Struct nalgebra::geometry::TranslationBase

#[repr(C)]
pub struct TranslationBase<N: Scalar, D: DimName, S> {
    pub vector: ColumnVector<N, D, S>,
}

A translation.

Fields

vector: ColumnVector<N, D, S>

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

Methods

impl<N, D: DimName, S> TranslationBase<N, D, S> where
    N: Scalar,
    S: Storage<N, D, U1>, 

fn from_vector(vector: ColumnVector<N, D, S>) -> TranslationBase<N, D, S>

Creates a new translation from the given vector.

fn inverse(&self) -> OwnedTranslation<N, D, S> where
    N: ClosedNeg, 

Inverts self.

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

Converts this translation into its equivalent homogeneous transformation matrix.

impl<N, D: DimName, S> TranslationBase<N, D, S> where
    N: Scalar + ClosedNeg,
    S: StorageMut<N, D, U1>, 

fn inverse_mut(&mut self)

Inverts self in-place.

impl<N, D: DimName, S> TranslationBase<N, D, S> where
    N: Scalar + Zero,
    S: OwnedStorage<N, D, U1>,
    S::Alloc: OwnedAllocator<N, D, U1, S>, 

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

Creates a new square identity rotation of the given dimension.

impl<N, S> TranslationBase<N, U1, S> where
    N: Scalar,
    S: OwnedStorage<N, U1, U1>,
    S::Alloc: OwnedAllocator<N, U1, U1, S>, 

fn new(x: N) -> Self

Initializes this matrix from its components.

impl<N, S> TranslationBase<N, U2, S> where
    N: Scalar,
    S: OwnedStorage<N, U2, U1>,
    S::Alloc: OwnedAllocator<N, U2, U1, S>, 

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

Initializes this matrix from its components.

impl<N, S> TranslationBase<N, U3, S> where
    N: Scalar,
    S: OwnedStorage<N, U3, U1>,
    S::Alloc: OwnedAllocator<N, U3, U1, S>, 

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

Initializes this matrix from its components.

impl<N, S> TranslationBase<N, U4, S> where
    N: Scalar,
    S: OwnedStorage<N, U4, U1>,
    S::Alloc: OwnedAllocator<N, U4, U1, S>, 

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

Initializes this matrix from its components.

impl<N, S> TranslationBase<N, U5, S> where
    N: Scalar,
    S: OwnedStorage<N, U5, U1>,
    S::Alloc: OwnedAllocator<N, U5, U1, S>, 

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

Initializes this matrix from its components.

impl<N, S> TranslationBase<N, U6, S> where
    N: Scalar,
    S: OwnedStorage<N, U6, U1>,
    S::Alloc: OwnedAllocator<N, U6, U1, S>, 

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

Initializes this matrix from its components.

Trait Implementations

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

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

Feeds this value into the given [Hasher].

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

Feeds a slice of this type into the given [Hasher].

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

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

Formats the value using the given formatter.

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

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

Returns a copy of the value.

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

Performs copy-assignment from source.

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

impl<N, D: DimName, S> Eq for TranslationBase<N, D, S> where
    N: Scalar + Eq,
    S: Storage<N, D, U1>, 

impl<N, D: DimName, S> PartialEq for TranslationBase<N, D, S> where
    N: Scalar + PartialEq,
    S: Storage<N, D, U1>, 

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

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

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

This method tests for !=.

impl<N, D: DimName, S> ApproxEq for TranslationBase<N, D, S> where
    N: Scalar + ApproxEq,
    S: Storage<N, D, U1>,
    N::Epsilon: Copy, 

type Epsilon = N::Epsilon

Used for specifying relative comparisons.

fn default_epsilon() -> Self::Epsilon

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

fn default_max_relative() -> Self::Epsilon

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

fn default_max_ulps() -> u32

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

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

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

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

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

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

The inverse of ApproxEq::relative_eq.

