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.

#[must_use = "Did you mean to use inverse_mut()?"]

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: Copy, 

type Epsilon = 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.

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

The inverse of AbsDiffEq::abs_diff_eq.

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

fn clone(&self) -> Self

Returns a copy of the value.

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

Performs copy-assignment from source.

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

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

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

Formats the value using the given formatter.

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<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<'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::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, 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::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_usize>> for &'a UnitDualQuaternion<T> where
    T::Element: SimdRealField, 

type Output = UnitDualQuaternion<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_usize>> for UnitDualQuaternion<T> where
    T::Element: SimdRealField, 

type Output = UnitDualQuaternion<T>

The resulting type after applying the / operator.

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

The resulting type after applying the / operator.

fn div(self, rhs: &'b Translation<T, 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::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, 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::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_usize>> for &'a UnitDualQuaternion<T> where
    T::Element: SimdRealField, 

type Output = UnitDualQuaternion<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_usize>> for UnitDualQuaternion<T> where
    T::Element: SimdRealField, 

type Output = UnitDualQuaternion<T>

The resulting type after applying the / operator.

fn div(self, rhs: Translation3<T>) -> 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, 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<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::Representative, D>

The resulting type after applying the / operator.

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

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<'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<T: SimdRealField> DivAssign<Translation<T, 3_usize>> for UnitDualQuaternion<T> where
    T::Element: SimdRealField, 

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

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

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

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

Performs the conversion.

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

Performs the conversion.

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

Performs the conversion.

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

Performs the conversion.

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

Performs the conversion.

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

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

Performs the conversion.

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

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

Performs the conversion.

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

Performs the conversion.

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

Performs the conversion.

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.

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

Feeds a slice of this type into the given Hasher.

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

fn into(self) -> [T; D]

Performs the conversion.

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: 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<'a, 'b, T, const D: usize> Mul<&'b Point<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 = Point<T, 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 Point<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 = Point<T, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<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, 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, 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: 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, 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::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, 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::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: SimdRealField> Mul<&'b Translation<T, 2_usize>> for UnitComplex<T> where
    T::Element: SimdRealField, 

type Output = Isometry<T, UnitComplex<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, 2_usize>> for &'a UnitComplex<T> where
    T::Element: SimdRealField, 

type Output = Isometry<T, UnitComplex<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_usize>> for &'a UnitDualQuaternion<T> where
    T::Element: SimdRealField, 

type Output = UnitDualQuaternion<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_usize>> for UnitDualQuaternion<T> where
    T::Element: SimdRealField, 

type Output = UnitDualQuaternion<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_usize>> for UnitQuaternion<T> where
    T::Element: SimdRealField, 

type Output = Isometry<T, UnitQuaternion<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> Mul<&'b Translation<T, 3_usize>> for &'a UnitQuaternion<T> where
    T::Element: SimdRealField, 

type Output = Isometry<T, UnitQuaternion<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, 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, 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<'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<'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<'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<'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<'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<'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<'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::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, 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::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: SimdRealField> Mul<&'b Unit<Complex<T>>> for Translation<T, 2> where
    T::Element: SimdRealField, 

type Output = Isometry<T, UnitComplex<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<Complex<T>>> for &'a Translation<T, 2> where
    T::Element: SimdRealField, 

type Output = Isometry<T, UnitComplex<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<Quaternion<T>>> for Translation<T, 3> where
    T::Element: SimdRealField, 

type Output = Isometry<T, UnitQuaternion<T>, 3>

The resulting type after applying the * operator.

fn mul(self, right: &'b UnitQuaternion<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, UnitQuaternion<T>, 3>

The resulting type after applying the * operator.

fn mul(self, right: &'b UnitQuaternion<T>) -> 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: 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<'a, T, const D: usize> Mul<Point<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 = Point<T, 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<Point<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 = Point<T, D>

The resulting type after applying the * operator.

fn mul(self, right: Point<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, 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, 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: 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, 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::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, 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::Representative, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<T, UnitComplex<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, 2_usize>> for &'a UnitComplex<T> where
    T::Element: SimdRealField, 

type Output = Isometry<T, UnitComplex<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_usize>> for &'a UnitDualQuaternion<T> where
    T::Element: SimdRealField, 

type Output = UnitDualQuaternion<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_usize>> for UnitDualQuaternion<T> where
    T::Element: SimdRealField, 

type Output = UnitDualQuaternion<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_usize>> for UnitQuaternion<T> where
    T::Element: SimdRealField, 

type Output = Isometry<T, UnitQuaternion<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> Mul<Translation<T, 3_usize>> for &'a UnitQuaternion<T> where
    T::Element: SimdRealField, 

type Output = Isometry<T, UnitQuaternion<T>, 3>

The resulting type after applying the * operator.

fn mul(self, right: Translation<T, 3>) -> 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, 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<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<'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<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<'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<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<'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<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::Representative, D>

The resulting type after applying the * operator.

fn mul(self, rhs: 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::Representative, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<T, UnitComplex<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<Complex<T>>> for &'a Translation<T, 2> where
    T::Element: SimdRealField, 

type Output = Isometry<T, UnitComplex<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<Quaternion<T>>> for Translation<T, 3> where
    T::Element: SimdRealField, 

type Output = Isometry<T, UnitQuaternion<T>, 3>

The resulting type after applying the * operator.

fn mul(self, right: UnitQuaternion<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, UnitQuaternion<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_usize>> for UnitDualQuaternion<T> where
    T::Element: SimdRealField, 

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

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<'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<T: SimdRealField> MulAssign<Translation<T, 3_usize>> for UnitDualQuaternion<T> where
    T::Element: SimdRealField, 

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

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

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

pub fn set_one(&mut self)

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

pub 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 ==.

#[must_use]

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

This method tests for !=.

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

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

The inverse of RelativeEq::relative_eq.

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

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

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

type SimdBool = T::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.

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

Applies a function to each lane of self.

pub 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<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.

pub 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_usize>>>::Output, <Const<D> as DimNameAdd<Const<1_usize>>>::Output, <DefaultAllocator as Allocator<T2, <Const<D> as DimNameAdd<Const<1_usize>>>::Output, <Const<D> as DimNameAdd<Const<1_usize>>>::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.

pub 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.

pub 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.

pub 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.

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

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

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

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

The inverse of UlpsEq::ulps_eq.