[]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, 

pub fn new() -> Id<O>

Creates a new identity element.

Trait Implementations

impl<O> Clone for Id<O> where
    O: Operator, 

default fn clone_from(&mut self, source: &Self)
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Performs copy-assignment from source. Read more

impl One for Id<Multiplicative>

default fn is_one(&self) -> bool where
    Self: PartialEq<Self>, 
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Returns true if self is equal to the multiplicative identity. Read more

impl<O> Display for Id<O> where
    O: Operator, 

impl<E> Scaling<E> for Id<Multiplicative> where
    E: EuclideanSpace, 

default fn to_real(&self) -> <E as EuclideanSpace>::RealField

Converts this scaling factor to a real. Same as self.to_superset().

default fn from_real(r: <E as EuclideanSpace>::RealField) -> Option<Self>

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

default fn powf(&self, n: <E as EuclideanSpace>::RealField) -> Option<Self>

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

default fn scale_between(
    a: &<E as EuclideanSpace>::Coordinates,
    b: &<E as EuclideanSpace>::Coordinates
) -> Option<Self>

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

impl<O> UlpsEq<Id<O>> for Id<O> where
    O: Operator, 

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

The inverse of ApproxEq::ulps_eq.

impl<E> Isometry<E> for Id<Multiplicative> where
    E: EuclideanSpace, 

impl<O> AbstractGroup<O> for Id<O> where
    O: Operator, 

impl<E> Similarity<E> for Id<Multiplicative> where
    E: EuclideanSpace, 

type Scaling = Id<Multiplicative>

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

default 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.

default 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<O> AbstractLoop<O> for Id<O> where
    O: Operator, 

impl<O> JoinSemilattice for Id<O> where
    O: Operator, 

impl<E> AffineTransformation<E> for Id<Multiplicative> where
    E: EuclideanSpace, 

type Rotation = Id<Multiplicative>

Type of the first rotation to be applied.

type NonUniformScaling = Id<Multiplicative>

Type of the non-uniform scaling to be applied.

type Translation = Id<Multiplicative>

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

default 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. Read more

impl<O> TwoSidedInverse<O> for Id<O> where
    O: Operator, 

impl<O> RelativeEq<Id<O>> for Id<O> where
    O: Operator, 

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

The inverse of ApproxEq::relative_eq.

impl<E> ProjectiveTransformation<E> for Id<Multiplicative> where
    E: EuclideanSpace, 

impl<E> Transformation<E> for Id<Multiplicative> where
    E: EuclideanSpace, 

impl<O> PartialOrd<Id<O>> for Id<O> where
    O: Operator, 

#[must_use]
default fn lt(&self, other: &Rhs) -> bool
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This method tests less than (for self and other) and is used by the < operator. Read more

#[must_use]
default fn le(&self, other: &Rhs) -> bool
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This method tests less than or equal to (for self and other) and is used by the <= operator. Read more

#[must_use]
default fn gt(&self, other: &Rhs) -> bool
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This method tests greater than (for self and other) and is used by the > operator. Read more

#[must_use]
default fn ge(&self, other: &Rhs) -> bool
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This method tests greater than or equal to (for self and other) and is used by the >= operator. Read more

impl<E> Rotation<E> for Id<Multiplicative> where
    E: EuclideanSpace, 

impl Div<Id<Multiplicative>> for Id<Multiplicative>

type Output = Id<Multiplicative>

The resulting type after applying the / operator.

impl<E> DirectIsometry<E> for Id<Multiplicative> where
    E: EuclideanSpace, 

impl<O, T> SubsetOf<T> for Id<O> where
    O: Operator,
    T: Identity<O> + PartialEq<T>, 

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

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

impl Add<Id<Additive>> for Id<Additive>

type Output = Id<Additive>

The resulting type after applying the + operator.

impl<O> MeetSemilattice for Id<O> where
    O: Operator, 

impl<O> AbstractQuasigroup<O> for Id<O> where
    O: Operator, 

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

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

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

Returns true if latin squareness holds for the given arguments. Read more

impl<O> Eq for Id<O> where
    O: Operator, 

impl<O> AbstractMagma<O> for Id<O> where
    O: Operator, 

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

Performs specific operation.

impl Zero for Id<Additive>

impl AddAssign<Id<Additive>> for Id<Additive>

impl<O> AbsDiffEq<Id<O>> for Id<O> where
    O: Operator, 

type Epsilon = Id<O>

Used for specifying relative comparisons.