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

The inverse of ApproxEq::ulps_eq.

impl<N, D: DimName, S> Display for TranslationBase<N, D, S> where
    N: Real + Display,
    S: Storage<N, D, U1>,
    S::Alloc: Allocator<usize, D, U1>, 

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

Formats the value using the given formatter.

impl<N, D: DimName, S> One for TranslationBase<N, D, S> where
    N: Scalar + Zero + ClosedAdd,
    S: OwnedStorage<N, D, U1>,
    S::Alloc: OwnedAllocator<N, D, U1, S>, 

fn one() -> Self

Returns the multiplicative identity element of Self, 1.

impl<N, D: DimName, S> Rand for TranslationBase<N, D, S> where
    N: Scalar + Rand,
    S: OwnedStorage<N, D, U1>,
    S::Alloc: OwnedAllocator<N, D, U1, S>, 

fn rand<G: Rng>(rng: &mut G) -> Self

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

impl<'a, 'b, N, D: DimName, SA, SB> Mul<&'b TranslationBase<N, D, SB>> for &'a TranslationBase<N, D, SA> where
    N: Scalar + ClosedAdd,
    SA: Storage<N, D, U1>,
    SB: Storage<N, D, U1>,
    SA::Alloc: SameShapeAllocator<N, D, U1, D, U1, SA>,
    ShapeConstraint: SameNumberOfRows<D, D, Representative = D> + SameNumberOfColumns<U1, U1>, 

type Output = OwnedTranslation<N, D, SA>

The resulting type after applying the * operator

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

The method for the * operator

impl<'a, N, D: DimName, SA, SB> Mul<TranslationBase<N, D, SA>> for &'a TranslationBase<N, D, SB> where
    N: Scalar + ClosedAdd,
    SA: Storage<N, D, U1>,
    SB: Storage<N, D, U1>,
    SA::Alloc: SameShapeAllocator<N, D, U1, D, U1, SA>,
    ShapeConstraint: SameNumberOfRows<D, D, Representative = D> + SameNumberOfColumns<U1, U1>, 

type Output = OwnedTranslation<N, D, SA>

The resulting type after applying the * operator

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

The method for the * operator

impl<'b, N, D: DimName, SA, SB> Mul<&'b TranslationBase<N, D, SB>> for TranslationBase<N, D, SA> where
    N: Scalar + ClosedAdd,
    SA: Storage<N, D, U1>,
    SB: Storage<N, D, U1>,
    SA::Alloc: SameShapeAllocator<N, D, U1, D, U1, SA>,
    ShapeConstraint: SameNumberOfRows<D, D, Representative = D> + SameNumberOfColumns<U1, U1>, 

type Output = OwnedTranslation<N, D, SA>

The resulting type after applying the * operator

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

The method for the * operator

impl<N, D: DimName, SA, SB> Mul<TranslationBase<N, D, SB>> for TranslationBase<N, D, SA> where
    N: Scalar + ClosedAdd,
    SA: Storage<N, D, U1>,
    SB: Storage<N, D, U1>,
    SA::Alloc: SameShapeAllocator<N, D, U1, D, U1, SA>,
    ShapeConstraint: SameNumberOfRows<D, D, Representative = D> + SameNumberOfColumns<U1, U1>, 

type Output = OwnedTranslation<N, D, SA>

The resulting type after applying the * operator

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

The method for the * operator

impl<'a, 'b, N, D: DimName, SA, SB> Div<&'b TranslationBase<N, D, SB>> for &'a TranslationBase<N, D, SA> where
    N: Scalar + ClosedSub,
    SA: Storage<N, D, U1>,
    SB: Storage<N, D, U1>,
    SA::Alloc: SameShapeAllocator<N, D, U1, D, U1, SA>,
    ShapeConstraint: SameNumberOfRows<D, D, Representative = D> + SameNumberOfColumns<U1, U1>, 

