impl<N, S> Div<UnitComplex<N>> for RotationBase<N, U2, S> where
    N: Real,
    S: Storage<N, U2, U2>, 

type Output = UnitComplex<N>

The resulting type after applying the / operator

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

The method for the / operator

impl<'a, N, S> Div<UnitComplex<N>> for &'a RotationBase<N, U2, S> where
    N: Real,
    S: Storage<N, U2, U2>, 

type Output = UnitComplex<N>

The resulting type after applying the / operator

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

The method for the / operator

impl<'b, N, S> Div<&'b UnitComplex<N>> for RotationBase<N, U2, S> where
    N: Real,
    S: Storage<N, U2, U2>, 

type Output = UnitComplex<N>

The resulting type after applying the / operator

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

The method for the / operator

impl<'a, 'b, N, S> Div<&'b UnitComplex<N>> for &'a RotationBase<N, U2, S> where
    N: Real,
    S: Storage<N, U2, U2>, 

type Output = UnitComplex<N>

The resulting type after applying the / operator

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

The method for the / operator

impl<N: Real, S> MulAssign<UnitComplex<N>> for RotationBase<N, U2, S> where
    S: OwnedStorage<N, U2, U2>,
    S::Alloc: OwnedAllocator<N, U2, U2, S>, 

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

The method for the *= operator

impl<'b, N: Real, S: Storage<N, U2, U2>> MulAssign<&'b UnitComplex<N>> for RotationBase<N, U2, S> where
    S: OwnedStorage<N, U2, U2>,
    S::Alloc: OwnedAllocator<N, U2, U2, S>, 

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

The method for the *= operator

impl<N: Real, S> DivAssign<UnitComplex<N>> for RotationBase<N, U2, S> where
    S: OwnedStorage<N, U2, U2>,
    S::Alloc: OwnedAllocator<N, U2, U2, S>, 

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

The method for the /= operator

impl<'b, N: Real, S: Storage<N, U2, U2>> DivAssign<&'b UnitComplex<N>> for RotationBase<N, U2, S> where
    S: OwnedStorage<N, U2, U2>,
    S::Alloc: OwnedAllocator<N, U2, U2, S>, 

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

The method for the /= operator

impl<N, D: DimName, SA, SB> Mul<TranslationBase<N, D, SB>> for RotationBase<N, D, SA> where
    N: Real,
    SA: OwnedStorage<N, D, D>,
    SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
    SA::Alloc: OwnedAllocator<N, D, D, SA>,
    SB::Alloc: OwnedAllocator<N, D, U1, SB>, 

type Output = IsometryBase<N, D, SB, RotationBase<N, D, SA>>

The resulting type after applying the * operator

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

The method for the * operator

impl<'a, N, D: DimName, SA, SB> Mul<TranslationBase<N, D, SB>> for &'a RotationBase<N, D, SA> where
    N: Real,
    SA: OwnedStorage<N, D, D>,
    SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
    SA::Alloc: OwnedAllocator<N, D, D, SA>,
    SB::Alloc: OwnedAllocator<N, D, U1, SB>, 

type Output = IsometryBase<N, D, SB, RotationBase<N, D, SA>>

The resulting type after applying the * operator

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

The method for the * operator

impl<'b, N, D: DimName, SA, SB> Mul<&'b TranslationBase<N, D, SB>> for RotationBase<N, D, SA> where
    N: Real,
    SA: OwnedStorage<N, D, D>,
    SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
    SA::Alloc: OwnedAllocator<N, D, D, SA>,
    SB::Alloc: OwnedAllocator<N, D, U1, SB>, 

type Output = IsometryBase<N, D, SB, RotationBase<N, D, SA>>

The resulting type after applying the * operator

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

The method for the * operator

impl<'a, 'b, N, D: DimName, SA, SB> Mul<&'b TranslationBase<N, D, SB>> for &'a RotationBase<N, D, SA> where
    N: Real,
    SA: OwnedStorage<N, D, D>,
    SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
    SA::Alloc: OwnedAllocator<N, D, D, SA>,
    SB::Alloc: OwnedAllocator<N, D, U1, SB>, 

type Output = IsometryBase<N, D, SB, RotationBase<N, D, SA>>

The resulting type after applying the * operator

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

The method for the * operator

impl<N, D: DimName, SA, SB> Mul<IsometryBase<N, D, SB, RotationBase<N, D, SA>>> for RotationBase<N, D, SA> where
    N: Real,
    SA: OwnedStorage<N, D, D>,
    SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
    SA::Alloc: OwnedAllocator<N, D, D, SA>,
    SB::Alloc: OwnedAllocator<N, D, U1, SB>, 

type Output = IsometryBase<N, D, SB, RotationBase<N, D, SA>>

The resulting type after applying the * operator

fn mul(
    self,
    right: IsometryBase<N, D, SB, RotationBase<N, D, SA>>
) -> Self::Output