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

The inverse of ApproxEq::abs_diff_eq.

impl<O> Identity<O> for Id<O> where
    O: Operator, 

default fn id(O) -> Self

Specific identity.

impl DivAssign<Id<Multiplicative>> for Id<Multiplicative>

impl MulAssign<Id<Multiplicative>> for Id<Multiplicative>

impl<E> Translation<E> for Id<Multiplicative> where
    E: EuclideanSpace, 

default fn powf(&self, n: <E as EuclideanSpace>::RealField) -> 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. Read more

default fn translation_between(a: &E, b: &E) -> Option<Self>

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

impl<O> Copy for Id<O> where
    O: Operator, 

impl<E> OrthogonalTransformation<E> for Id<Multiplicative> where
    E: EuclideanSpace, 

impl<O> AbstractGroupAbelian<O> for Id<O> where
    O: Operator, 

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

Returns true if the operator is commutative for the given argument tuple. Approximate equality is used for verifications. Read more

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

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

impl<O> AbstractMonoid<O> for Id<O> where
    O: Operator, 

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

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

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

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

impl<O> Lattice for Id<O> where
    O: Operator, 

default fn meet_join(&self, other: &Self) -> (Self, Self)

Returns the infimum and the supremum simultaneously.

default fn partial_min(&'a self, other: &'a Self) -> Option<&'a Self>

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

default fn partial_max(&'a self, other: &'a Self) -> Option<&'a Self>

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

default fn partial_sort2(
    &'a self,
    other: &'a Self
) -> Option<(&'a Self, &'a Self)>

Sorts two values in increasing order using a partial ordering.

default fn partial_clamp(
    &'a self,
    min: &'a Self,
    max: &'a Self
) -> Option<&'a Self>

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

impl<O> AbstractSemigroup<O> for Id<O> where
    O: Operator, 

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

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

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

Returns true if associativity holds for the given arguments.

impl<O> Debug for Id<O> where
    O: Operator + Debug

impl Mul<Id<Multiplicative>> for Id<Multiplicative>

type Output = Id<Multiplicative>

The resulting type after applying the * operator.

impl<O> PartialEq<Id<O>> for Id<O> where
    O: Operator, 

#[must_use]
default fn ne(&self, other: &Rhs) -> bool
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This method tests for !=.

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> ToOwned for T where
    T: Clone
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type Owned = T

impl<T> From for T[src]

impl<T, U> Into for T where
    U: From<T>, 
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impl<T, U> TryFrom for T where
    U: Into<T>, 
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type Error = Infallible

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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type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.

impl<T> Same for T

type Output = T

Should always be Self

impl<T, Right> ClosedAdd for T where
    T: Add<Right, Output = T> + AddAssign<Right>, 

impl<T, Right> ClosedMul for T where
    T: Mul<Right, Output = T> + MulAssign<Right>, 

impl<T, Right> ClosedDiv for T where
    T: Div<Right, Output = T> + DivAssign<Right>, 

impl<SS, SP> SupersetOf for SP where
    SS: SubsetOf<SP>, 

impl<T> AdditiveMagma for T where
    T: AbstractMagma<Additive>, 

impl<T> AdditiveSemigroup for T where
    T: AbstractSemigroup<Additive> + ClosedAdd<T> + AdditiveMagma, 

impl<T> AdditiveMonoid for T where
    T: AbstractMonoid<Additive> + AdditiveSemigroup + Zero

impl<T> MultiplicativeMagma for T where
    T: AbstractMagma<Multiplicative>, 

impl<T> MultiplicativeQuasigroup for T where
    T: AbstractQuasigroup<Multiplicative> + ClosedDiv<T> + MultiplicativeMagma, 

impl<T> MultiplicativeLoop for T where
    T: AbstractLoop<Multiplicative> + MultiplicativeQuasigroup + One

impl<T> MultiplicativeSemigroup for T where
    T: AbstractSemigroup<Multiplicative> + ClosedMul<T> + MultiplicativeMagma, 

impl<T> MultiplicativeMonoid for T where
    T: AbstractMonoid<Multiplicative> + MultiplicativeSemigroup + One

impl<T> MultiplicativeGroup for T where
    T: AbstractGroup<Multiplicative> + MultiplicativeLoop + MultiplicativeMonoid, 

impl<T> MultiplicativeGroupAbelian for T where
    T: AbstractGroupAbelian<Multiplicative> + MultiplicativeGroup, 

impl<R, E> Transformation for R where
    E: EuclideanSpace<RealField = R>,
    R: RealField,
    <E as EuclideanSpace>::Coordinates: ClosedMul<R>,
    <E as EuclideanSpace>::Coordinates: ClosedDiv<R>,
    <E as EuclideanSpace>::Coordinates: ClosedNeg, 

impl<R, E> ProjectiveTransformation for R where
    E: EuclideanSpace<RealField = R>,
    R: RealField,
    <E as EuclideanSpace>::Coordinates: ClosedMul<R>,
    <E as EuclideanSpace>::Coordinates: ClosedDiv<R>,
    <E as EuclideanSpace>::Coordinates: ClosedNeg, 

impl<R, E> AffineTransformation for R where
    E: EuclideanSpace<RealField = R>,
    R: RealField,
    <E as EuclideanSpace>::Coordinates: ClosedMul<R>,
    <E as EuclideanSpace>::Coordinates: ClosedDiv<R>,
    <E as EuclideanSpace>::Coordinates: ClosedNeg, 

type Rotation = Id<Multiplicative>

Type of the first rotation to be applied.

type NonUniformScaling = R

Type of the non-uniform scaling to be applied.

type Translation = Id<Multiplicative>

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

default 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. Read more

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

type Scaling = R

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

default 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.

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