type Output = OwnedTranslation<N, D, SA>

The resulting type after applying the / operator

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

The method for the / operator

impl<'a, N, D: DimName, SA, SB> Div<TranslationBase<N, D, SA>> for &'a TranslationBase<N, D, SB> where
    N: Scalar + ClosedSub,
    SA: Storage<N, D, U1>,
    SB: Storage<N, D, U1>,
    SA::Alloc: SameShapeAllocator<N, D, U1, D, U1, SA>,
    ShapeConstraint: SameNumberOfRows<D, D, Representative = D> + SameNumberOfColumns<U1, U1>, 

type Output = OwnedTranslation<N, D, SA>

The resulting type after applying the / operator

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

The method for the / operator

impl<'b, N, D: DimName, SA, SB> Div<&'b TranslationBase<N, D, SB>> for TranslationBase<N, D, SA> where
    N: Scalar + ClosedSub,
    SA: Storage<N, D, U1>,
    SB: Storage<N, D, U1>,
    SA::Alloc: SameShapeAllocator<N, D, U1, D, U1, SA>,
    ShapeConstraint: SameNumberOfRows<D, D, Representative = D> + SameNumberOfColumns<U1, U1>, 

type Output = OwnedTranslation<N, D, SA>

The resulting type after applying the / operator

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

The method for the / operator

impl<N, D: DimName, SA, SB> Div<TranslationBase<N, D, SB>> for TranslationBase<N, D, SA> where
    N: Scalar + ClosedSub,
    SA: Storage<N, D, U1>,
    SB: Storage<N, D, U1>,
    SA::Alloc: SameShapeAllocator<N, D, U1, D, U1, SA>,
    ShapeConstraint: SameNumberOfRows<D, D, Representative = D> + SameNumberOfColumns<U1, U1>, 

type Output = OwnedTranslation<N, D, SA>

The resulting type after applying the / operator

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

The method for the / operator

impl<'a, 'b, N, D: DimName, SA, SB> Mul<&'b PointBase<N, D, SA>> for &'a TranslationBase<N, D, SB> where
    N: Scalar + ClosedAdd,
    SA: Storage<N, D, U1>,
    SB: Storage<N, D, U1>,
    SA::Alloc: SameShapeAllocator<N, D, U1, D, U1, SA>,
    ShapeConstraint: SameNumberOfRows<D, D, Representative = D> + SameNumberOfColumns<U1, U1>, 

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

The resulting type after applying the * operator

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

The method for the * operator

impl<'a, N, D: DimName, SA, SB> Mul<PointBase<N, D, SA>> for &'a TranslationBase<N, D, SB> where
    N: Scalar + ClosedAdd,
    SA: Storage<N, D, U1>,
    SB: Storage<N, D, U1>,
    SA::Alloc: SameShapeAllocator<N, D, U1, D, U1, SA>,
    ShapeConstraint: SameNumberOfRows<D, D, Representative = D> + SameNumberOfColumns<U1, U1>, 

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

The resulting type after applying the * operator

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

The method for the * operator

impl<'b, N, D: DimName, SA, SB> Mul<&'b PointBase<N, D, SB>> for TranslationBase<N, D, SA> where
    N: Scalar + ClosedAdd,
    SA: Storage<N, D, U1>,
    SB: Storage<N, D, U1>,
    SA::Alloc: SameShapeAllocator<N, D, U1, D, U1, SA>,
    ShapeConstraint: SameNumberOfRows<D, D, Representative = D> + SameNumberOfColumns<U1, U1>, 

type Output = OwnedPoint<N, D, SB::Alloc>

The resulting type after applying the * operator

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

The method for the * operator

impl<N, D: DimName, SA, SB> Mul<PointBase<N, D, SA>> for TranslationBase<N, D, SB> where
    N: Scalar + ClosedAdd,
    SA: Storage<N, D, U1>,
    SB: Storage<N, D, U1>,
    SA::Alloc: SameShapeAllocator<N, D, U1, D, U1, SA>,
    ShapeConstraint: SameNumberOfRows<D, D, Representative = D> + SameNumberOfColumns<U1, U1>, 

