Struct na::Translation

#[repr(C)]
pub struct Translation<T, const D: usize> {
    pub vector: Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>,
}

A translation.

Fields

vector: Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>

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

Implementations

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

pub fn from_vector( vector: Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>> ) -> 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 ) -> Matrix<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output, <DefaultAllocator as Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>>::Buffer>where T: Zero + One, Const<D>: DimNameAdd<Const<1>>, DefaultAllocator: Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>,

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

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

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

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>(self) -> Translation<To, D>where To: Scalar, Translation<To, D>: SupersetOf<Translation<T, D>>,

Cast the components of self to another type.

Example

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

impl<T> Translation<T, 1>

pub const fn new(x: T) -> Translation<T, 1>

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) -> Translation<T, 2>

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) -> Translation<T, 3>

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) -> Translation<T, 4>

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) -> Translation<T, 5>

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) -> Translation<T, 6>

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, const D: usize> AbsDiffEq<Translation<T, D>> for Translation<T, D>where T: Scalar + AbsDiffEq<T>, <T as AbsDiffEq<T>>::Epsilon: Clone,

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

Used for specifying relative comparisons.

fn default_epsilon( ) -> <Translation<T, D> as AbsDiffEq<Translation<T, D>>>::Epsilon

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

fn abs_diff_eq( &self, other: &Translation<T, D>, epsilon: <Translation<T, D> as AbsDiffEq<Translation<T, D>>>::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, const D: usize> Clone for Translation<T, D>where T: Clone,

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

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

Formats the value using the given formatter.

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

fn default() -> Translation<T, D>

Returns the “default value” for a type.

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

type Target = X<T>

The resulting type after dereferencing.

fn deref(&self) -> &<Translation<T, 1> as Deref>::Target

Dereferences the value.

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

type Target = XY<T>

The resulting type after dereferencing.

fn deref(&self) -> &<Translation<T, 2> as Deref>::Target

Dereferences the value.

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

type Target = XYZ<T>

The resulting type after dereferencing.

fn deref(&self) -> &<Translation<T, 3> as Deref>::Target

Dereferences the value.

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

type Target = XYZW<T>

The resulting type after dereferencing.

fn deref(&self) -> &<Translation<T, 4> as Deref>::Target

Dereferences the value.

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

type Target = XYZWA<T>

The resulting type after dereferencing.

fn deref(&self) -> &<Translation<T, 5> as Deref>::Target

Dereferences the value.

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

type Target = XYZWAB<T>

The resulting type after dereferencing.

fn deref(&self) -> &<Translation<T, 6> as Deref>::Target

Dereferences the value.

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

fn deref_mut(&mut self) -> &mut <Translation<T, 1> as Deref>::Target

Mutably dereferences the value.

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

fn deref_mut(&mut self) -> &mut <Translation<T, 2> as Deref>::Target

Mutably dereferences the value.

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

fn deref_mut(&mut self) -> &mut <Translation<T, 3> as Deref>::Target

Mutably dereferences the value.

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

fn deref_mut(&mut self) -> &mut <Translation<T, 4> as Deref>::Target

Mutably dereferences the value.

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

fn deref_mut(&mut self) -> &mut <Translation<T, 5> as Deref>::Target

Mutably dereferences the value.

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

fn deref_mut(&mut self) -> &mut <Translation<T, 6> as Deref>::Target

Mutably dereferences the value.

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

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

Formats the value using the given formatter.

impl<'a, 'b, T> Div<&'a Unit<DualQuaternion<T>>> for &'b Translation<T, 3>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div( self, rhs: &'a Unit<DualQuaternion<T>> ) -> <&'b Translation<T, 3> as Div<&'a Unit<DualQuaternion<T>>>>::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<T> + ClosedMul<T> + RealField, Const<D>: DimNameAdd<Const<1>>, C: TCategoryMul<TAffine>, DefaultAllocator: Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>,

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> ) -> <&'a Translation<T, D> as Div<&'b Transform<T, C, D>>>::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<T> + ClosedMul<T> + RealField, Const<D>: DimNameAdd<Const<1>>, C: TCategoryMul<TAffine>, DefaultAllocator: Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>,

