Struct nalgebra::geometry::Translation

#[repr(C)]
pub struct Translation<N: Scalar, D: DimName> where
    DefaultAllocator: Allocator<N, D>,  {
    pub vector: VectorN<N, D>,
}

A translation.

Fields

vector: VectorN<N, D>

The translation coordinates, i.e., how much is added to a point’s coordinates when it is translated.

Implementations

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

pub fn from_vector(vector: VectorN<N, D>) -> Translation<N, D>

👎 Deprecated:

Use ::from instead.

Creates a new translation from the given vector.

pub fn inverse(&self) -> Translation<N, D> where
    N: ClosedNeg, 

Inverts self.

Example

let t = Translation3::new(1.0, 2.0, 3.0);
assert_eq!(t * t.inverse(), Translation3::identity());
assert_eq!(t.inverse() * t, Translation3::identity());

// Work in all dimensions.
let t = Translation2::new(1.0, 2.0);
assert_eq!(t * t.inverse(), Translation2::identity());
assert_eq!(t.inverse() * t, Translation2::identity());

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 translation into its equivalent homogeneous transformation matrix.

Example

let t = Translation3::new(10.0, 20.0, 30.0);
let expected = Matrix4::new(1.0, 0.0, 0.0, 10.0,
                            0.0, 1.0, 0.0, 20.0,
                            0.0, 0.0, 1.0, 30.0,
                            0.0, 0.0, 0.0, 1.0);
assert_eq!(t.to_homogeneous(), expected);

let t = Translation2::new(10.0, 20.0);
let expected = Matrix3::new(1.0, 0.0, 10.0,
                            0.0, 1.0, 20.0,
                            0.0, 0.0, 1.0);
assert_eq!(t.to_homogeneous(), expected);

pub fn inverse_mut(&mut self) where
    N: ClosedNeg, 

Inverts self in-place.

Example

let t = Translation3::new(1.0, 2.0, 3.0);
let mut inv_t = Translation3::new(1.0, 2.0, 3.0);
inv_t.inverse_mut();
assert_eq!(t * inv_t, Translation3::identity());
assert_eq!(inv_t * t, Translation3::identity());

// Work in all dimensions.
let t = Translation2::new(1.0, 2.0);
let mut inv_t = Translation2::new(1.0, 2.0);
inv_t.inverse_mut();
assert_eq!(t * inv_t, Translation2::identity());
assert_eq!(inv_t * t, Translation2::identity());

impl<N: Scalar + ClosedAdd, D: DimName> Translation<N, D> where
    DefaultAllocator: Allocator<N, D>, 

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

Translate the given point.

This is the same as the multiplication self * pt.

Example

let t = Translation3::new(1.0, 2.0, 3.0);
let transformed_point = t.transform_point(&Point3::new(4.0, 5.0, 6.0));
assert_eq!(transformed_point, Point3::new(5.0, 7.0, 9.0));

impl<N: Scalar + ClosedSub, D: DimName> Translation<N, D> where
    DefaultAllocator: Allocator<N, D>, 

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

Translate the given point by the inverse of this translation.

Example

let t = Translation3::new(1.0, 2.0, 3.0);
let transformed_point = t.inverse_transform_point(&Point3::new(4.0, 5.0, 6.0));
assert_eq!(transformed_point, Point3::new(3.0, 3.0, 3.0));

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

pub fn identity() -> Translation<N, D> where
    N: Zero, 

Creates a new identity translation.

Example

let t = Translation2::identity();
let p = Point2::new(1.0, 2.0);
assert_eq!(t * p, p);

// Works in all dimensions.
let t = Translation3::identity();
let p = Point3::new(1.0, 2.0, 3.0);
assert_eq!(t * p, p);

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

Cast the components of self to another type.

Example

let tra = Translation2::new(1.0f64, 2.0);
let tra2 = tra.cast::<f32>();
assert_eq!(tra2, Translation2::new(1.0f32, 2.0));

impl<N: Scalar> Translation<N, U1> where
    DefaultAllocator: Allocator<N, U1>, 

pub fn new(x: N) -> Self

Initializes this translation from its components.

Example

let t = Translation1::new(1.0);
assert!(t.vector.x == 1.0);

impl<N: Scalar> Translation<N, U2> where
    DefaultAllocator: Allocator<N, U2>, 

pub fn new(x: N, y: N) -> Self

Initializes this translation from its components.

