Struct nalgebra::geometry::Translation

#[repr(C)]
pub struct Translation<T, const D: usize> {
    pub vector: SVector<T, D>,
}

A translation.

Fields

vector: SVector<T, D>

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

Implementations

impl<T: Scalar, const D: usize> Translation<T, D>

pub fn from_vector(vector: SVector<T, D>) -> Translation<T, D>

👎 Deprecated:

Use ::from instead.

Creates a new translation from the given vector.

pub fn inverse(&self) -> Translation<T, D> where
    T: 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
) -> OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> where
    T: Zero + One,
    Const<D>: DimNameAdd<U1>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<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
    T: 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<T: Scalar + ClosedAdd, const D: usize> Translation<T, D>

pub fn transform_point(&self, pt: &Point<T, D>) -> Point<T, 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<T: Scalar + ClosedSub, const D: usize> Translation<T, D>

pub fn inverse_transform_point(&self, pt: &Point<T, D>) -> Point<T, 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<T: Scalar, const D: usize> Translation<T, D>

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

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<T> Translation<T, 1>

pub const fn new(x: T) -> Self

Initializes this translation from its components.

Example

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

impl<T> Translation<T, 2>

pub const fn new(x: T, y: T) -> 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<T> Translation<T, 3>

pub const fn new(x: T, y: T, z: T) -> 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<T> Translation<T, 4>

pub const fn new(x: T, y: T, z: T, w: T) -> 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<T> Translation<T, 5>

pub const fn new(x: T, y: T, z: T, w: T, a: T) -> 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<T> Translation<T, 6>

pub const fn new(x: T, y: T, z: T, w: T, a: T, b: T) -> 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<T: Scalar + AbsDiffEq, const D: usize> AbsDiffEq<Translation<T, D>> for Translation<T, D> where
    T::Epsilon: Clone, 

type Epsilon = <T as AbsDiffEq<T>>::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<T: RealField + RealField, const D: usize> AbstractMagma<Multiplicative> for Translation<T, D>

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

Performs an operation.

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

Performs specific operation.

impl<T: RealField + RealField, const D: usize> AbstractMonoid<Multiplicative> for Translation<T, D>

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

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

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

impl<T: RealField + RealField, const D: usize> AbstractQuasigroup<Multiplicative> for Translation<T, D>

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

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<T: RealField + RealField, const D: usize> AbstractSemigroup<Multiplicative> for Translation<T, D>

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

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<T: RealField + RealField, const D: usize> AffineTransformation<OPoint<T, Const<D>>> for Translation<T, D>

type Rotation = Id<Multiplicative>

Type of the first rotation to be applied.

type NonUniformScaling = Id<Multiplicative>

Type of the non-uniform scaling to be applied.

type Translation = Translation<T, D>

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

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

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, t: &Self::Translation) -> Self

Appends a translation to this similarity.

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

Prepends a translation to this similarity.

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

Appends a rotation to this similarity.

fn prepend_rotation(&self, _: &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<T: Scalar + Arbitrary + Send, const D: usize> Arbitrary for Translation<T, D> where
    Owned<T, Const<D>>: Send, 

fn arbitrary(rng: &mut Gen) -> Self

Return an arbitrary value.

fn shrink(&self) -> Box<dyn Iterator<Item = Self> + 'static, Global>

Return an iterator of values that are smaller than itself.

impl<T, const D: usize> Archive for Translation<T, D> where
    SVector<T, D>: Archive, 

type Archived = ArchivedTranslation<T, D>

The archived representation of this type.

type Resolver = TranslationResolver<T, D>

The resolver for this type. It must contain all the additional information from serializing needed to make the archived type from the normal type.

unsafe fn resolve(
    &self,
    pos: usize,
    resolver: Self::Resolver,
    out: *mut Self::Archived
)

Creates the archived version of this value at the given position and writes it to the given output.

impl<__C: ?Sized, T, const D: usize> CheckBytes<__C> for Translation<T, D> where
    SVector<T, D>: CheckBytes<__C>, 

type Error = StructCheckError

The error that may result from checking the type.

unsafe fn check_bytes<'__bytecheck>(
    value: *const Self,
    context: &mut __C
) -> Result<&'__bytecheck Self, StructCheckError>

Checks whether the given pointer points to a valid value within the given context.

impl<T: Clone, const D: usize> Clone for Translation<T, D>

fn clone(&self) -> Translation<T, D>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<T: Debug, const D: usize> Debug for Translation<T, D>

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

Formats the value using the given formatter.

impl<T: Scalar + Zero, const D: usize> Default for Translation<T, D>

fn default() -> Self

Returns the “default value” for a type.

impl<T: Scalar> Deref for Translation<T, 1>

type Target = X<T>

The resulting type after dereferencing.

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

Dereferences the value.

impl<T: Scalar> Deref for Translation<T, 2>

type Target = XY<T>

The resulting type after dereferencing.

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

Dereferences the value.

impl<T: Scalar> Deref for Translation<T, 3>

type Target = XYZ<T>

The resulting type after dereferencing.