The method for the * operator

impl<'a, N, D: DimName, SA, SB> Mul<IsometryBase<N, D, SB, RotationBase<N, D, SA>>> for &'a RotationBase<N, D, SA> where
    N: Real,
    SA: OwnedStorage<N, D, D>,
    SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
    SA::Alloc: OwnedAllocator<N, D, D, SA>,
    SB::Alloc: OwnedAllocator<N, D, U1, SB>, 

type Output = IsometryBase<N, D, SB, RotationBase<N, D, SA>>

The resulting type after applying the * operator

fn mul(
    self,
    right: IsometryBase<N, D, SB, RotationBase<N, D, SA>>
) -> Self::Output

The method for the * operator

impl<'b, N, D: DimName, SA, SB> Mul<&'b IsometryBase<N, D, SB, RotationBase<N, D, SA>>> for RotationBase<N, D, SA> where
    N: Real,
    SA: OwnedStorage<N, D, D>,
    SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
    SA::Alloc: OwnedAllocator<N, D, D, SA>,
    SB::Alloc: OwnedAllocator<N, D, U1, SB>, 

type Output = IsometryBase<N, D, SB, RotationBase<N, D, SA>>

The resulting type after applying the * operator

fn mul(
    self,
    right: &'b IsometryBase<N, D, SB, RotationBase<N, D, SA>>
) -> Self::Output

The method for the * operator

impl<'a, 'b, N, D: DimName, SA, SB> Mul<&'b IsometryBase<N, D, SB, RotationBase<N, D, SA>>> for &'a RotationBase<N, D, SA> where
    N: Real,
    SA: OwnedStorage<N, D, D>,
    SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
    SA::Alloc: OwnedAllocator<N, D, D, SA>,
    SB::Alloc: OwnedAllocator<N, D, U1, SB>, 

type Output = IsometryBase<N, D, SB, RotationBase<N, D, SA>>

The resulting type after applying the * operator

fn mul(
    self,
    right: &'b IsometryBase<N, D, SB, RotationBase<N, D, SA>>
) -> Self::Output

The method for the * operator

impl<N, D: DimName, SA, SB> Div<IsometryBase<N, D, SB, RotationBase<N, D, SA>>> for RotationBase<N, D, SA> where
    N: Real,
    SA: OwnedStorage<N, D, D>,
    SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
    SA::Alloc: OwnedAllocator<N, D, D, SA>,
    SB::Alloc: OwnedAllocator<N, D, U1, SB>, 

type Output = IsometryBase<N, D, SB, RotationBase<N, D, SA>>

The resulting type after applying the / operator

fn div(
    self,
    right: IsometryBase<N, D, SB, RotationBase<N, D, SA>>
) -> Self::Output

The method for the / operator

impl<'a, N, D: DimName, SA, SB> Div<IsometryBase<N, D, SB, RotationBase<N, D, SA>>> for &'a RotationBase<N, D, SA> where
    N: Real,
    SA: OwnedStorage<N, D, D>,
    SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
    SA::Alloc: OwnedAllocator<N, D, D, SA>,
    SB::Alloc: OwnedAllocator<N, D, U1, SB>, 

type Output = IsometryBase<N, D, SB, RotationBase<N, D, SA>>

The resulting type after applying the / operator

fn div(
    self,
    right: IsometryBase<N, D, SB, RotationBase<N, D, SA>>
) -> Self::Output

The method for the / operator

impl<'b, N, D: DimName, SA, SB> Div<&'b IsometryBase<N, D, SB, RotationBase<N, D, SA>>> for RotationBase<N, D, SA> where
    N: Real,
    SA: OwnedStorage<N, D, D>,
    SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
    SA::Alloc: OwnedAllocator<N, D, D, SA>,
    SB::Alloc: OwnedAllocator<N, D, U1, SB>, 

type Output = IsometryBase<N, D, SB, RotationBase<N, D, SA>>

The resulting type after applying the / operator

fn div(
    self,
    right: &'b IsometryBase<N, D, SB, RotationBase<N, D, SA>>
) -> Self::Output

The method for the / operator

impl<'a, 'b, N, D: DimName, SA, SB> Div<&'b IsometryBase<N, D, SB, RotationBase<N, D, SA>>> for &'a RotationBase<N, D, SA> where
    N: Real,
    SA: OwnedStorage<N, D, D>,
    SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
    SA::Alloc: OwnedAllocator<N, D, D, SA>,
    SB::Alloc: OwnedAllocator<N, D, U1, SB>, 

type Output = IsometryBase<N, D, SB, RotationBase<N, D, SA>>

The resulting type after applying the / operator

fn div(
    self,
    right: &'b IsometryBase<N, D, SB, RotationBase<N, D, SA>>
) -> Self::Output