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> ) -> <Translation<T, D> as Div<&'b Transform<T, C, D>>>::Output

Performs the / operation.

impl<'a, 'b, T> Div<&'b Translation<T, 3>> for &'a Unit<DualQuaternion<T>>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div( self, rhs: &'b Translation<T, 3> ) -> <&'a Unit<DualQuaternion<T>> as Div<&'b Translation<T, 3>>>::Output

Performs the / operation.

impl<'b, T> Div<&'b Translation<T, 3>> for Unit<DualQuaternion<T>>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div( self, rhs: &'b Translation<T, 3> ) -> <Unit<DualQuaternion<T>> as Div<&'b Translation<T, 3>>>::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<T> + ClosedMul<T> + RealField, Const<D>: DimNameAdd<Const<1>>, C: TCategoryMul<TAffine>, DefaultAllocator: Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>,

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> ) -> <&'a Transform<T, C, D> as Div<&'b Translation<T, D>>>::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<T>, ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<Const<1>, Const<1>, Representative = Const<1>>,

type Output = Translation<T, D>

The resulting type after applying the / operator.

fn div( self, right: &'b Translation<T, D> ) -> <&'a Translation<T, D> as Div<&'b Translation<T, D>>>::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<T> + ClosedMul<T> + RealField, Const<D>: DimNameAdd<Const<1>>, C: TCategoryMul<TAffine>, DefaultAllocator: Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>,

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> ) -> <Transform<T, C, D> as Div<&'b Translation<T, D>>>::Output

Performs the / operation.

impl<'b, T, const D: usize> Div<&'b Translation<T, D>> for Translation<T, D>where T: Scalar + ClosedSub<T>, ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<Const<1>, Const<1>, Representative = Const<1>>,

type Output = Translation<T, D>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'b, T> Div<&'b Unit<DualQuaternion<T>>> for Translation<T, 3>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div( self, rhs: &'b Unit<DualQuaternion<T>> ) -> <Translation<T, 3> as Div<&'b Unit<DualQuaternion<T>>>>::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<T> + ClosedMul<T> + RealField, Const<D>: DimNameAdd<Const<1>>, C: TCategoryMul<TAffine>, DefaultAllocator: Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>,

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> ) -> <&'a Translation<T, D> as Div<Transform<T, C, D>>>::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<T> + ClosedMul<T> + RealField, Const<D>: DimNameAdd<Const<1>>, C: TCategoryMul<TAffine>, DefaultAllocator: Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>,

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> ) -> <Translation<T, D> as Div<Transform<T, C, D>>>::Output

Performs the / operation.

impl<'a, T> Div<Translation<T, 3>> for &'a Unit<DualQuaternion<T>>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div( self, rhs: Translation<T, 3> ) -> <&'a Unit<DualQuaternion<T>> as Div<Translation<T, 3>>>::Output

Performs the / operation.

impl<T> Div<Translation<T, 3>> for Unit<DualQuaternion<T>>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div( self, rhs: Translation<T, 3> ) -> <Unit<DualQuaternion<T>> as Div<Translation<T, 3>>>::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<T> + ClosedMul<T> + RealField, Const<D>: DimNameAdd<Const<1>>, C: TCategoryMul<TAffine>, DefaultAllocator: Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>,

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

The resulting type after applying the / operator.

fn div( self, rhs: Translation<T, D> ) -> <&'a Transform<T, C, D> as Div<Translation<T, D>>>::Output

Performs the / operation.

impl<'a, T, const D: usize> Div<Translation<T, D>> for &'a Translation<T, D>where T: Scalar + ClosedSub<T>, ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<Const<1>, Const<1>, Representative = Const<1>>,

type Output = Translation<T, D>

The resulting type after applying the / operator.

fn div( self, right: Translation<T, D> ) -> <&'a Translation<T, D> as Div<Translation<T, D>>>::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<T> + ClosedMul<T> + RealField, Const<D>: DimNameAdd<Const<1>>, C: TCategoryMul<TAffine>, DefaultAllocator: Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>,

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

The resulting type after applying the / operator.