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

Dereferences the value.

impl<T: Scalar> Deref for Translation<T, 4>

type Target = XYZW<T>

The resulting type after dereferencing.

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

Dereferences the value.

impl<T: Scalar> Deref for Translation<T, 5>

type Target = XYZWA<T>

The resulting type after dereferencing.

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

Dereferences the value.

impl<T: Scalar> Deref for Translation<T, 6>

type Target = XYZWAB<T>

The resulting type after dereferencing.

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

Dereferences the value.

impl<T: Scalar> DerefMut for Translation<T, 1>

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

Mutably dereferences the value.

impl<T: Scalar> DerefMut for Translation<T, 2>

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

Mutably dereferences the value.

impl<T: Scalar> DerefMut for Translation<T, 3>

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

Mutably dereferences the value.

impl<T: Scalar> DerefMut for Translation<T, 4>

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

Mutably dereferences the value.

impl<T: Scalar> DerefMut for Translation<T, 5>

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

Mutably dereferences the value.

impl<T: Scalar> DerefMut for Translation<T, 6>

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

Mutably dereferences the value.

impl<'a, T: Scalar, const D: usize> Deserialize<'a> for Translation<T, D> where
    Owned<T, Const<D>>: Deserialize<'a>, 

fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error> where
    Des: Deserializer<'a>, 

Deserialize this value from the given Serde deserializer.

impl<__D: Fallible + ?Sized, T, const D: usize> Deserialize<Translation<T, D>, __D> for Archived<Translation<T, D>> where
    SVector<T, D>: Archive,
    Archived<SVector<T, D>>: Deserialize<SVector<T, D>, __D>, 

fn deserialize(
    &self,
    deserializer: &mut __D
) -> Result<Translation<T, D>, __D::Error>

Deserializes using the given deserializer

impl<T: Scalar + Display, const D: usize> Display for Translation<T, D>

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

Formats the value using the given formatter.

impl<T: Scalar, const D: usize> Distribution<Translation<T, D>> for Standard where
    Standard: Distribution<T>, 

fn sample<G: Rng + ?Sized>(&self, rng: &mut G) -> Translation<T, D>

Generate an arbitrary random variate for testing purposes.

fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T> where
    R: Rng, 

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

fn map<F, S>(self, func: F) -> DistMap<Self, F, T, S> where
    F: Fn(T) -> S, 

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F

impl<'a, 'b, T, C, const D: usize> Div<&'b Transform<T, C, D>> for &'a Translation<T, D> where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, 

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

The resulting type after applying the / operator.

fn div(self, rhs: &'b Transform<T, C, D>) -> Self::Output

Performs the / operation.

impl<'b, T, C, const D: usize> Div<&'b Transform<T, C, D>> for Translation<T, D> where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, 

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

The resulting type after applying the / operator.

fn div(self, rhs: &'b Transform<T, C, D>) -> Self::Output

Performs the / operation.

impl<'a, 'b, T: SimdRealField> Div<&'b Translation<T, 3>> for &'a UnitDualQuaternion<T> where
    T::Element: SimdRealField, 

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div(self, rhs: &'b Translation3<T>) -> Self::Output

Performs the / operation.

impl<'b, T: SimdRealField> Div<&'b Translation<T, 3>> for UnitDualQuaternion<T> where
    T::Element: SimdRealField, 

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div(self, rhs: &'b Translation3<T>) -> Self::Output

Performs the / operation.

impl<'a, 'b, T, C, const D: usize> Div<&'b Translation<T, D>> for &'a Transform<T, C, D> where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, 

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

The resulting type after applying the / operator.

fn div(self, rhs: &'b Translation<T, D>) -> Self::Output

Performs the / operation.

impl<'a, 'b, T, const D: usize> Div<&'b Translation<T, D>> for &'a Translation<T, D> where
    T: Scalar + ClosedSub,
    ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>, 

type Output = Translation<T, D>

The resulting type after applying the / operator.

fn div(self, right: &'b Translation<T, D>) -> Self::Output

Performs the / operation.

impl<'b, T, C, const D: usize> Div<&'b Translation<T, D>> for Transform<T, C, D> where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, 

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

The resulting type after applying the / operator.

fn div(self, rhs: &'b Translation<T, D>) -> Self::Output

Performs the / operation.

impl<'b, T, const D: usize> Div<&'b Translation<T, D>> for Translation<T, D> where
    T: Scalar + ClosedSub,
    ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>, 

type Output = Translation<T, D>

The resulting type after applying the / operator.

fn div(self, right: &'b Translation<T, D>) -> Self::Output

Performs the / operation.

impl<'a, T, C, const D: usize> Div<Transform<T, C, D>> for &'a Translation<T, D> where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, 

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, T: SimdRealField> Div<Translation<T, 3>> for &'a UnitDualQuaternion<T> where
    T::Element: SimdRealField, 

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<T: SimdRealField> Div<Translation<T, 3>> for UnitDualQuaternion<T> where
    T::Element: SimdRealField, 

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, T, C, const D: usize> Div<Translation<T, D>> for &'a Transform<T, C, D> where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, 