The method for the / operator

impl<N, D: DimName, SA, SB> Mul<SimilarityBase<N, D, SB, RotationBase<N, D, SA>>> for RotationBase<N, D, SA> where
    N: Real,
    SA: OwnedStorage<N, D, D>,
    SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
    SA::Alloc: OwnedAllocator<N, D, D, SA>,
    SB::Alloc: OwnedAllocator<N, D, U1, SB>, 

type Output = SimilarityBase<N, D, SB, RotationBase<N, D, SA>>

The resulting type after applying the * operator

fn mul(
    self,
    right: SimilarityBase<N, D, SB, RotationBase<N, D, SA>>
) -> Self::Output

The method for the * operator

impl<'a, N, D: DimName, SA, SB> Mul<SimilarityBase<N, D, SB, RotationBase<N, D, SA>>> for &'a RotationBase<N, D, SA> where
    N: Real,
    SA: OwnedStorage<N, D, D>,
    SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
    SA::Alloc: OwnedAllocator<N, D, D, SA>,
    SB::Alloc: OwnedAllocator<N, D, U1, SB>, 

type Output = SimilarityBase<N, D, SB, RotationBase<N, D, SA>>

The resulting type after applying the * operator

fn mul(
    self,
    right: SimilarityBase<N, D, SB, RotationBase<N, D, SA>>
) -> Self::Output

The method for the * operator

impl<'b, N, D: DimName, SA, SB> Mul<&'b SimilarityBase<N, D, SB, RotationBase<N, D, SA>>> for RotationBase<N, D, SA> where
    N: Real,
    SA: OwnedStorage<N, D, D>,
    SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
    SA::Alloc: OwnedAllocator<N, D, D, SA>,
    SB::Alloc: OwnedAllocator<N, D, U1, SB>, 

type Output = SimilarityBase<N, D, SB, RotationBase<N, D, SA>>

The resulting type after applying the * operator

fn mul(
    self,
    right: &'b SimilarityBase<N, D, SB, RotationBase<N, D, SA>>
) -> Self::Output

The method for the * operator

impl<'a, 'b, N, D: DimName, SA, SB> Mul<&'b SimilarityBase<N, D, SB, RotationBase<N, D, SA>>> for &'a RotationBase<N, D, SA> where
    N: Real,
    SA: OwnedStorage<N, D, D>,
    SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
    SA::Alloc: OwnedAllocator<N, D, D, SA>,
    SB::Alloc: OwnedAllocator<N, D, U1, SB>, 

type Output = SimilarityBase<N, D, SB, RotationBase<N, D, SA>>

The resulting type after applying the * operator

fn mul(
    self,
    right: &'b SimilarityBase<N, D, SB, RotationBase<N, D, SA>>
) -> Self::Output

The method for the * operator

impl<N, D: DimName, SA, SB> Div<SimilarityBase<N, D, SB, RotationBase<N, D, SA>>> for RotationBase<N, D, SA> where
    N: Real,
    SA: OwnedStorage<N, D, D>,
    SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
    SA::Alloc: OwnedAllocator<N, D, D, SA>,
    SB::Alloc: OwnedAllocator<N, D, U1, SB>, 

type Output = SimilarityBase<N, D, SB, RotationBase<N, D, SA>>

The resulting type after applying the / operator

fn div(
    self,
    right: SimilarityBase<N, D, SB, RotationBase<N, D, SA>>
) -> Self::Output

The method for the / operator

impl<'a, N, D: DimName, SA, SB> Div<SimilarityBase<N, D, SB, RotationBase<N, D, SA>>> for &'a RotationBase<N, D, SA> where
    N: Real,
    SA: OwnedStorage<N, D, D>,
    SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
    SA::Alloc: OwnedAllocator<N, D, D, SA>,
    SB::Alloc: OwnedAllocator<N, D, U1, SB>, 

type Output = SimilarityBase<N, D, SB, RotationBase<N, D, SA>>

The resulting type after applying the / operator

fn div(
    self,
    right: SimilarityBase<N, D, SB, RotationBase<N, D, SA>>
) -> Self::Output