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

Performs the / operation.

impl<T, const D: usize> Div<Translation<T, D>> for Translation<T, D>where T: Scalar + ClosedSub<T>, ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<Const<1>, Const<1>, Representative = Const<1>>,

type Output = Translation<T, D>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, T> Div<Unit<DualQuaternion<T>>> for &'a Translation<T, 3>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div( self, rhs: Unit<DualQuaternion<T>> ) -> <&'a Translation<T, 3> as Div<Unit<DualQuaternion<T>>>>::Output

Performs the / operation.

impl<T> Div<Unit<DualQuaternion<T>>> for Translation<T, 3>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div( self, rhs: Unit<DualQuaternion<T>> ) -> <Translation<T, 3> as Div<Unit<DualQuaternion<T>>>>::Output

Performs the / operation.

impl<'b, T> DivAssign<&'b Translation<T, 3>> for Unit<DualQuaternion<T>>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

fn div_assign(&mut self, rhs: &'b Translation<T, 3>)

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<T> + ClosedMul<T> + RealField, Const<D>: DimNameAdd<Const<1>>, C: TCategory, DefaultAllocator: Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>,

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<T>,

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

Performs the /= operation.

impl<T> DivAssign<Translation<T, 3>> for Unit<DualQuaternion<T>>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

fn div_assign(&mut self, rhs: Translation<T, 3>)

Performs the /= operation.

impl<T, C, const D: usize> DivAssign<Translation<T, D>> for Transform<T, C, D>where T: Scalar + Zero + One + ClosedAdd<T> + ClosedMul<T> + RealField, Const<D>: DimNameAdd<Const<1>>, C: TCategory, DefaultAllocator: Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>,

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<T>,

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

Performs the /= operation.

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

fn from(coords: [T; D]) -> Translation<T, D>

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

fn from( vector: Matrix<T, Const<D>, Const<1>, <DefaultAllocator as Allocator<T, Const<D>, Const<1>>>::Buffer> ) -> Translation<T, D>

Converts to this type from the input type.

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

fn from(pt: OPoint<T, Const<D>>) -> Translation<T, D>

Converts to this type from the input type.

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

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

Converts to this type from the input type.

impl<T, const D: usize> From<Translation<T, D>> for Matrix<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output, <DefaultAllocator as Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>>::Buffer>where T: Scalar + Zero + One, Const<D>: DimNameAdd<Const<1>>, DefaultAllocator: Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output> + Allocator<T, Const<D>, Const<1>>,

fn from( t: Translation<T, D> ) -> Matrix<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output, <DefaultAllocator as Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>>::Buffer>

Converts to this type from the input type.

impl<T, const D: usize> Hash for Translation<T, D>where T: Scalar + Hash, <DefaultAllocator as Allocator<T, Const<D>, Const<1>>>::Buffer: Hash,

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

Feeds this value into the given Hasher.

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

Feeds a slice of this type into the given Hasher.

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

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul( self, rhs: &'a Unit<DualQuaternion<T>> ) -> <&'b Translation<T, 3> as Mul<&'a Unit<DualQuaternion<T>>>>::Output

Performs the * operation.

impl<'a, 'b, T, R, const D: usize> Mul<&'b Isometry<T, R, D>> for &'a Translation<T, D>where T: SimdRealField, <T as SimdValue>::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> ) -> <&'a Translation<T, D> as Mul<&'b Isometry<T, R, D>>>::Output

Performs the * operation.

impl<'b, T, R, const D: usize> Mul<&'b Isometry<T, R, D>> for Translation<T, D>where T: SimdRealField, <T as SimdValue>::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> ) -> <Translation<T, D> as Mul<&'b Isometry<T, R, D>>>::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<T>, ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<Const<1>, Const<1>, Representative = Const<1>>,

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

The resulting type after applying the * operator.