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

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, T, const D: usize> Div<Translation<T, D>> for &'a Translation<T, D> where
    T: Scalar + ClosedSub,
    ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>, 

type Output = Translation<T, D>

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

impl<T, const D: usize> Div<Translation<T, D>> for Translation<T, D> where
    T: Scalar + ClosedSub,
    ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>, 

type Output = Translation<T, D>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'b, T: SimdRealField> DivAssign<&'b Translation<T, 3>> for UnitDualQuaternion<T> where
    T::Element: SimdRealField, 

fn div_assign(&mut self, rhs: &'b Translation3<T>)

Performs the /= operation.

impl<'b, T, C, const D: usize> DivAssign<&'b Translation<T, D>> for Transform<T, C, D> where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategory,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, 

fn div_assign(&mut self, rhs: &'b Translation<T, D>)

Performs the /= operation.

impl<'b, T, const D: usize> DivAssign<&'b Translation<T, D>> for Translation<T, D> where
    T: Scalar + ClosedSub, 

fn div_assign(&mut self, right: &'b Translation<T, D>)

Performs the /= operation.

impl<T: SimdRealField> DivAssign<Translation<T, 3>> for UnitDualQuaternion<T> where
    T::Element: SimdRealField, 

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

Performs the /= operation.

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

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

Performs the /= operation.

impl<T, const D: usize> DivAssign<Translation<T, D>> for Translation<T, D> where
    T: Scalar + ClosedSub, 

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

Performs the /= operation.

impl<T: Scalar, const D: usize> From<[T; D]> for Translation<T, D>

fn from(coords: [T; D]) -> Self

Converts to this type from the input type.

impl<T: Scalar + PrimitiveSimdValue, const D: usize> From<[Translation<<T as SimdValue>::Element, D>; 16]> for Translation<T, D> where
    T: From<[<T as SimdValue>::Element; 16]>,
    T::Element: Scalar, 

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

Converts to this type from the input type.

impl<T: Scalar + PrimitiveSimdValue, const D: usize> From<[Translation<<T as SimdValue>::Element, D>; 2]> for Translation<T, D> where
    T: From<[<T as SimdValue>::Element; 2]>,
    T::Element: Scalar, 

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

Converts to this type from the input type.

impl<T: Scalar + PrimitiveSimdValue, const D: usize> From<[Translation<<T as SimdValue>::Element, D>; 4]> for Translation<T, D> where
    T: From<[<T as SimdValue>::Element; 4]>,
    T::Element: Scalar, 

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

Converts to this type from the input type.

impl<T: Scalar + PrimitiveSimdValue, const D: usize> From<[Translation<<T as SimdValue>::Element, D>; 8]> for Translation<T, D> where
    T: From<[<T as SimdValue>::Element; 8]>,
    T::Element: Scalar, 

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

Converts to this type from the input type.

impl<T: Scalar, const D: usize> From<Matrix<T, Const<D>, Const<1>, <DefaultAllocator as Allocator<T, Const<D>, Const<1>>>::Buffer>> for Translation<T, D>

fn from(vector: OVector<T, Const<D>>) -> Self

Converts to this type from the input type.

impl<T: Scalar, const D: usize> From<OPoint<T, Const<D>>> for Translation<T, D>

fn from(pt: Point<T, D>) -> Self

Converts to this type from the input type.

impl<T: Scalar, const D: usize> From<Translation<T, D>> for [T; D]

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

Converts to this type from the input type.

impl<T: SimdRealField, R: AbstractRotation<T, D>, const D: usize> From<Translation<T, D>> for Isometry<T, R, D>

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

Converts to this type from the input type.

impl<T: Scalar + Zero + One, const D: usize> From<Translation<T, D>> for OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> where
    Const<D>: DimNameAdd<U1>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> + Allocator<T, Const<D>>, 

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

Converts to this type from the input type.

impl From<Translation<f32, 2>> for Vec2

fn from(e: Translation2<f32>) -> Vec2

Converts to this type from the input type.

impl From<Translation<f32, 2>> for Vec2

fn from(e: Translation2<f32>) -> Vec2

Converts to this type from the input type.

impl From<Translation<f32, 2>> for Vec2

fn from(e: Translation2<f32>) -> Vec2

Converts to this type from the input type.

impl From<Translation<f32, 2>> for Vec2

fn from(e: Translation2<f32>) -> Vec2

Converts to this type from the input type.

impl From<Translation<f32, 2>> for Vec2

fn from(e: Translation2<f32>) -> Vec2

Converts to this type from the input type.

impl From<Translation<f32, 2>> for Vec2

fn from(e: Translation2<f32>) -> Vec2

Converts to this type from the input type.

impl From<Translation<f32, 2>> for Vec2

fn from(e: Translation2<f32>) -> Vec2

Converts to this type from the input type.

impl From<Translation<f32, 2>> for Vec2

fn from(e: Translation2<f32>) -> Vec2

Converts to this type from the input type.

impl From<Translation<f32, 3>> for Vec3

fn from(e: Translation3<f32>) -> Vec3

Converts to this type from the input type.

impl From<Translation<f32, 3>> for Vec3

fn from(e: Translation3<f32>) -> Vec3

Converts to this type from the input type.