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

The resulting type after applying the * operator

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

The method for the * operator

impl<'b, N, D: DimName, SA, SB> MulAssign<&'b TranslationBase<N, D, SB>> for TranslationBase<N, D, SA> where
    N: Scalar + ClosedAdd,
    SA: OwnedStorage<N, D, U1>,
    SB: Storage<N, D, U1>,
    SA::Alloc: OwnedAllocator<N, D, U1, SA>,
    ShapeConstraint: SameNumberOfRows<D, D> + SameNumberOfColumns<U1, U1>, 

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

The method for the *= operator

impl<N, D: DimName, SA, SB> MulAssign<TranslationBase<N, D, SB>> for TranslationBase<N, D, SA> where
    N: Scalar + ClosedAdd,
    SA: OwnedStorage<N, D, U1>,
    SB: Storage<N, D, U1>,
    SA::Alloc: OwnedAllocator<N, D, U1, SA>,
    ShapeConstraint: SameNumberOfRows<D, D> + SameNumberOfColumns<U1, U1>, 

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

The method for the *= operator

impl<'b, N, D: DimName, SA, SB> DivAssign<&'b TranslationBase<N, D, SB>> for TranslationBase<N, D, SA> where
    N: Scalar + ClosedSub,
    SA: OwnedStorage<N, D, U1>,
    SB: Storage<N, D, U1>,
    SA::Alloc: OwnedAllocator<N, D, U1, SA>,
    ShapeConstraint: SameNumberOfRows<D, D> + SameNumberOfColumns<U1, U1>, 

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

The method for the /= operator

impl<N, D: DimName, SA, SB> DivAssign<TranslationBase<N, D, SB>> for TranslationBase<N, D, SA> where
    N: Scalar + ClosedSub,
    SA: OwnedStorage<N, D, U1>,
    SB: Storage<N, D, U1>,
    SA::Alloc: OwnedAllocator<N, D, U1, SA>,
    ShapeConstraint: SameNumberOfRows<D, D> + SameNumberOfColumns<U1, U1>, 

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

The method for the /= operator

impl<N, D: DimName, S> Identity<Multiplicative> for TranslationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, U1>,
    S::Alloc: OwnedAllocator<N, D, U1, S>, 

fn identity() -> Self

The identity element.

impl<N, D: DimName, S> Inverse<Multiplicative> for TranslationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, U1>,
    S::Alloc: OwnedAllocator<N, D, U1, S>, 

fn inverse(&self) -> Self

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

fn inverse_mut(&mut self)

In-place inversin of self.

impl<N, D: DimName, S> AbstractMagma<Multiplicative> for TranslationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, U1>,
    S::Alloc: OwnedAllocator<N, D, U1, S>, 

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

Performs an operation.

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

Performs specific operation.

impl<N, D: DimName, S> AbstractSemigroup<Multiplicative> for TranslationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, U1>,
    S::Alloc: OwnedAllocator<N, D, U1, S>, 

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

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

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

Returns true if associativity holds for the given arguments.

impl<N, D: DimName, S> AbstractMonoid<Multiplicative> for TranslationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, U1>,
    S::Alloc: OwnedAllocator<N, D, U1, S>, 

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

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

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

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

impl<N, D: DimName, S> AbstractQuasigroup<Multiplicative> for TranslationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, U1>,
    S::Alloc: OwnedAllocator<N, D, U1, S>, 

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

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

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

Returns true if latin squareness holds for the given arguments.

impl<N, D: DimName, S> AbstractLoop<Multiplicative> for TranslationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, U1>,
    S::Alloc: OwnedAllocator<N, D, U1, S>, 

impl<N, D: DimName, S> AbstractGroup<Multiplicative> for TranslationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, U1>,
    S::Alloc: OwnedAllocator<N, D, U1, S>, 

impl<N, D: DimName, S> Transformation<PointBase<N, D, S>> for TranslationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, U1>,
    S::Alloc: OwnedAllocator<N, D, U1, S>, 

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

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

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

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

impl<N, D: DimName, S> ProjectiveTransformation<PointBase<N, D, S>> for TranslationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, U1>,
    S::Alloc: OwnedAllocator<N, D, U1, S>, 

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

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

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

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

impl<N, D: DimName, S> AffineTransformation<PointBase<N, D, S>> for TranslationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, U1>,
    S::Alloc: OwnedAllocator<N, D, U1, S>, 

type Rotation = Id

Type of the first rotation to be applied.

type NonUniformScaling = Id

Type of the non-uniform scaling to be applied.

type Translation = Self

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

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

Decomposes this affine transformation into a rotation followed by a non-uniform scaling, followed by a rotation, followed by a translation.

