[][src]Struct nalgebra::Id

#[repr(C)]
pub struct Id<O = Multiplicative> where
    O: Operator
{ /* fields omitted */ }

The universal identity element wrt. a given operator, usually noted Id with a context-dependent subscript.

By default, it is the multiplicative identity element. It represents the degenerate set containing only the identity element of any group-like structure. It has no dimension known at compile-time. All its operations are no-ops.

Methods

impl<O> Id<O> where
    O: Operator
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Creates a new identity element.

Trait Implementations

impl<O> JoinSemilattice for Id<O> where
    O: Operator
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impl<E> OrthogonalTransformation<E> for Id<Multiplicative> where
    E: EuclideanSpace
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impl<O> PartialEq<Id<O>> for Id<O> where
    O: Operator
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This method tests for !=.

impl<O> RelativeEq for Id<O> where
    O: Operator
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The inverse of ApproxEq::relative_eq.

impl<O> Debug for Id<O> where
    O: Operator + Debug
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impl<O> AbstractGroup<O> for Id<O> where
    O: Operator
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impl<O> AbstractLoop<O> for Id<O> where
    O: Operator
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impl Div<Id<Multiplicative>> for Id<Multiplicative>
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The resulting type after applying the / operator.

impl<O> Clone for Id<O> where
    O: Operator
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Performs copy-assignment from source. Read more

impl<O> PartialOrd<Id<O>> for Id<O> where
    O: Operator
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This method tests less than (for self and other) and is used by the < operator. Read more

This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

This method tests greater than (for self and other) and is used by the > operator. Read more

This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl<O> AbsDiffEq for Id<O> where
    O: Operator
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Used for specifying relative comparisons.

The inverse of ApproxEq::abs_diff_eq.

impl Add<Id<Additive>> for Id<Additive>
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The resulting type after applying the + operator.

impl<O> Inverse<O> for Id<O> where
    O: Operator
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impl<E> Scaling<E> for Id<Multiplicative> where
    E: EuclideanSpace
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Converts this scaling factor to a real. Same as self.to_superset().

Attempts to convert a real to an element of this scaling subgroup. Same as Self::from_superset(). Returns None if no such scaling is possible for this subgroup. Read more

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

The scaling required to make a have the same norm as b, i.e., |b| = |a| * norm_ratio(a, b). Read more

impl<O> MeetSemilattice for Id<O> where
    O: Operator
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impl<E> Isometry<E> for Id<Multiplicative> where
    E: EuclideanSpace
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impl<E> Similarity<E> for Id<Multiplicative> where
    E: EuclideanSpace
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The type of the pure (uniform) scaling part of this similarity transformation.

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

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

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

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

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

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

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

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

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

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

impl<O> Display for Id<O> where
    O: Operator
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impl AddAssign<Id<Additive>> for Id<Additive>
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impl DivAssign<Id<Multiplicative>> for Id<Multiplicative>
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impl MulAssign<Id<Multiplicative>> for Id<Multiplicative>
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impl<O> Copy for Id<O> where
    O: Operator
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impl<E> AffineTransformation<E> for Id<Multiplicative> where
    E: EuclideanSpace
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Type of the first rotation to be applied.

Type of the non-uniform scaling to be applied.

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

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

impl<E> ProjectiveTransformation<E> for Id<Multiplicative> where
    E: EuclideanSpace
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impl<E> Transformation<E> for Id<Multiplicative> where
    E: EuclideanSpace
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impl<O> AbstractQuasigroup<O> for Id<O> where
    O: Operator
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Returns true if latin squareness holds for the given arguments. Approximate equality is used for verifications. Read more

Returns true if latin squareness holds for the given arguments.

impl<O> AbstractMagma<O> for Id<O> where
    O: Operator
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Performs specific operation.

impl<O> Eq for Id<O> where
    O: Operator
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impl<E> Rotation<E> for Id<Multiplicative> where
    E: EuclideanSpace
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impl Mul<Id<Multiplicative>> for Id<Multiplicative>
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The resulting type after applying the * operator.

impl<O> Lattice for Id<O> where
    O: Operator
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Returns the infimum and the supremum simultaneously.

Return the minimum of self and other if they are comparable.

Return the maximum of self and other if they are comparable.

Sorts two values in increasing order using a partial ordering.

Clamp value between min and max. Returns None if value is not comparable to min or max. Read more

impl<E> DirectIsometry<E> for Id<Multiplicative> where
    E: EuclideanSpace
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impl<O> Identity<O> for Id<O> where
    O: Operator
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Specific identity.

impl<O> AbstractGroupAbelian<O> for Id<O> where
    O: Operator
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Returns true if the operator is commutative for the given argument tuple. Approximate equality is used for verifications. Read more

Returns true if the operator is commutative for the given argument tuple.

impl<O> AbstractMonoid<O> for Id<O> where
    O: Operator
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Checks whether operating with the identity element is a no-op for the given argument. Approximate equality is used for verifications. Read more

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

impl<O> AbstractSemigroup<O> for Id<O> where
    O: Operator
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Returns true if associativity holds for the given arguments. Approximate equality is used for verifications. Read more

Returns true if associativity holds for the given arguments.