impl From<Translation<f32, 3>> for Vec3

fn from(e: Translation3<f32>) -> Vec3

Converts to this type from the input type.

impl From<Translation<f32, 3>> for Vec3

fn from(e: Translation3<f32>) -> Vec3

Converts to this type from the input type.

impl From<Translation<f32, 3>> for Vec3

fn from(e: Translation3<f32>) -> Vec3

Converts to this type from the input type.

impl From<Translation<f32, 3>> for Vec3

fn from(e: Translation3<f32>) -> Vec3

Converts to this type from the input type.

impl From<Translation<f32, 3>> for Vec3

fn from(e: Translation3<f32>) -> Vec3

Converts to this type from the input type.

impl From<Translation<f32, 3>> for Vec3

fn from(e: Translation3<f32>) -> Vec3

Converts to this type from the input type.

impl From<Translation<f32, 3>> for Vec3A

fn from(e: Translation3<f32>) -> Vec3A

Converts to this type from the input type.

impl From<Translation<f32, 3>> for Vec3A

fn from(e: Translation3<f32>) -> Vec3A

Converts to this type from the input type.

impl From<Translation<f32, 3>> for Vec3A

fn from(e: Translation3<f32>) -> Vec3A

Converts to this type from the input type.

impl From<Translation<f32, 3>> for Vec3A

fn from(e: Translation3<f32>) -> Vec3A

Converts to this type from the input type.

impl From<Translation<f32, 3>> for Vec3A

fn from(e: Translation3<f32>) -> Vec3A

Converts to this type from the input type.

impl From<Translation<f32, 3>> for Vec3A

fn from(e: Translation3<f32>) -> Vec3A

Converts to this type from the input type.

impl From<Translation<f32, 3>> for Vec3A

fn from(e: Translation3<f32>) -> Vec3A

Converts to this type from the input type.

impl From<Translation<f32, 3>> for Vec3A

fn from(e: Translation3<f32>) -> Vec3A

Converts to this type from the input type.

impl From<Translation<f32, 4>> for Vec4

fn from(e: Translation4<f32>) -> Vec4

Converts to this type from the input type.

impl From<Translation<f32, 4>> for Vec4

fn from(e: Translation4<f32>) -> Vec4

Converts to this type from the input type.

impl From<Translation<f32, 4>> for Vec4

fn from(e: Translation4<f32>) -> Vec4

Converts to this type from the input type.

impl From<Translation<f32, 4>> for Vec4

fn from(e: Translation4<f32>) -> Vec4

Converts to this type from the input type.

impl From<Translation<f32, 4>> for Vec4

fn from(e: Translation4<f32>) -> Vec4

Converts to this type from the input type.

impl From<Translation<f32, 4>> for Vec4

fn from(e: Translation4<f32>) -> Vec4

Converts to this type from the input type.

impl From<Translation<f32, 4>> for Vec4

fn from(e: Translation4<f32>) -> Vec4

Converts to this type from the input type.

impl From<Translation<f32, 4>> for Vec4

fn from(e: Translation4<f32>) -> Vec4

Converts to this type from the input type.

impl From<Translation<f64, 2>> for DVec2

fn from(e: Translation2<f64>) -> DVec2

Converts to this type from the input type.

impl From<Translation<f64, 2>> for DVec2

fn from(e: Translation2<f64>) -> DVec2

Converts to this type from the input type.

impl From<Translation<f64, 2>> for DVec2

fn from(e: Translation2<f64>) -> DVec2

Converts to this type from the input type.

impl From<Translation<f64, 2>> for DVec2

fn from(e: Translation2<f64>) -> DVec2

Converts to this type from the input type.

impl From<Translation<f64, 2>> for DVec2

fn from(e: Translation2<f64>) -> DVec2

Converts to this type from the input type.

impl From<Translation<f64, 2>> for DVec2

fn from(e: Translation2<f64>) -> DVec2

Converts to this type from the input type.

impl From<Translation<f64, 2>> for DVec2

fn from(e: Translation2<f64>) -> DVec2

Converts to this type from the input type.

impl From<Translation<f64, 2>> for DVec2

fn from(e: Translation2<f64>) -> DVec2

Converts to this type from the input type.

impl From<Translation<f64, 3>> for DVec3

fn from(e: Translation3<f64>) -> DVec3

Converts to this type from the input type.

impl From<Translation<f64, 3>> for DVec3

fn from(e: Translation3<f64>) -> DVec3

Converts to this type from the input type.

impl From<Translation<f64, 3>> for DVec3

fn from(e: Translation3<f64>) -> DVec3

Converts to this type from the input type.

impl From<Translation<f64, 3>> for DVec3

fn from(e: Translation3<f64>) -> DVec3

Converts to this type from the input type.

impl From<Translation<f64, 3>> for DVec3

fn from(e: Translation3<f64>) -> DVec3

Converts to this type from the input type.

impl From<Translation<f64, 3>> for DVec3

fn from(e: Translation3<f64>) -> DVec3

Converts to this type from the input type.

impl From<Translation<f64, 3>> for DVec3

fn from(e: Translation3<f64>) -> DVec3

Converts to this type from the input type.