fn mul( self, right: &'b OPoint<T, Const<D>> ) -> <&'a Translation<T, D> as Mul<&'b OPoint<T, Const<D>>>>::Output

Performs the * operation.

impl<'b, T, const D: usize> Mul<&'b OPoint<T, Const<D>>> for Translation<T, D>where T: Scalar + ClosedAdd<T>, ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<Const<1>, Const<1>, Representative = Const<1>>,

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

The resulting type after applying the * operator.

fn mul( self, right: &'b OPoint<T, Const<D>> ) -> <Translation<T, D> as Mul<&'b OPoint<T, Const<D>>>>::Output

Performs the * operation.

impl<'a, 'b, T, const D: usize> Mul<&'b Rotation<T, D>> for &'a Translation<T, D>where T: SimdRealField, <T as SimdValue>::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> ) -> <&'a Translation<T, D> as Mul<&'b Rotation<T, D>>>::Output

Performs the * operation.

impl<'b, T, const D: usize> Mul<&'b Rotation<T, D>> for Translation<T, D>where T: SimdRealField, <T as SimdValue>::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> ) -> <Translation<T, D> as Mul<&'b Rotation<T, D>>>::Output

Performs the * operation.

impl<'a, 'b, T, R, const D: usize> Mul<&'b Similarity<T, R, D>> for &'a Translation<T, D>where T: SimdRealField, <T as SimdValue>::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> ) -> <&'a Translation<T, D> as Mul<&'b Similarity<T, R, D>>>::Output

Performs the * operation.

impl<'b, T, R, const D: usize> Mul<&'b Similarity<T, R, D>> for Translation<T, D>where T: SimdRealField, <T as SimdValue>::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> ) -> <Translation<T, D> as Mul<&'b Similarity<T, R, D>>>::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<T> + ClosedMul<T> + RealField, Const<D>: DimNameAdd<Const<1>>, C: TCategoryMul<TAffine>, DefaultAllocator: Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>,

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> ) -> <&'a Translation<T, D> as Mul<&'b Transform<T, C, D>>>::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<T> + ClosedMul<T> + RealField, Const<D>: DimNameAdd<Const<1>>, C: TCategoryMul<TAffine>, DefaultAllocator: Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>,

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> ) -> <Translation<T, D> as Mul<&'b Transform<T, C, D>>>::Output

Performs the * operation.

impl<'a, 'b, T> Mul<&'b Translation<T, 2>> for &'a Unit<Complex<T>>where T: SimdRealField, <T as SimdValue>::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> ) -> <&'a Unit<Complex<T>> as Mul<&'b Translation<T, 2>>>::Output

Performs the * operation.

impl<'b, T> Mul<&'b Translation<T, 2>> for Unit<Complex<T>>where T: SimdRealField, <T as SimdValue>::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> ) -> <Unit<Complex<T>> as Mul<&'b Translation<T, 2>>>::Output

Performs the * operation.

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

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul( self, rhs: &'b Translation<T, 3> ) -> <&'a Unit<DualQuaternion<T>> as Mul<&'b Translation<T, 3>>>::Output

Performs the * operation.

impl<'a, 'b, T> Mul<&'b Translation<T, 3>> for &'a Unit<Quaternion<T>>where T: SimdRealField, <T as SimdValue>::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> ) -> <&'a Unit<Quaternion<T>> as Mul<&'b Translation<T, 3>>>::Output

Performs the * operation.

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

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul( self, rhs: &'b Translation<T, 3> ) -> <Unit<DualQuaternion<T>> as Mul<&'b Translation<T, 3>>>::Output

Performs the * operation.

impl<'b, T> Mul<&'b Translation<T, 3>> for Unit<Quaternion<T>>where T: SimdRealField, <T as SimdValue>::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> ) -> <Unit<Quaternion<T>> as Mul<&'b Translation<T, 3>>>::Output

Performs the * operation.

impl<'a, 'b, T, R, const D: usize> Mul<&'b Translation<T, D>> for &'a Isometry<T, R, D>where T: SimdRealField, <T as SimdValue>::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> ) -> <&'a Isometry<T, R, D> as Mul<&'b Translation<T, D>>>::Output