Example

let t = Translation2::new(1.0, 2.0);
assert!(t.vector.x == 1.0 && t.vector.y == 2.0);

impl<N: Scalar> Translation<N, U3> where
    DefaultAllocator: Allocator<N, U3>, 

pub fn new(x: N, y: N, z: N) -> Self

Initializes this translation from its components.

Example

let t = Translation3::new(1.0, 2.0, 3.0);
assert!(t.vector.x == 1.0 && t.vector.y == 2.0 && t.vector.z == 3.0);

impl<N: Scalar> Translation<N, U4> where
    DefaultAllocator: Allocator<N, U4>, 

pub fn new(x: N, y: N, z: N, w: N) -> Self

Initializes this translation from its components.

Example

let t = Translation4::new(1.0, 2.0, 3.0, 4.0);
assert!(t.vector.x == 1.0 && t.vector.y == 2.0 && t.vector.z == 3.0 && t.vector.w == 4.0);

impl<N: Scalar> Translation<N, U5> where
    DefaultAllocator: Allocator<N, U5>, 

pub fn new(x: N, y: N, z: N, w: N, a: N) -> Self

Initializes this translation from its components.

Example

let t = Translation5::new(1.0, 2.0, 3.0, 4.0, 5.0);
assert!(t.vector.x == 1.0 && t.vector.y == 2.0 && t.vector.z == 3.0 && t.vector.w == 4.0 && t.vector.a == 5.0);

impl<N: Scalar> Translation<N, U6> where
    DefaultAllocator: Allocator<N, U6>, 

pub fn new(x: N, y: N, z: N, w: N, a: N, b: N) -> Self

Initializes this translation from its components.

Example

let t = Translation6::new(1.0, 2.0, 3.0, 4.0, 5.0, 6.0);
assert!(t.vector.x == 1.0 && t.vector.y == 2.0 && t.vector.z == 3.0 && t.vector.w == 4.0 && t.vector.a == 5.0 && t.vector.b == 6.0);

Trait Implementations

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

type Epsilon = N::Epsilon

Used for specifying relative comparisons.

fn default_epsilon() -> Self::Epsilon

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

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

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

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

The inverse of AbsDiffEq::abs_diff_eq.

impl<N: Scalar, D: DimName> Clone for Translation<N, D> where
    DefaultAllocator: Allocator<N, D>,
    Owned<N, D>: 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 Translation<N, D> where
    DefaultAllocator: Allocator<N, D>, 

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

Formats the value using the given formatter.

impl<N: Scalar> Deref for Translation<N, U1> where
    DefaultAllocator: Allocator<N, U1>, 

type Target = X<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar> Deref for Translation<N, U2> where
    DefaultAllocator: Allocator<N, U2>, 

type Target = XY<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar> Deref for Translation<N, U3> where
    DefaultAllocator: Allocator<N, U3>, 

type Target = XYZ<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar> Deref for Translation<N, U4> where
    DefaultAllocator: Allocator<N, U4>, 

type Target = XYZW<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar> Deref for Translation<N, U5> where
    DefaultAllocator: Allocator<N, U5>, 

type Target = XYZWA<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar> Deref for Translation<N, U6> where
    DefaultAllocator: Allocator<N, U6>, 

type Target = XYZWAB<N>

The resulting type after dereferencing.

fn deref(&self) -> &Self::Target

Dereferences the value.

impl<N: Scalar> DerefMut for Translation<N, U1> where
    DefaultAllocator: Allocator<N, U1>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar> DerefMut for Translation<N, U2> where
    DefaultAllocator: Allocator<N, U2>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar> DerefMut for Translation<N, U3> where
    DefaultAllocator: Allocator<N, U3>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar> DerefMut for Translation<N, U4> where
    DefaultAllocator: Allocator<N, U4>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar> DerefMut for Translation<N, U5> where
    DefaultAllocator: Allocator<N, U5>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar> DerefMut for Translation<N, U6> where
    DefaultAllocator: Allocator<N, U6>, 

fn deref_mut(&mut self) -> &mut Self::Target

Mutably dereferences the value.