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

Appends a translation to this similarity.

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

Prepends a translation to this similarity.

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

Appends a rotation to this similarity.

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

Prepends a rotation to this similarity.

fn append_scaling(&self, _: &Self::NonUniformScaling) -> Self

Appends a scaling factor to this similarity.

fn prepend_scaling(&self, _: &Self::NonUniformScaling) -> Self

Prepends a scaling factor to this similarity.

fn append_rotation_wrt_point(&self, r: &Self::Rotation, p: &E) -> Option<Self>

Appends to this similarity a rotation centered at the point p, i.e., this point is left invariant.

impl<N, D: DimName, S> Similarity<PointBase<N, D, S>> for TranslationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, U1>,
    S::Alloc: OwnedAllocator<N, D, U1, S>, 

type Scaling = Id

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

fn translation(&self) -> Self

The pure translational component of this similarity transformation.

fn rotation(&self) -> Id

The pure rotational component of this similarity transformation.

fn scaling(&self) -> Id

The pure scaling component of this similarity transformation.

fn translate_point(&self, pt: &E) -> E

Applies this transformation's pure translational part to a point.

fn rotate_point(&self, pt: &E) -> E

Applies this transformation's pure rotational part to a point.

fn scale_point(&self, pt: &E) -> E

Applies this transformation's pure scaling part to a point.

fn rotate_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation's pure rotational part to a vector.

fn scale_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation's pure scaling part to a vector.

fn inverse_translate_point(&self, pt: &E) -> E

Applies this transformation inverse's pure translational part to a point.

fn inverse_rotate_point(&self, pt: &E) -> E

Applies this transformation inverse's pure rotational part to a point.

fn inverse_scale_point(&self, pt: &E) -> E

Applies this transformation inverse's pure scaling part to a point.

fn inverse_rotate_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation inverse's pure rotational part to a vector.

fn inverse_scale_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

Applies this transformation inverse's pure scaling part to a vector.

impl<N, D: DimName, S> Isometry<PointBase<N, D, S>> for TranslationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, U1>,
    S::Alloc: OwnedAllocator<N, D, U1, S>, 

impl<N, D: DimName, S> DirectIsometry<PointBase<N, D, S>> for TranslationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, U1>,
    S::Alloc: OwnedAllocator<N, D, U1, S>, 

impl<N, D: DimName, S> Translation<PointBase<N, D, S>> for TranslationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, U1>,
    S::Alloc: OwnedAllocator<N, D, U1, S>, 

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

fn to_vector(&self) -> ColumnVector<N, D, S>

Converts this translation to a vector.

fn from_vector(v: ColumnVector<N, D, S>) -> Option<Self>

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

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

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

fn translation_between(
    a: &PointBase<N, D, S>,
    b: &PointBase<N, D, S>
) -> Option<Self>

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

impl<N1, N2, D: DimName, SA, SB> SubsetOf<TranslationBase<N2, D, SB>> for TranslationBase<N1, D, SA> where
    N1: Scalar,
    N2: Scalar + SupersetOf<N1>,
    SA: OwnedStorage<N1, D, U1>,
    SB: OwnedStorage<N2, D, U1>,
    SA::Alloc: OwnedAllocator<N1, D, U1, SA>,
    SB::Alloc: OwnedAllocator<N2, D, U1, SB>, 