Performs the * operation.

impl<'a, 'b, T, const D: usize> Mul<&'b Translation<T, D>> for &'a Rotation<T, D>where T: SimdRealField, <T as SimdValue>::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> ) -> <&'a Rotation<T, D> as Mul<&'b Translation<T, D>>>::Output

Performs the * operation.

impl<'a, 'b, T, R, const D: usize> Mul<&'b Translation<T, D>> for &'a Similarity<T, R, D>where T: SimdRealField, <T as SimdValue>::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> ) -> <&'a Similarity<T, R, D> as Mul<&'b Translation<T, D>>>::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<T> + ClosedMul<T> + RealField, Const<D>: DimNameAdd<Const<1>>, C: TCategoryMul<TAffine>, DefaultAllocator: Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>,

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> ) -> <&'a Transform<T, C, D> as Mul<&'b Translation<T, D>>>::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<T>, ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<Const<1>, Const<1>, Representative = Const<1>>,

type Output = Translation<T, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, T, R, const D: usize> Mul<&'b Translation<T, D>> for Isometry<T, R, D>where T: SimdRealField, <T as SimdValue>::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> ) -> <Isometry<T, R, D> as Mul<&'b Translation<T, D>>>::Output

Performs the * operation.

impl<'b, T, const D: usize> Mul<&'b Translation<T, D>> for Rotation<T, D>where T: SimdRealField, <T as SimdValue>::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> ) -> <Rotation<T, D> as Mul<&'b Translation<T, D>>>::Output

Performs the * operation.

impl<'b, T, R, const D: usize> Mul<&'b Translation<T, D>> for Similarity<T, R, D>where T: SimdRealField, <T as SimdValue>::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> ) -> <Similarity<T, R, D> as Mul<&'b Translation<T, D>>>::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<T> + ClosedMul<T> + RealField, Const<D>: DimNameAdd<Const<1>>, C: TCategoryMul<TAffine>, DefaultAllocator: Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>,

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> ) -> <Transform<T, C, D> as Mul<&'b Translation<T, D>>>::Output

Performs the * operation.

impl<'b, T, const D: usize> Mul<&'b Translation<T, D>> for Translation<T, D>where T: Scalar + ClosedAdd<T>, ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<Const<1>, Const<1>, Representative = Const<1>>,

type Output = Translation<T, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

fn mul( self, right: &'b Unit<Complex<T>> ) -> <&'a Translation<T, 2> as Mul<&'b Unit<Complex<T>>>>::Output

Performs the * operation.

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

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

The resulting type after applying the * operator.

fn mul( self, right: &'b Unit<Complex<T>> ) -> <Translation<T, 2> as Mul<&'b Unit<Complex<T>>>>::Output

Performs the * operation.

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

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul( self, rhs: &'b Unit<DualQuaternion<T>> ) -> <Translation<T, 3> as Mul<&'b Unit<DualQuaternion<T>>>>::Output

Performs the * operation.

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

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

The resulting type after applying the * operator.

fn mul( self, right: &'b Unit<Quaternion<T>> ) -> <&'a Translation<T, 3> as Mul<&'b Unit<Quaternion<T>>>>::Output

Performs the * operation.

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

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

The resulting type after applying the * operator.

fn mul( self, right: &'b Unit<Quaternion<T>> ) -> <Translation<T, 3> as Mul<&'b Unit<Quaternion<T>>>>::Output

Performs the * operation.

impl<'a, T, R, const D: usize> Mul<Isometry<T, R, D>> for &'a Translation<T, D>where T: SimdRealField, <T as SimdValue>::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> ) -> <&'a Translation<T, D> as Mul<Isometry<T, R, D>>>::Output

Performs the * operation.

impl<T, R, const D: usize> Mul<Isometry<T, R, D>> for Translation<T, D>where T: SimdRealField, <T as SimdValue>::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> ) -> <Translation<T, D> as Mul<Isometry<T, R, D>>>::Output