impl<N: Scalar + Display, D: DimName> Display for Translation<N, D> where
    DefaultAllocator: Allocator<N, D> + Allocator<usize, D>, 

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

Formats the value using the given formatter.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, 'b, N, D: DimName> Div<&'b Translation<N, D>> for &'a Translation<N, D> where
    N: Scalar + ClosedSub,
    DefaultAllocator: Allocator<N, D, U1> + SameShapeAllocator<N, D, U1, D, U1>,
    ShapeConstraint: SameNumberOfRows<D, D, Representative = D> + SameNumberOfColumns<U1, U1>, 

type Output = Translation<N, D>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'b, N, D: DimName> Div<&'b Translation<N, D>> for Translation<N, D> where
    N: Scalar + ClosedSub,
    DefaultAllocator: Allocator<N, D, U1> + SameShapeAllocator<N, D, U1, D, U1>,
    ShapeConstraint: SameNumberOfRows<D, D, Representative = D> + SameNumberOfColumns<U1, U1>, 

type Output = Translation<N, D>

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, 'b, N: SimdRealField> Div<&'b Translation<N, U3>> for &'a UnitDualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>, 

type Output = UnitDualQuaternion<N>

The resulting type after applying the / operator.

fn div(self, rhs: &'b Translation3<N>) -> Self::Output

Performs the / operation.

impl<'b, N: SimdRealField> Div<&'b Translation<N, U3>> for UnitDualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U3>, 

type Output = UnitDualQuaternion<N>

The resulting type after applying the / operator.

fn div(self, rhs: &'b Translation3<N>) -> Self::Output

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, N, D: DimName> Div<Translation<N, D>> for &'a Translation<N, D> where
    N: Scalar + ClosedSub,
    DefaultAllocator: Allocator<N, D, U1> + SameShapeAllocator<N, D, U1, D, U1>,
    ShapeConstraint: SameNumberOfRows<D, D, Representative = D> + SameNumberOfColumns<U1, U1>, 

type Output = Translation<N, D>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<N, D: DimName> Div<Translation<N, D>> for Translation<N, D> where
    N: Scalar + ClosedSub,
    DefaultAllocator: Allocator<N, D, U1> + SameShapeAllocator<N, D, U1, D, U1>,
    ShapeConstraint: SameNumberOfRows<D, D, Representative = D> + SameNumberOfColumns<U1, U1>, 

type Output = Translation<N, D>

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, N: SimdRealField> Div<Translation<N, U3>> for &'a UnitDualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U3>, 

type Output = UnitDualQuaternion<N>

The resulting type after applying the / operator.

fn div(self, rhs: Translation3<N>) -> Self::Output

Performs the / operation.

impl<N: SimdRealField> Div<Translation<N, U3>> for UnitDualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U3>, 

type Output = UnitDualQuaternion<N>

The resulting type after applying the / operator.

fn div(self, rhs: Translation3<N>) -> Self::Output

Performs the / operation.

impl<'b, N, D: DimName> DivAssign<&'b Translation<N, D>> for Translation<N, D> where
    N: Scalar + ClosedSub,
    DefaultAllocator: Allocator<N, D, U1>,
    ShapeConstraint: SameNumberOfRows<D, D> + SameNumberOfColumns<U1, U1>, 

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

Performs the /= operation.

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

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

Performs the /= operation.

impl<'b, N: SimdRealField> DivAssign<&'b Translation<N, U3>> for UnitDualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

fn div_assign(&mut self, rhs: &'b Translation3<N>)

Performs the /= operation.

impl<N, D: DimName> DivAssign<Translation<N, D>> for Translation<N, D> where
    N: Scalar + ClosedSub,
    DefaultAllocator: Allocator<N, D, U1>,
    ShapeConstraint: SameNumberOfRows<D, D> + SameNumberOfColumns<U1, U1>, 

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

Performs the /= operation.

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

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

Performs the /= operation.

impl<N: SimdRealField> DivAssign<Translation<N, U3>> for UnitDualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

fn div_assign(&mut self, rhs: Translation3<N>)

Performs the /= operation.

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

fn from(arr: [Translation<N::Element, D>; 16]) -> Self

Performs the conversion.

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

fn from(arr: [Translation<N::Element, D>; 2]) -> Self

Performs the conversion.

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

fn from(arr: [Translation<N::Element, D>; 4]) -> Self

Performs the conversion.