impl From<Translation<f64, 3>> for DVec3

fn from(e: Translation3<f64>) -> DVec3

Converts to this type from the input type.

impl From<Translation<f64, 4>> for DVec4

fn from(e: Translation4<f64>) -> DVec4

Converts to this type from the input type.

impl From<Translation<f64, 4>> for DVec4

fn from(e: Translation4<f64>) -> DVec4

Converts to this type from the input type.

impl From<Translation<f64, 4>> for DVec4

fn from(e: Translation4<f64>) -> DVec4

Converts to this type from the input type.

impl From<Translation<f64, 4>> for DVec4

fn from(e: Translation4<f64>) -> DVec4

Converts to this type from the input type.

impl From<Translation<f64, 4>> for DVec4

fn from(e: Translation4<f64>) -> DVec4

Converts to this type from the input type.

impl From<Translation<f64, 4>> for DVec4

fn from(e: Translation4<f64>) -> DVec4

Converts to this type from the input type.

impl From<Translation<f64, 4>> for DVec4

fn from(e: Translation4<f64>) -> DVec4

Converts to this type from the input type.

impl From<Translation<f64, 4>> for DVec4

fn from(e: Translation4<f64>) -> DVec4

Converts to this type from the input type.

impl<T: Scalar + Hash, const D: usize> Hash for Translation<T, D> where
    Owned<T, Const<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<T: RealField + RealField, const D: usize> Identity<Multiplicative> for Translation<T, D>

fn identity() -> Self

The identity element.

fn id(O) -> Self

Specific identity.

impl<'a, 'b, T: SimdRealField, R, const D: usize> Mul<&'b Isometry<T, R, D>> for &'a Translation<T, D> where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>, 

type Output = Isometry<T, R, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Isometry<T, R, D>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField, R, const D: usize> Mul<&'b Isometry<T, R, D>> for Translation<T, D> where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>, 

type Output = Isometry<T, R, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Isometry<T, R, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T, const D: usize> Mul<&'b OPoint<T, Const<D>>> for &'a Translation<T, D> where
    T: Scalar + ClosedAdd,
    ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>, 

type Output = OPoint<T, Const<D>>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<T, D>) -> Self::Output

Performs the * operation.

impl<'b, T, const D: usize> Mul<&'b OPoint<T, Const<D>>> for Translation<T, D> where
    T: Scalar + ClosedAdd,
    ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>, 

type Output = OPoint<T, Const<D>>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<T, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField, const D: usize> Mul<&'b Rotation<T, D>> for &'a Translation<T, D> where
    T::Element: SimdRealField, 

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

The resulting type after applying the * operator.

fn mul(self, right: &'b Rotation<T, D>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField, const D: usize> Mul<&'b Rotation<T, D>> for Translation<T, D> where
    T::Element: SimdRealField, 

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

The resulting type after applying the * operator.

fn mul(self, right: &'b Rotation<T, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField, R, const D: usize> Mul<&'b Similarity<T, R, D>> for &'a Translation<T, D> where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>, 

type Output = Similarity<T, R, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Similarity<T, R, D>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField, R, const D: usize> Mul<&'b Similarity<T, R, D>> for Translation<T, D> where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>, 

type Output = Similarity<T, R, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Similarity<T, R, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T, C, const D: usize> Mul<&'b Transform<T, C, D>> for &'a Translation<T, D> where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, 

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Transform<T, C, D>) -> Self::Output

Performs the * operation.

impl<'b, T, C, const D: usize> Mul<&'b Transform<T, C, D>> for Translation<T, D> where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, 

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Transform<T, C, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField> Mul<&'b Translation<T, 2>> for &'a UnitComplex<T> where
    T::Element: SimdRealField, 

type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Translation<T, 2>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField> Mul<&'b Translation<T, 2>> for UnitComplex<T> where
    T::Element: SimdRealField, 

type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Translation<T, 2>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField> Mul<&'b Translation<T, 3>> for &'a UnitDualQuaternion<T> where
    T::Element: SimdRealField, 

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Translation3<T>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField> Mul<&'b Translation<T, 3>> for &'a UnitQuaternion<T> where
    T::Element: SimdRealField, 

type Output = Isometry<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the * operator.

fn mul(self, right: &'b Translation<T, 3>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField> Mul<&'b Translation<T, 3>> for UnitDualQuaternion<T> where
    T::Element: SimdRealField, 

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Translation3<T>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField> Mul<&'b Translation<T, 3>> for UnitQuaternion<T> where
    T::Element: SimdRealField, 

type Output = Isometry<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the * operator.

fn mul(self, right: &'b Translation<T, 3>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField, R, const D: usize> Mul<&'b Translation<T, D>> for &'a Isometry<T, R, D> where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>, 

type Output = Isometry<T, R, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Translation<T, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField, const D: usize> Mul<&'b Translation<T, D>> for &'a Rotation<T, D> where
    T::Element: SimdRealField, 

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

The resulting type after applying the * operator.