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

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

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

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

unsafe fn from_superset_unchecked(rot: &TranslationBase<N2, D, SB>) -> Self

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

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

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

impl<N1, N2, D: DimName, SA, SB, R> SubsetOf<IsometryBase<N2, D, SB, R>> for TranslationBase<N1, D, SA> where
    N1: Real,
    N2: Real + SupersetOf<N1>,
    SA: OwnedStorage<N1, D, U1>,
    SB: OwnedStorage<N2, D, U1>,
    R: Rotation<PointBase<N2, D, SB>>,
    SA::Alloc: OwnedAllocator<N1, D, U1, SA>,
    SB::Alloc: OwnedAllocator<N2, D, U1, SB>, 

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

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

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

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

unsafe fn from_superset_unchecked(iso: &IsometryBase<N2, D, SB, R>) -> Self

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

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

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

impl<N1, N2, D: DimName, SA, SB, R> SubsetOf<SimilarityBase<N2, D, SB, R>> for TranslationBase<N1, D, SA> where
    N1: Real,
    N2: Real + SupersetOf<N1>,
    SA: OwnedStorage<N1, D, U1>,
    SB: OwnedStorage<N2, D, U1>,
    R: Rotation<PointBase<N2, D, SB>>,
    SA::Alloc: OwnedAllocator<N1, D, U1, SA>,
    SB::Alloc: OwnedAllocator<N2, D, U1, SB>, 

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

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

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

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

unsafe fn from_superset_unchecked(sim: &SimilarityBase<N2, D, SB, R>) -> Self

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

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

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

impl<N1, N2, D, SA, SB, C> SubsetOf<TransformBase<N2, D, SB, C>> for TranslationBase<N1, D, SA> where
    N1: Real,
    N2: Real + SupersetOf<N1>,
    SA: OwnedStorage<N1, D, U1>,
    SB: OwnedStorage<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>,
    C: SuperTCategoryOf<TAffine>,
    D: DimNameAdd<U1>,
    SA::Alloc: OwnedAllocator<N1, D, U1, SA> + Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>>,
    SB::Alloc: OwnedAllocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>, SB> + Allocator<N2, D, U1> + Allocator<N2, DimNameSum<D, U1>, D>, 

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

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

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

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

unsafe fn from_superset_unchecked(t: &TransformBase<N2, D, SB, C>) -> Self

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

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

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

impl<N1, N2, D, SA, SB> SubsetOf<SquareMatrix<N2, DimNameSum<D, U1>, SB>> for TranslationBase<N1, D, SA> where
    N1: Real,
    N2: Real + SupersetOf<N1>,
    SA: OwnedStorage<N1, D, U1>,
    SB: OwnedStorage<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>,
    D: DimNameAdd<U1>,
    SA::Alloc: OwnedAllocator<N1, D, U1, SA> + Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>>,
    SB::Alloc: OwnedAllocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>, SB> + Allocator<N2, D, U1> + Allocator<N2, DimNameSum<D, U1>, D>, 

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

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

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

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

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

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

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

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

impl<N, D: DimName, S, R> Mul<IsometryBase<N, D, S, R>> for TranslationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, U1>,
    R: Rotation<PointBase<N, D, S>>,
    S::Alloc: OwnedAllocator<N, D, U1, S>, 

type Output = IsometryBase<N, D, S, R>

The resulting type after applying the * operator

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

The method for the * operator

impl<'a, N, D: DimName, S, R> Mul<IsometryBase<N, D, S, R>> for &'a TranslationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, U1>,
    R: Rotation<PointBase<N, D, S>>,
    S::Alloc: OwnedAllocator<N, D, U1, S>, 

type Output = IsometryBase<N, D, S, R>

The resulting type after applying the * operator

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

The method for the * operator

impl<'b, N, D: DimName, S, R> Mul<&'b IsometryBase<N, D, S, R>> for TranslationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, U1>,
    R: Rotation<PointBase<N, D, S>>,
    S::Alloc: OwnedAllocator<N, D, U1, S>, 