impl Zero for Id<Additive>
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impl<O, T> SubsetOf<T> for Id<O> where
    O: Operator,
    T: Identity<O> + PartialEq<T>, 
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The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more

impl<O> UlpsEq for Id<O> where
    O: Operator
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The inverse of ApproxEq::ulps_eq.

impl One for Id<Multiplicative>
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Returns true if self is equal to the multiplicative identity. Read more

impl<E> Translation<E> for Id<Multiplicative> where
    E: EuclideanSpace
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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. Read more

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

Auto Trait Implementations

impl<O> Send for Id<O> where
    O: Send

impl<O> Sync for Id<O> where
    O: Sync

Blanket Implementations

impl<T> ToString for T where
    T: Display + ?Sized
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impl<T> From for T
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impl<T, U> Into for T where
    U: From<T>, 
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impl<T> ToOwned for T where
    T: Clone
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impl<T, U> TryFrom for T where
    T: From<U>, 
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🔬 This is a nightly-only experimental API. (try_from)

The type returned in the event of a conversion error.

impl<T> Borrow for T where
    T: ?Sized
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impl<T> Any for T where
    T: 'static + ?Sized
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impl<T> BorrowMut for T where
    T: ?Sized
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impl<T, U> TryInto for T where
    U: TryFrom<T>, 
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🔬 This is a nightly-only experimental API. (try_from)

The type returned in the event of a conversion error.

impl<T> Same for T
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Should always be Self

impl<T, Right> ClosedAdd for T where
    T: Add<Right, Output = T> + AddAssign<Right>, 
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impl<T, Right> ClosedMul for T where
    T: Mul<Right, Output = T> + MulAssign<Right>, 
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impl<T, Right> ClosedDiv for T where
    T: Div<Right, Output = T> + DivAssign<Right>, 
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impl<SS, SP> SupersetOf for SP where
    SS: SubsetOf<SP>, 
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impl<T> AdditiveMagma for T where
    T: AbstractMagma<Additive>, 
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impl<T> AdditiveSemigroup for T where
    T: AbstractSemigroup<Additive> + ClosedAdd<T> + AdditiveMagma
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impl<T> AdditiveMonoid for T where
    T: AbstractMonoid<Additive> + AdditiveSemigroup + Zero
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impl<T> MultiplicativeMagma for T where
    T: AbstractMagma<Multiplicative>, 
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impl<T> MultiplicativeQuasigroup for T where
    T: AbstractQuasigroup<Multiplicative> + ClosedDiv<T> + MultiplicativeMagma
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impl<T> MultiplicativeLoop for T where
    T: AbstractLoop<Multiplicative> + MultiplicativeQuasigroup + One
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impl<T> MultiplicativeSemigroup for T where
    T: AbstractSemigroup<Multiplicative> + ClosedMul<T> + MultiplicativeMagma
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impl<T> MultiplicativeMonoid for T where
    T: AbstractMonoid<Multiplicative> + MultiplicativeSemigroup + One
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impl<T> MultiplicativeGroup for T where
    T: AbstractGroup<Multiplicative> + MultiplicativeLoop + MultiplicativeMonoid
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impl<T> MultiplicativeGroupAbelian for T where
    T: AbstractGroupAbelian<Multiplicative> + MultiplicativeGroup
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impl<R, E> Transformation for R where
    E: EuclideanSpace<Real = R>,
    R: Real,
    <E as EuclideanSpace>::Coordinates: ClosedMul<R>,
    <E as EuclideanSpace>::Coordinates: ClosedDiv<R>,
    <E as EuclideanSpace>::Coordinates: ClosedNeg
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impl<R, E> ProjectiveTransformation for R where
    E: EuclideanSpace<Real = R>,
    R: Real,
    <E as EuclideanSpace>::Coordinates: ClosedMul<R>,
    <E as EuclideanSpace>::Coordinates: ClosedDiv<R>,
    <E as EuclideanSpace>::Coordinates: ClosedNeg
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impl<R, E> AffineTransformation for R where
    E: EuclideanSpace<Real = R>,
    R: Real,
    <E as EuclideanSpace>::Coordinates: ClosedMul<R>,
    <E as EuclideanSpace>::Coordinates: ClosedDiv<R>,
    <E as EuclideanSpace>::Coordinates: ClosedNeg
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Type of the first rotation to be applied.

Type of the non-uniform scaling to be applied.

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

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

impl<R, E> Similarity for R where
    E: EuclideanSpace<Real = R>,
    R: Real + SubsetOf<R>,
    <E as EuclideanSpace>::Coordinates: ClosedMul<R>,
    <E as EuclideanSpace>::Coordinates: ClosedDiv<R>,
    <E as EuclideanSpace>::Coordinates: ClosedNeg
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The type of the pure (uniform) scaling part of this similarity transformation.

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

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

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

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

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

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

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

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

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

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

impl<R, E> Scaling for R where
    E: EuclideanSpace<Real = R>,
    R: Real + SubsetOf<R>,
    <E as EuclideanSpace>::Coordinates: ClosedMul<R>,
    <E as EuclideanSpace>::Coordinates: ClosedDiv<R>,
    <E as EuclideanSpace>::Coordinates: ClosedNeg
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