Performs the * operation.

impl<'a, T, const D: usize> Mul<OPoint<T, Const<D>>> for &'a Translation<T, D>where T: Scalar + ClosedAdd<T>, ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<Const<1>, Const<1>, Representative = Const<1>>,

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

The resulting type after applying the * operator.

fn mul( self, right: OPoint<T, Const<D>> ) -> <&'a Translation<T, D> as Mul<OPoint<T, Const<D>>>>::Output

Performs the * operation.

impl<T, const D: usize> Mul<OPoint<T, Const<D>>> for Translation<T, D>where T: Scalar + ClosedAdd<T>, ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<Const<1>, Const<1>, Representative = Const<1>>,

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

The resulting type after applying the * operator.

fn mul( self, right: OPoint<T, Const<D>> ) -> <Translation<T, D> as Mul<OPoint<T, Const<D>>>>::Output

Performs the * operation.

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

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

The resulting type after applying the * operator.

fn mul( self, right: Rotation<T, D> ) -> <&'a Translation<T, D> as Mul<Rotation<T, D>>>::Output

Performs the * operation.

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

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

The resulting type after applying the * operator.

fn mul( self, right: Rotation<T, D> ) -> <Translation<T, D> as Mul<Rotation<T, D>>>::Output

Performs the * operation.

impl<'a, T, R, const D: usize> Mul<Similarity<T, R, D>> for &'a Translation<T, D>where T: SimdRealField, <T as SimdValue>::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> ) -> <&'a Translation<T, D> as Mul<Similarity<T, R, D>>>::Output

Performs the * operation.

impl<T, R, const D: usize> Mul<Similarity<T, R, D>> for Translation<T, D>where T: SimdRealField, <T as SimdValue>::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> ) -> <Translation<T, D> as Mul<Similarity<T, R, D>>>::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<T> + ClosedMul<T> + RealField, Const<D>: DimNameAdd<Const<1>>, C: TCategoryMul<TAffine>, DefaultAllocator: Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>,

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> ) -> <&'a Translation<T, D> as Mul<Transform<T, C, D>>>::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<T> + ClosedMul<T> + RealField, Const<D>: DimNameAdd<Const<1>>, C: TCategoryMul<TAffine>, DefaultAllocator: Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>,

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> ) -> <Translation<T, D> as Mul<Transform<T, C, D>>>::Output

Performs the * operation.

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

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

The resulting type after applying the * operator.

fn mul( self, rhs: Translation<T, 2> ) -> <&'a Unit<Complex<T>> as Mul<Translation<T, 2>>>::Output

Performs the * operation.

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

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

The resulting type after applying the * operator.

fn mul( self, rhs: Translation<T, 2> ) -> <Unit<Complex<T>> as Mul<Translation<T, 2>>>::Output

Performs the * operation.

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

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul( self, rhs: Translation<T, 3> ) -> <&'a Unit<DualQuaternion<T>> as Mul<Translation<T, 3>>>::Output

Performs the * operation.

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

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

The resulting type after applying the * operator.

fn mul( self, right: Translation<T, 3> ) -> <&'a Unit<Quaternion<T>> as Mul<Translation<T, 3>>>::Output

Performs the * operation.

impl<T> Mul<Translation<T, 3>> for Unit<DualQuaternion<T>>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul( self, rhs: Translation<T, 3> ) -> <Unit<DualQuaternion<T>> as Mul<Translation<T, 3>>>::Output

Performs the * operation.

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

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

The resulting type after applying the * operator.

fn mul( self, right: Translation<T, 3> ) -> <Unit<Quaternion<T>> as Mul<Translation<T, 3>>>::Output

Performs the * operation.

impl<'a, T, R, const D: usize> Mul<Translation<T, D>> for &'a Isometry<T, R, D>where T: SimdRealField, <T as SimdValue>::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> ) -> <&'a Isometry<T, R, D> as Mul<Translation<T, D>>>::Output

Performs the * operation.