fn mul(self, right: &'b Translation<T, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField, R, const D: usize> Mul<&'b Translation<T, D>> for &'a Similarity<T, R, D> where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>, 

type Output = Similarity<T, R, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Translation<T, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T, C, const D: usize> Mul<&'b Translation<T, D>> for &'a Transform<T, C, D> where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, 

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Translation<T, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T, const D: usize> Mul<&'b Translation<T, D>> for &'a Translation<T, D> where
    T: Scalar + ClosedAdd,
    ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>, 

type Output = Translation<T, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Translation<T, D>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField, R, const D: usize> Mul<&'b Translation<T, D>> for Isometry<T, R, D> where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>, 

type Output = Isometry<T, R, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Translation<T, D>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField, const D: usize> Mul<&'b Translation<T, D>> for Rotation<T, D> where
    T::Element: SimdRealField, 

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

The resulting type after applying the * operator.

fn mul(self, right: &'b Translation<T, D>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField, R, const D: usize> Mul<&'b Translation<T, D>> for Similarity<T, R, D> where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>, 

type Output = Similarity<T, R, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Translation<T, D>) -> Self::Output

Performs the * operation.

impl<'b, T, C, const D: usize> Mul<&'b Translation<T, D>> for Transform<T, C, D> where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, 

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Translation<T, D>) -> Self::Output

Performs the * operation.

impl<'b, T, const D: usize> Mul<&'b Translation<T, D>> for Translation<T, D> where
    T: Scalar + ClosedAdd,
    ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>, 

type Output = Translation<T, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Translation<T, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for &'a Translation<T, 2> where
    T::Element: SimdRealField, 

type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the * operator.

fn mul(self, right: &'b UnitComplex<T>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for Translation<T, 2> where
    T::Element: SimdRealField, 

type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the * operator.

fn mul(self, right: &'b UnitComplex<T>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for &'a Translation<T, 3> where
    T::Element: SimdRealField, 

type Output = Isometry<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the * operator.

fn mul(self, right: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for Translation<T, 3> where
    T::Element: SimdRealField, 

type Output = Isometry<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the * operator.

fn mul(self, right: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField, R, const D: usize> Mul<Isometry<T, R, D>> for &'a Translation<T, D> where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>, 

type Output = Isometry<T, R, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T: SimdRealField, R, const D: usize> Mul<Isometry<T, R, D>> for Translation<T, D> where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>, 

type Output = Isometry<T, R, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, T, const D: usize> Mul<OPoint<T, Const<D>>> for &'a Translation<T, D> where
    T: Scalar + ClosedAdd,
    ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>, 

type Output = OPoint<T, Const<D>>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T, const D: usize> Mul<OPoint<T, Const<D>>> for Translation<T, D> where
    T: Scalar + ClosedAdd,
    ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>, 

type Output = OPoint<T, Const<D>>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, T: SimdRealField, const D: usize> Mul<Rotation<T, D>> for &'a Translation<T, D> where
    T::Element: SimdRealField, 

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T: SimdRealField, const D: usize> Mul<Rotation<T, D>> for Translation<T, D> where
    T::Element: SimdRealField, 

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, T: SimdRealField, R, const D: usize> Mul<Similarity<T, R, D>> for &'a Translation<T, D> where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>, 

type Output = Similarity<T, R, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T: SimdRealField, R, const D: usize> Mul<Similarity<T, R, D>> for Translation<T, D> where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>, 

type Output = Similarity<T, R, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, T, C, const D: usize> Mul<Transform<T, C, D>> for &'a Translation<T, D> where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, 

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, T: SimdRealField> Mul<Translation<T, 2>> for &'a UnitComplex<T> where
    T::Element: SimdRealField, 

type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the * operator.

fn mul(self, rhs: Translation<T, 2>) -> Self::Output

Performs the * operation.

impl<T: SimdRealField> Mul<Translation<T, 2>> for UnitComplex<T> where
    T::Element: SimdRealField, 

type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the * operator.

fn mul(self, rhs: Translation<T, 2>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField> Mul<Translation<T, 3>> for &'a UnitDualQuaternion<T> where
    T::Element: SimdRealField, 

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, T: SimdRealField> Mul<Translation<T, 3>> for &'a UnitQuaternion<T> where
    T::Element: SimdRealField, 

type Output = Isometry<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the * operator.

fn mul(self, right: Translation<T, 3>) -> Self::Output

Performs the * operation.

impl<T: SimdRealField> Mul<Translation<T, 3>> for UnitDualQuaternion<T> where
    T::Element: SimdRealField, 

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T: SimdRealField> Mul<Translation<T, 3>> for UnitQuaternion<T> where
    T::Element: SimdRealField, 

type Output = Isometry<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the * operator.

fn mul(self, right: Translation<T, 3>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField, R, const D: usize> Mul<Translation<T, D>> for &'a Isometry<T, R, D> where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>, 

type Output = Isometry<T, R, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, T: SimdRealField, const D: usize> Mul<Translation<T, D>> for &'a Rotation<T, D> where
    T::Element: SimdRealField, 