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

fn from(arr: [Translation<N::Element, D>; 8]) -> Self

Performs the conversion.

impl<N: Scalar, D: DimName> From<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>> for Translation<N, D> where
    DefaultAllocator: Allocator<N, D>, 

fn from(vector: VectorN<N, D>) -> Self

Performs the conversion.

impl<N: Scalar + Zero + One, D: DimName> From<Translation<N, D>> for MatrixN<N, DimNameSum<D, U1>> where
    D: DimNameAdd<U1>,
    DefaultAllocator: Allocator<N, D> + Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>, 

fn from(t: Translation<N, D>) -> Self

Performs the conversion.

impl<N: SimdRealField, D: DimName, R: AbstractRotation<N, D>> From<Translation<N, D>> for Isometry<N, D, R> where
    DefaultAllocator: Allocator<N, D>, 

fn from(tra: Translation<N, D>) -> Self

Performs the conversion.

impl<N: Scalar + Hash, D: DimName + Hash> Hash for Translation<N, D> where
    DefaultAllocator: Allocator<N, D>,
    Owned<N, D>: Hash, 

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

Feeds this value into the given Hasher.

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

Feeds a slice of this type into the given Hasher.

impl<'b, N: SimdRealField, D: DimName, R> Mul<&'b Isometry<N, D, R>> for Translation<N, D> where
    N::Element: SimdRealField,
    R: AbstractRotation<N, D>,
    DefaultAllocator: Allocator<N, D>, 

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b, N: SimdRealField, D: DimName, R> Mul<&'b Isometry<N, D, R>> for &'a Translation<N, D> where
    N::Element: SimdRealField,
    R: AbstractRotation<N, D>,
    DefaultAllocator: Allocator<N, D>, 

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b, N, D: DimName> Mul<&'b Point<N, D>> for &'a Translation<N, D> where
    N: Scalar + ClosedAdd,
    DefaultAllocator: Allocator<N, D, U1> + SameShapeAllocator<N, D, U1, D, U1>,
    ShapeConstraint: SameNumberOfRows<D, D, Representative = D> + SameNumberOfColumns<U1, 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 Translation<N, D> where
    N: Scalar + ClosedAdd,
    DefaultAllocator: Allocator<N, D, U1> + SameShapeAllocator<N, D, U1, D, U1>,
    ShapeConstraint: SameNumberOfRows<D, D, Representative = D> + SameNumberOfColumns<U1, 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: SimdRealField, D: DimName> Mul<&'b Rotation<N, D>> for Translation<N, D> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, N: SimdRealField, D: DimName, R> Mul<&'b Similarity<N, D, R>> for Translation<N, D> where
    N::Element: SimdRealField,
    R: AbstractRotation<N, D>,
    DefaultAllocator: Allocator<N, D>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b, N: SimdRealField, D: DimName, R> Mul<&'b Similarity<N, D, R>> for &'a Translation<N, D> where
    N::Element: SimdRealField,
    R: AbstractRotation<N, D>,
    DefaultAllocator: Allocator<N, D>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b, N, D: DimName> Mul<&'b Translation<N, D>> for &'a Translation<N, D> where
    N: Scalar + ClosedAdd,
    DefaultAllocator: Allocator<N, D, U1> + SameShapeAllocator<N, D, U1, D, U1>,
    ShapeConstraint: SameNumberOfRows<D, D, Representative = D> + SameNumberOfColumns<U1, U1>, 

type Output = Translation<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, D: DimName> Mul<&'b Translation<N, D>> for Translation<N, D> where
    N: Scalar + ClosedAdd,
    DefaultAllocator: Allocator<N, D, U1> + SameShapeAllocator<N, D, U1, D, U1>,
    ShapeConstraint: SameNumberOfRows<D, D, Representative = D> + SameNumberOfColumns<U1, U1>, 

type Output = Translation<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, N: SimdRealField, D: DimName, R> Mul<&'b Translation<N, D>> for Isometry<N, D, R> where
    N::Element: SimdRealField,
    R: AbstractRotation<N, D>,
    DefaultAllocator: Allocator<N, D>, 

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b, N: SimdRealField, D: DimName, R> Mul<&'b Translation<N, D>> for &'a Isometry<N, D, R> where
    N::Element: SimdRealField,
    R: AbstractRotation<N, D>,
    DefaultAllocator: Allocator<N, D>, 