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

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

The resulting type after applying the * operator.

fn mul( self, right: Translation<T, D> ) -> <&'a Rotation<T, D> as Mul<Translation<T, D>>>::Output

Performs the * operation.

impl<'a, T, R, const D: usize> Mul<Translation<T, D>> for &'a Similarity<T, R, D>where T: SimdRealField, <T as SimdValue>::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> ) -> <&'a Similarity<T, R, D> as Mul<Translation<T, D>>>::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<T> + ClosedMul<T> + RealField, Const<D>: DimNameAdd<Const<1>>, C: TCategoryMul<TAffine>, DefaultAllocator: Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>,

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

The resulting type after applying the * operator.

fn mul( self, rhs: Translation<T, D> ) -> <&'a Transform<T, C, D> as Mul<Translation<T, D>>>::Output

Performs the * operation.

impl<'a, T, const D: usize> Mul<Translation<T, D>> for &'a Translation<T, D>where T: Scalar + ClosedAdd<T>, ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<Const<1>, Const<1>, Representative = Const<1>>,

type Output = Translation<T, D>

The resulting type after applying the * operator.

fn mul( self, right: Translation<T, D> ) -> <&'a Translation<T, D> as Mul<Translation<T, D>>>::Output

Performs the * operation.

impl<T, R, const D: usize> Mul<Translation<T, D>> for Isometry<T, R, D>where T: SimdRealField, <T as SimdValue>::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> ) -> <Isometry<T, R, D> as Mul<Translation<T, D>>>::Output

Performs the * operation.

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

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

The resulting type after applying the * operator.

fn mul( self, right: Translation<T, D> ) -> <Rotation<T, D> as Mul<Translation<T, D>>>::Output

Performs the * operation.

impl<T, R, const D: usize> Mul<Translation<T, D>> for Similarity<T, R, D>where T: SimdRealField, <T as SimdValue>::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> ) -> <Similarity<T, R, D> as Mul<Translation<T, D>>>::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<T> + ClosedMul<T> + RealField, Const<D>: DimNameAdd<Const<1>>, C: TCategoryMul<TAffine>, DefaultAllocator: Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>,

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T, const D: usize> Mul<Translation<T, D>> for Translation<T, D>where T: Scalar + ClosedAdd<T>, ShapeConstraint: SameNumberOfRows<Const<D>, Const<D>, Representative = Const<D>> + SameNumberOfColumns<Const<1>, Const<1>, Representative = Const<1>>,

type Output = Translation<T, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

fn mul( self, right: Unit<Complex<T>> ) -> <&'a Translation<T, 2> as Mul<Unit<Complex<T>>>>::Output

Performs the * operation.

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

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

The resulting type after applying the * operator.

fn mul( self, right: Unit<Complex<T>> ) -> <Translation<T, 2> as Mul<Unit<Complex<T>>>>::Output

Performs the * operation.

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

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul( self, rhs: Unit<DualQuaternion<T>> ) -> <&'a Translation<T, 3> as Mul<Unit<DualQuaternion<T>>>>::Output

Performs the * operation.

impl<T> Mul<Unit<DualQuaternion<T>>> for Translation<T, 3>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul( self, rhs: Unit<DualQuaternion<T>> ) -> <Translation<T, 3> as Mul<Unit<DualQuaternion<T>>>>::Output

Performs the * operation.

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

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

The resulting type after applying the * operator.

fn mul( self, right: Unit<Quaternion<T>> ) -> <&'a Translation<T, 3> as Mul<Unit<Quaternion<T>>>>::Output

Performs the * operation.

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

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

The resulting type after applying the * operator.

fn mul( self, right: Unit<Quaternion<T>> ) -> <Translation<T, 3> as Mul<Unit<Quaternion<T>>>>::Output

Performs the * operation.

impl<'b, T> MulAssign<&'b Translation<T, 3>> for Unit<DualQuaternion<T>>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

fn mul_assign(&mut self, rhs: &'b Translation<T, 3>)

Performs the *= operation.