The method for the / operator

impl<'b, N, D: DimName, SA, SB> Div<&'b SimilarityBase<N, D, SB, RotationBase<N, D, SA>>> for RotationBase<N, D, SA> where
    N: Real,
    SA: OwnedStorage<N, D, D>,
    SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
    SA::Alloc: OwnedAllocator<N, D, D, SA>,
    SB::Alloc: OwnedAllocator<N, D, U1, SB>, 

type Output = SimilarityBase<N, D, SB, RotationBase<N, D, SA>>

The resulting type after applying the / operator

fn div(
    self,
    right: &'b SimilarityBase<N, D, SB, RotationBase<N, D, SA>>
) -> Self::Output

The method for the / operator

impl<'a, 'b, N, D: DimName, SA, SB> Div<&'b SimilarityBase<N, D, SB, RotationBase<N, D, SA>>> for &'a RotationBase<N, D, SA> where
    N: Real,
    SA: OwnedStorage<N, D, D>,
    SB: OwnedStorage<N, D, U1, Alloc = SA::Alloc>,
    SA::Alloc: OwnedAllocator<N, D, D, SA>,
    SB::Alloc: OwnedAllocator<N, D, U1, SB>, 

type Output = SimilarityBase<N, D, SB, RotationBase<N, D, SA>>

The resulting type after applying the / operator

fn div(
    self,
    right: &'b SimilarityBase<N, D, SB, RotationBase<N, D, SA>>
) -> Self::Output

The method for the / operator

impl<N, D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, SA, SB> Mul<TransformBase<N, D, SB, C>> for RotationBase<N, D, SA> where
    N: Scalar + Zero + ClosedAdd + ClosedMul + One,
    SA: Storage<N, D, D>,
    SB: Storage<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
    SA::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>, 

type Output = OwnedTransform<N, D, SA::Alloc, C::Representative>

The resulting type after applying the * operator

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

The method for the * operator

impl<'a, N, D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, SA, SB> Mul<TransformBase<N, D, SB, C>> for &'a RotationBase<N, D, SA> where
    N: Scalar + Zero + ClosedAdd + ClosedMul + One,
    SA: Storage<N, D, D>,
    SB: Storage<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
    SA::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>, 

type Output = OwnedTransform<N, D, SA::Alloc, C::Representative>

The resulting type after applying the * operator

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

The method for the * operator

impl<'b, N, D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, SA, SB> Mul<&'b TransformBase<N, D, SB, C>> for RotationBase<N, D, SA> where
    N: Scalar + Zero + ClosedAdd + ClosedMul + One,
    SA: Storage<N, D, D>,
    SB: Storage<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
    SA::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>, 

type Output = OwnedTransform<N, D, SA::Alloc, C::Representative>

The resulting type after applying the * operator

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

The method for the * operator

impl<'a, 'b, N, D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, SA, SB> Mul<&'b TransformBase<N, D, SB, C>> for &'a RotationBase<N, D, SA> where
    N: Scalar + Zero + ClosedAdd + ClosedMul + One,
    SA: Storage<N, D, D>,
    SB: Storage<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
    SA::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>, 

type Output = OwnedTransform<N, D, SA::Alloc, C::Representative>

The resulting type after applying the * operator

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

The method for the * operator

impl<N, D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, SA, SB> Div<TransformBase<N, D, SB, C>> for RotationBase<N, D, SA> where
    N: Scalar + Zero + ClosedAdd + ClosedMul + One,
    SA: Storage<N, D, D>,
    SB: Storage<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
    SA::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>, 

type Output = OwnedTransform<N, D, SA::Alloc, C::Representative>

The resulting type after applying the / operator

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

The method for the / operator

impl<'a, N, D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, SA, SB> Div<TransformBase<N, D, SB, C>> for &'a RotationBase<N, D, SA> where
    N: Scalar + Zero + ClosedAdd + ClosedMul + One,
    SA: Storage<N, D, D>,
    SB: Storage<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
    SA::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>, 

type Output = OwnedTransform<N, D, SA::Alloc, C::Representative>

The resulting type after applying the / operator

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

The method for the / operator

impl<'b, N, D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, SA, SB> Div<&'b TransformBase<N, D, SB, C>> for RotationBase<N, D, SA> where
    N: Scalar + Zero + ClosedAdd + ClosedMul + One,
    SA: Storage<N, D, D>,
    SB: Storage<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
    SA::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>, 

type Output = OwnedTransform<N, D, SA::Alloc, C::Representative>

The resulting type after applying the / operator

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

The method for the / operator

impl<'a, 'b, N, D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, SA, SB> Div<&'b TransformBase<N, D, SB, C>> for &'a RotationBase<N, D, SA> where
    N: Scalar + Zero + ClosedAdd + ClosedMul + One,
    SA: Storage<N, D, D>,
    SB: Storage<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
    SA::Alloc: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>, 

type Output = OwnedTransform<N, D, SA::Alloc, C::Representative>

The resulting type after applying the / operator

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

The method for the / operator