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, N: SimdRealField, D: DimName, R> Mul<&'b Translation<N, D>> for Similarity<N, D, R> where
    N::Element: SimdRealField,
    R: AbstractRotation<N, D>,
    DefaultAllocator: Allocator<N, D>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b, N: SimdRealField, D: DimName, R> Mul<&'b Translation<N, D>> for &'a Similarity<N, D, R> where
    N::Element: SimdRealField,
    R: AbstractRotation<N, D>,
    DefaultAllocator: Allocator<N, D>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, N: SimdRealField> Mul<&'b Translation<N, U2>> for UnitComplex<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Isometry<N, U2, UnitComplex<N>>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b, N: SimdRealField> Mul<&'b Translation<N, U2>> for &'a UnitComplex<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Isometry<N, U2, UnitComplex<N>>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b, N: SimdRealField> Mul<&'b Translation<N, U3>> for &'a UnitDualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>, 

type Output = UnitDualQuaternion<N>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Translation3<N>) -> Self::Output

Performs the * operation.

impl<'b, N: SimdRealField> Mul<&'b Translation<N, U3>> for UnitDualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U3>, 

type Output = UnitDualQuaternion<N>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Translation3<N>) -> Self::Output

Performs the * operation.

impl<'b, N: SimdRealField> Mul<&'b Translation<N, U3>> for UnitQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>, 

type Output = Isometry<N, U3, UnitQuaternion<N>>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, U3, UnitQuaternion<N>>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, N: SimdRealField> Mul<&'b Unit<Complex<N>>> for Translation<N, U2> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Isometry<N, U2, UnitComplex<N>>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b, N: SimdRealField> Mul<&'b Unit<Complex<N>>> for &'a Translation<N, U2> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Isometry<N, U2, UnitComplex<N>>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, U3, UnitQuaternion<N>>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, U3, UnitQuaternion<N>>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N: SimdRealField, D: DimName, R> Mul<Isometry<N, D, R>> for Translation<N, D> where
    N::Element: SimdRealField,
    R: AbstractRotation<N, D>,
    DefaultAllocator: Allocator<N, D>, 

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N: SimdRealField, D: DimName, R> Mul<Isometry<N, D, R>> for &'a Translation<N, D> where
    N::Element: SimdRealField,
    R: AbstractRotation<N, D>,
    DefaultAllocator: Allocator<N, D>, 

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N, D: DimName> Mul<Point<N, D>> for &'a Translation<N, D> where
    N: Scalar + ClosedAdd,
    DefaultAllocator: Allocator<N, D, U1> + SameShapeAllocator<N, D, U1, D, U1>,
    ShapeConstraint: SameNumberOfRows<D, D, Representative = D> + SameNumberOfColumns<U1, 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 Translation<N, D> where
    N: Scalar + ClosedAdd,
    DefaultAllocator: Allocator<N, D, U1> + SameShapeAllocator<N, D, U1, D, U1>,
    ShapeConstraint: SameNumberOfRows<D, D, Representative = D> + SameNumberOfColumns<U1, 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: SimdRealField, D: DimName> Mul<Rotation<N, D>> for Translation<N, D> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>, 

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N: SimdRealField, D: DimName, R> Mul<Similarity<N, D, R>> for Translation<N, D> where
    N::Element: SimdRealField,
    R: AbstractRotation<N, D>,
    DefaultAllocator: Allocator<N, D>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N: SimdRealField, D: DimName, R> Mul<Similarity<N, D, R>> for &'a Translation<N, D> where
    N::Element: SimdRealField,
    R: AbstractRotation<N, D>,
    DefaultAllocator: Allocator<N, D>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N, D: DimName> Mul<Translation<N, D>> for &'a Translation<N, D> where
    N: Scalar + ClosedAdd,
    DefaultAllocator: Allocator<N, D, U1> + SameShapeAllocator<N, D, U1, D, U1>,
    ShapeConstraint: SameNumberOfRows<D, D, Representative = D> + SameNumberOfColumns<U1, U1>, 

type Output = Translation<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N, D: DimName> Mul<Translation<N, D>> for Translation<N, D> where
    N: Scalar + ClosedAdd,
    DefaultAllocator: Allocator<N, D, U1> + SameShapeAllocator<N, D, U1, D, U1>,
    ShapeConstraint: SameNumberOfRows<D, D, Representative = D> + SameNumberOfColumns<U1, U1>, 

type Output = Translation<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N: SimdRealField, D: DimName, R> Mul<Translation<N, D>> for Isometry<N, D, R> where
    N::Element: SimdRealField,
    R: AbstractRotation<N, D>,
    DefaultAllocator: Allocator<N, D>, 