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

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

Performs the *= operation.

impl<'b, T, R, const D: usize> MulAssign<&'b Translation<T, D>> for Similarity<T, R, D>where T: SimdRealField, <T as SimdValue>::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<T> + ClosedMul<T> + RealField, Const<D>: DimNameAdd<Const<1>>, C: TCategory, DefaultAllocator: Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>,

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<T>,

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

Performs the *= operation.

impl<T> MulAssign<Translation<T, 3>> for Unit<DualQuaternion<T>>where T: SimdRealField, <T as SimdValue>::Element: SimdRealField,

fn mul_assign(&mut self, rhs: Translation<T, 3>)

Performs the *= operation.

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

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

Performs the *= operation.

impl<T, R, const D: usize> MulAssign<Translation<T, D>> for Similarity<T, R, D>where T: SimdRealField, <T as SimdValue>::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<T> + ClosedMul<T> + RealField, Const<D>: DimNameAdd<Const<1>>, C: TCategory, DefaultAllocator: Allocator<T, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>,

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<T>,

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

Performs the *= operation.

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

fn one() -> Translation<T, D>

Returns the multiplicative identity element of Self, 1.

fn set_one(&mut self)

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

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

Returns true if self is equal to the multiplicative identity.

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

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 !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

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

fn default_max_relative( ) -> <Translation<T, D> as AbsDiffEq<Translation<T, D>>>::Epsilon

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

fn relative_eq( &self, other: &Translation<T, D>, epsilon: <Translation<T, D> as AbsDiffEq<Translation<T, D>>>::Epsilon, max_relative: <Translation<T, D> as AbsDiffEq<Translation<T, D>>>::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<T, const D: usize> SimdValue for Translation<T, D>where T: Scalar + SimdValue, <T as SimdValue>::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: <Translation<T, D> as SimdValue>::Element) -> Translation<T, D>

Initializes an SIMD value with each lanes set to val.

fn extract(&self, i: usize) -> <Translation<T, D> as SimdValue>::Element

Extracts the i-th lane of self.

unsafe fn extract_unchecked( &self, i: usize ) -> <Translation<T, D> as SimdValue>::Element

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

fn replace(&mut self, i: usize, val: <Translation<T, D> as SimdValue>::Element)

Replaces the i-th lane of self by val.

unsafe fn replace_unchecked( &mut self, i: usize, val: <Translation<T, D> as SimdValue>::Element )

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

fn select( self, cond: <Translation<T, D> as SimdValue>::SimdBool, other: Translation<T, D> ) -> Translation<T, D>

Merges self and other depending on the lanes of cond.

fn map_lanes(self, f: impl Fn(Self::Element) -> Self::Element) -> Selfwhere 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 ) -> Selfwhere 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>) -> Translation<T1, D>

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<Const<1>>, DefaultAllocator: Allocator<T1, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output> + Allocator<T2, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>,

fn to_superset( &self ) -> 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>

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

fn is_in_subset( m: &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> ) -> bool

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

fn from_superset_unchecked( m: &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> ) -> Translation<T1, D>

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>) -> Translation<T1, D>

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<Const<1>>, DefaultAllocator: Allocator<T1, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output> + Allocator<T2, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>,

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>) -> Translation<T1, D>

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>) -> Translation<T1, D>

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> SubsetOf<Unit<DualQuaternion<T2>>> for Translation<T1, 3>where T1: RealField, T2: RealField + SupersetOf<T1>,

fn to_superset(&self) -> Unit<DualQuaternion<T2>>

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

fn is_in_subset(dq: &Unit<DualQuaternion<T2>>) -> bool

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

fn from_superset_unchecked(dq: &Unit<DualQuaternion<T2>>) -> Translation<T1, 3>

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, const D: usize> UlpsEq<Translation<T, D>> for Translation<T, D>where T: Scalar + UlpsEq<T>, <T as AbsDiffEq<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: &Translation<T, D>, epsilon: <Translation<T, D> as AbsDiffEq<Translation<T, D>>>::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> Copy for Translation<T, D>where T: Copy,

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