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, T: SimdRealField, R, const D: usize> Mul<Translation<T, D>> for &'a Similarity<T, R, D> where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>, 

type Output = Similarity<T, R, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, T, C, const D: usize> Mul<Translation<T, D>> for &'a Transform<T, C, D> where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, 

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, T, const D: usize> Mul<Translation<T, D>> for &'a Translation<T, D> where
    T: Scalar + ClosedAdd,
    ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>, 

type Output = Translation<T, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T: SimdRealField, R, const D: usize> Mul<Translation<T, D>> for Isometry<T, R, D> where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>, 

type Output = Isometry<T, R, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T: SimdRealField, const D: usize> Mul<Translation<T, D>> for Rotation<T, D> where
    T::Element: SimdRealField, 

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T: SimdRealField, R, const D: usize> Mul<Translation<T, D>> for Similarity<T, R, D> where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>, 

type Output = Similarity<T, R, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T, const D: usize> Mul<Translation<T, D>> for Translation<T, D> where
    T: Scalar + ClosedAdd,
    ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<U1, U1, Representative = U1>, 

type Output = Translation<T, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, T: SimdRealField> Mul<Unit<Complex<T>>> for &'a Translation<T, 2> where
    T::Element: SimdRealField, 

type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T: SimdRealField> Mul<Unit<Complex<T>>> for Translation<T, 2> where
    T::Element: SimdRealField, 

type Output = Isometry<T, Unit<Complex<T>>, 2>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, T: SimdRealField> Mul<Unit<Quaternion<T>>> for &'a Translation<T, 3> where
    T::Element: SimdRealField, 

type Output = Isometry<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T: SimdRealField> Mul<Unit<Quaternion<T>>> for Translation<T, 3> where
    T::Element: SimdRealField, 

type Output = Isometry<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, T: SimdRealField> MulAssign<&'b Translation<T, 3>> for UnitDualQuaternion<T> where
    T::Element: SimdRealField, 

fn mul_assign(&mut self, rhs: &'b Translation3<T>)

Performs the *= operation.

impl<'b, T: SimdRealField, R, const D: usize> MulAssign<&'b Translation<T, D>> for Isometry<T, R, D> where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>, 

fn mul_assign(&mut self, rhs: &'b Translation<T, D>)

Performs the *= operation.

impl<'b, T: SimdRealField, R, const D: usize> MulAssign<&'b Translation<T, D>> for Similarity<T, R, D> where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>, 

fn mul_assign(&mut self, rhs: &'b Translation<T, D>)

Performs the *= operation.

impl<'b, T, C, const D: usize> MulAssign<&'b Translation<T, D>> for Transform<T, C, D> where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategory,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, 

fn mul_assign(&mut self, rhs: &'b Translation<T, D>)

Performs the *= operation.

impl<'b, T, const D: usize> MulAssign<&'b Translation<T, D>> for Translation<T, D> where
    T: Scalar + ClosedAdd, 

fn mul_assign(&mut self, right: &'b Translation<T, D>)

Performs the *= operation.

impl<T: SimdRealField> MulAssign<Translation<T, 3>> for UnitDualQuaternion<T> where
    T::Element: SimdRealField, 

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

Performs the *= operation.

impl<T: SimdRealField, R, const D: usize> MulAssign<Translation<T, D>> for Isometry<T, R, D> where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>, 

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

Performs the *= operation.

impl<T: SimdRealField, R, const D: usize> MulAssign<Translation<T, D>> for Similarity<T, R, D> where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>, 

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

Performs the *= operation.

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

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

Performs the *= operation.

impl<T, const D: usize> MulAssign<Translation<T, D>> for Translation<T, D> where
    T: Scalar + ClosedAdd, 

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

Performs the *= operation.

impl<T: Scalar + Zero + ClosedAdd, const D: usize> One for Translation<T, 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<T: Scalar + PartialEq, const D: usize> PartialEq<Translation<T, D>> for Translation<T, D>

fn eq(&self, right: &Translation<T, 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<T: RealField + RealField, const D: usize> ProjectiveTransformation<OPoint<T, Const<D>>> for Translation<T, D>

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

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

fn inverse_transform_vector(&self, v: &SVector<T, D>) -> SVector<T, D>

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

impl<T: Scalar + RelativeEq, const D: usize> RelativeEq<Translation<T, D>> for Translation<T, D> where
    T::Epsilon: Clone, 

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<__S: Fallible + ?Sized, T, const D: usize> Serialize<__S> for Translation<T, D> where
    SVector<T, D>: Serialize<__S>, 

fn serialize(&self, serializer: &mut __S) -> Result<Self::Resolver, __S::Error>

Writes the dependencies for the object and returns a resolver that can create the archived type.

impl<T: Scalar, const D: usize> Serialize for Translation<T, D> where
    Owned<T, Const<D>>: Serialize, 

fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error> where
    S: Serializer, 

Serialize this value into the given Serde serializer.

impl<T: Scalar + SimdValue, const D: usize> SimdValue for Translation<T, D> where
    T::Element: Scalar, 

type Element = Translation<<T as SimdValue>::Element, D>

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

type SimdBool = <T as SimdValue>::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<T: RealField + RealField, const D: usize> Similarity<OPoint<T, Const<D>>> for Translation<T, D>

type Scaling = Id<Multiplicative>

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

fn translation(&self) -> Self

The pure translational component of this similarity transformation.