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N: SimdRealField, D: DimName, R> Mul<Translation<N, D>> for &'a Isometry<N, D, R> where
    N::Element: SimdRealField,
    R: AbstractRotation<N, D>,
    DefaultAllocator: Allocator<N, D>, 

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N: SimdRealField, D: DimName, R> Mul<Translation<N, D>> for Similarity<N, D, R> where
    N::Element: SimdRealField,
    R: AbstractRotation<N, D>,
    DefaultAllocator: Allocator<N, D>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N: SimdRealField, D: DimName, R> Mul<Translation<N, D>> for &'a Similarity<N, D, R> where
    N::Element: SimdRealField,
    R: AbstractRotation<N, D>,
    DefaultAllocator: Allocator<N, D>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N: SimdRealField> Mul<Translation<N, U2>> for UnitComplex<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Isometry<N, U2, UnitComplex<N>>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N: SimdRealField> Mul<Translation<N, U2>> for &'a UnitComplex<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Isometry<N, U2, UnitComplex<N>>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N: SimdRealField> Mul<Translation<N, U3>> for &'a UnitDualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U3>, 

type Output = UnitDualQuaternion<N>

The resulting type after applying the * operator.

fn mul(self, rhs: Translation3<N>) -> Self::Output

Performs the * operation.

impl<N: SimdRealField> Mul<Translation<N, U3>> for UnitDualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U3>, 

type Output = UnitDualQuaternion<N>

The resulting type after applying the * operator.

fn mul(self, rhs: Translation3<N>) -> Self::Output

Performs the * operation.

impl<N: SimdRealField> Mul<Translation<N, U3>> for UnitQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>, 

type Output = Isometry<N, U3, UnitQuaternion<N>>

The resulting type after applying the * operator.

fn mul(self, right: Translation<N, U3>) -> Self::Output

Performs the * operation.

impl<'a, N: SimdRealField> Mul<Translation<N, U3>> for &'a UnitQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>, 

type Output = Isometry<N, U3, UnitQuaternion<N>>

The resulting type after applying the * operator.

fn mul(self, right: Translation<N, U3>) -> Self::Output

Performs the * operation.

impl<N: SimdRealField> Mul<Unit<Complex<N>>> for Translation<N, U2> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Isometry<N, U2, UnitComplex<N>>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N: SimdRealField> Mul<Unit<Complex<N>>> for &'a Translation<N, U2> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Isometry<N, U2, UnitComplex<N>>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N: SimdRealField> Mul<Unit<Quaternion<N>>> for Translation<N, U3> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>, 

type Output = Isometry<N, U3, UnitQuaternion<N>>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, U3, UnitQuaternion<N>>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, N, D: DimName> MulAssign<&'b Translation<N, D>> for Translation<N, D> where
    N: Scalar + ClosedAdd,
    DefaultAllocator: Allocator<N, D, U1>,
    ShapeConstraint: SameNumberOfRows<D, D> + SameNumberOfColumns<U1, U1>, 

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

Performs the *= operation.

impl<'b, N: SimdRealField, D: DimName, R> MulAssign<&'b Translation<N, D>> for Isometry<N, D, R> where
    N::Element: SimdRealField,
    R: AbstractRotation<N, D>,
    DefaultAllocator: Allocator<N, D>, 

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

Performs the *= operation.

impl<'b, N: SimdRealField, D: DimName, R> MulAssign<&'b Translation<N, D>> for Similarity<N, D, R> where
    N::Element: SimdRealField,
    R: AbstractRotation<N, D>,
    DefaultAllocator: Allocator<N, D>, 

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

Performs the *= operation.