type Output = IsometryBase<N, D, S, R>

The resulting type after applying the * operator

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

The method for the * operator

impl<'a, 'b, N, D: DimName, S, R> Mul<&'b IsometryBase<N, D, S, R>> for &'a TranslationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, U1>,
    R: Rotation<PointBase<N, D, S>>,
    S::Alloc: OwnedAllocator<N, D, U1, S>, 

type Output = IsometryBase<N, D, S, R>

The resulting type after applying the * operator

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

The method for the * operator

impl<N, D: DimName, S, R> Mul<R> for TranslationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, U1>,
    R: Rotation<PointBase<N, D, S>>,
    S::Alloc: OwnedAllocator<N, D, U1, S>, 

type Output = IsometryBase<N, D, S, R>

The resulting type after applying the * operator

fn mul(self, right: R) -> Self::Output

The method for the * operator

impl<'a, N, D: DimName, S, R> Mul<R> for &'a TranslationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, U1>,
    R: Rotation<PointBase<N, D, S>>,
    S::Alloc: OwnedAllocator<N, D, U1, S>, 

type Output = IsometryBase<N, D, S, R>

The resulting type after applying the * operator

fn mul(self, right: R) -> Self::Output

The method for the * operator

impl<'b, N, D: DimName, S, R> Mul<&'b R> for TranslationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, U1>,
    R: Rotation<PointBase<N, D, S>>,
    S::Alloc: OwnedAllocator<N, D, U1, S>, 

type Output = IsometryBase<N, D, S, R>

The resulting type after applying the * operator

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

The method for the * operator

impl<'a, 'b, N, D: DimName, S, R> Mul<&'b R> for &'a TranslationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, U1>,
    R: Rotation<PointBase<N, D, S>>,
    S::Alloc: OwnedAllocator<N, D, U1, S>, 

type Output = IsometryBase<N, D, S, R>

The resulting type after applying the * operator

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

The method for the * operator

impl<N, D: DimName, S, R> Mul<SimilarityBase<N, D, S, R>> for TranslationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, U1>,
    R: Rotation<PointBase<N, D, S>>,
    S::Alloc: OwnedAllocator<N, D, U1, S>, 

type Output = SimilarityBase<N, D, S, R>

The resulting type after applying the * operator

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

The method for the * operator

impl<'a, N, D: DimName, S, R> Mul<SimilarityBase<N, D, S, R>> for &'a TranslationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, U1>,
    R: Rotation<PointBase<N, D, S>>,
    S::Alloc: OwnedAllocator<N, D, U1, S>, 

type Output = SimilarityBase<N, D, S, R>

The resulting type after applying the * operator

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

The method for the * operator

impl<'b, N, D: DimName, S, R> Mul<&'b SimilarityBase<N, D, S, R>> for TranslationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, U1>,
    R: Rotation<PointBase<N, D, S>>,
    S::Alloc: OwnedAllocator<N, D, U1, S>, 

type Output = SimilarityBase<N, D, S, R>

The resulting type after applying the * operator

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

The method for the * operator

impl<'a, 'b, N, D: DimName, S, R> Mul<&'b SimilarityBase<N, D, S, R>> for &'a TranslationBase<N, D, S> where
    N: Real,
    S: OwnedStorage<N, D, U1>,
    R: Rotation<PointBase<N, D, S>>,
    S::Alloc: OwnedAllocator<N, D, U1, S>, 

type Output = SimilarityBase<N, D, S, R>

The resulting type after applying the * operator

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

The method for the * operator

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

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

The resulting type after applying the * operator

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

The method for the * operator

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

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

The resulting type after applying the * operator

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

The method for the * operator

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

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

The resulting type after applying the * operator

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

The method for the * operator

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

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

The resulting type after applying the * operator

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

The method for the * operator

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

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

The resulting type after applying the / operator

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

The method for the / operator

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

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

The resulting type after applying the / operator

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

The method for the / operator

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

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

The resulting type after applying the / operator

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

The method for the / operator

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

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

The resulting type after applying the / operator

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

The method for the / operator