fn rotation(&self) -> Id

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<T1, T2, R, const D: usize> SubsetOf<Isometry<T2, R, D>> for Translation<T1, D> where
    T1: RealField,
    T2: RealField + SupersetOf<T1>,
    R: AbstractRotation<T2, D>, 

fn to_superset(&self) -> Isometry<T2, R, D>

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

fn is_in_subset(iso: &Isometry<T2, R, D>) -> bool

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

fn from_superset_unchecked(iso: &Isometry<T2, R, 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<T1, T2, const D: usize> SubsetOf<Matrix<T2, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output, <DefaultAllocator as Allocator<T2, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>>::Buffer>> for Translation<T1, D> where
    T1: RealField,
    T2: RealField + SupersetOf<T1>,
    Const<D>: DimNameAdd<U1>,
    DefaultAllocator: Allocator<T1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> + Allocator<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, 

fn to_superset(
    &self
) -> OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>

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

fn is_in_subset(
    m: &OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
) -> bool

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

fn from_superset_unchecked(
    m: &OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<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<T1, T2, R, const D: usize> SubsetOf<Similarity<T2, R, D>> for Translation<T1, D> where
    T1: RealField,
    T2: RealField + SupersetOf<T1>,
    R: AbstractRotation<T2, D>, 

fn to_superset(&self) -> Similarity<T2, R, D>

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

fn is_in_subset(sim: &Similarity<T2, R, D>) -> bool

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

fn from_superset_unchecked(sim: &Similarity<T2, R, 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<T1, T2, C, const D: usize> SubsetOf<Transform<T2, C, D>> for Translation<T1, D> where
    T1: RealField,
    T2: RealField + SupersetOf<T1>,
    C: SuperTCategoryOf<TAffine>,
    Const<D>: DimNameAdd<U1>,
    DefaultAllocator: Allocator<T1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> + Allocator<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>, 

fn to_superset(&self) -> Transform<T2, C, D>

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

fn is_in_subset(t: &Transform<T2, C, D>) -> bool

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

fn from_superset_unchecked(t: &Transform<T2, C, 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<T1, T2, const D: usize> SubsetOf<Translation<T2, D>> for Translation<T1, D> where
    T1: Scalar,
    T2: Scalar + SupersetOf<T1>, 

fn to_superset(&self) -> Translation<T2, D>

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

fn is_in_subset(rot: &Translation<T2, D>) -> bool

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

fn from_superset_unchecked(rot: &Translation<T2, 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<T: RealField + RealField, const D: usize> Transformation<OPoint<T, Const<D>>> for Translation<T, D>

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

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

fn transform_vector(&self, v: &SVector<T, D>) -> SVector<T, D>

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

impl<T: RealField + RealField, const D: usize> Translation<OPoint<T, Const<D>>> for Translation<T, D>

Subgroups of the n-dimensional translation group T(n).

fn to_vector(&self) -> SVector<T, D>

Converts this translation to a vector.

fn from_vector(v: SVector<T, D>) -> Option<Self>

Attempts to convert a vector to this translation. Returns None if the translation represented by v is not part of the translation subgroup represented by Self.

fn powf(&self, n: T) -> Option<Self>

Raises the translation to a power. The result must be equivalent to self.to_superset() * n. Returns None if the result is not representable by Self.

fn translation_between(a: &Point<T, D>, b: &Point<T, D>) -> Option<Self>

The translation needed to make a coincide with b, i.e., b = a * translation_to(a, b).

impl<T: RealField + RealField, const D: usize> TwoSidedInverse<Multiplicative> for Translation<T, D>

fn two_sided_inverse(&self) -> Self

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

fn two_sided_inverse_mut(&mut self)

In-place inversion of self, relative to the operator O.

impl<T: Scalar + UlpsEq, const D: usize> UlpsEq<Translation<T, D>> for Translation<T, D> where
    T::Epsilon: Clone, 

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<T, const D: usize> Zeroable for Translation<T, D> where
    T: Scalar + Zeroable,
    SVector<T, D>: Zeroable, 

fn zeroed() -> Self

Calls zeroed.

impl<T: RealField + RealField, const D: usize> AbstractGroup<Multiplicative> for Translation<T, D>

impl<T: RealField + RealField, const D: usize> AbstractLoop<Multiplicative> for Translation<T, D>

impl<T: Copy, const D: usize> Copy for Translation<T, D>

impl<T: DeviceCopy, const D: usize> DeviceCopy for Translation<T, D>

impl<T: RealField + RealField, const D: usize> DirectIsometry<OPoint<T, Const<D>>> for Translation<T, D>

impl<T: Scalar + Eq, const D: usize> Eq for Translation<T, D>

impl<T: RealField + RealField, const D: usize> Isometry<OPoint<T, Const<D>>> for Translation<T, D>

impl<T, const D: usize> Pod for Translation<T, D> where
    T: Scalar + Pod,
    SVector<T, D>: Pod,