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

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

Performs the *= operation.

impl<'b, N: SimdRealField> MulAssign<&'b Translation<N, U3>> for UnitDualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

fn mul_assign(&mut self, rhs: &'b Translation3<N>)

Performs the *= operation.

impl<N, D: DimName> MulAssign<Translation<N, D>> for Translation<N, D> where
    N: Scalar + ClosedAdd,
    DefaultAllocator: Allocator<N, D, U1>,
    ShapeConstraint: SameNumberOfRows<D, D> + SameNumberOfColumns<U1, U1>, 

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

Performs the *= operation.

impl<N: SimdRealField, D: DimName, R> MulAssign<Translation<N, D>> for Isometry<N, D, R> where
    N::Element: SimdRealField,
    R: AbstractRotation<N, D>,
    DefaultAllocator: Allocator<N, D>, 

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

Performs the *= operation.

impl<N: SimdRealField, D: DimName, R> MulAssign<Translation<N, D>> for Similarity<N, D, R> where
    N::Element: SimdRealField,
    R: AbstractRotation<N, D>,
    DefaultAllocator: Allocator<N, D>, 

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

Performs the *= operation.

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

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

Performs the *= operation.

impl<N: SimdRealField> MulAssign<Translation<N, U3>> for UnitDualQuaternion<N> where
    N::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>, 

fn mul_assign(&mut self, rhs: Translation3<N>)

Performs the *= operation.

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

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

fn set_one(&mut self)

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

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

Returns true if self is equal to the multiplicative identity.

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

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

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

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

This method tests for !=.

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

fn default_max_relative() -> Self::Epsilon

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

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

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

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

The inverse of RelativeEq::relative_eq.

impl<N: Scalar + SimdValue, D: DimName> SimdValue for Translation<N, D> where
    N::Element: Scalar,
    DefaultAllocator: Allocator<N, D> + Allocator<N::Element, D>, 

type Element = Translation<N::Element, D>

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

type SimdBool = N::SimdBool

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

fn lanes() -> usize

The number of lanes of this SIMD value.

fn splat(val: Self::Element) -> Self

Initializes an SIMD value with each lanes set to val.

fn extract(&self, i: usize) -> Self::Element

Extracts the i-th lane of self.

unsafe fn extract_unchecked(&self, i: usize) -> Self::Element

Extracts the i-th lane of self without bound-checking.

fn replace(&mut self, i: usize, val: Self::Element)

Replaces the i-th lane of self by val.

unsafe fn replace_unchecked(&mut self, i: usize, val: Self::Element)

Replaces the i-th lane of self by val without bound-checking.

fn select(self, cond: Self::SimdBool, other: Self) -> Self

Merges self and other depending on the lanes of cond.

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

Applies a function to each lane of self.

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

Applies a function to each lane of self paired with the corresponding lane of b.

impl<N1, N2, D: DimName, R> SubsetOf<Isometry<N2, D, R>> for Translation<N1, D> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    R: AbstractRotation<N2, D>,
    DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>, 

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

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

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

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

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

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

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

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

impl<N1, N2, D> SubsetOf<Matrix<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>> for Translation<N1, D> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    D: DimNameAdd<U1>,
    DefaultAllocator: Allocator<N1, D> + Allocator<N2, D> + Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>, 

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

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

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

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

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

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

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

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

impl<N1, N2, D: DimName, R> SubsetOf<Similarity<N2, D, R>> for Translation<N1, D> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    R: AbstractRotation<N2, D>,
    DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>, 

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

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

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

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

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

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

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

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

impl<N1, N2, D, C> SubsetOf<Transform<N2, D, C>> for Translation<N1, D> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    C: SuperTCategoryOf<TAffine>,
    D: DimNameAdd<U1>,
    DefaultAllocator: Allocator<N1, D> + Allocator<N2, D> + Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>, 

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

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

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

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

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

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

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

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

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

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

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

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

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

fn from_superset_unchecked(rot: &Translation<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<N: Scalar + UlpsEq, D: DimName> UlpsEq<Translation<N, D>> for Translation<N, D> where
    DefaultAllocator: Allocator<N, D>,
    N::Epsilon: Copy, 

fn default_max_ulps() -> u32

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

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

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

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

The inverse of UlpsEq::ulps_eq.

impl<N: Scalar + Copy, D: DimName> Copy for Translation<N, D> where
    DefaultAllocator: Allocator<N, D>,
    Owned<N, D>: Copy, 

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