[]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, 

Creates a new identity element.

Trait Implementations

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

This method returns an ordering between self and other values if one exists. Read more

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

Returns the join (aka. supremum) of two values.

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

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

The resulting type after applying the + operator.

Performs the + operation.

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

Formats the value using the given formatter. Read more

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

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

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

The inverse of ApproxEq::relative_eq.

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

Performs the /= operation.

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

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

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

Performs the += operation.

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

Used for specifying relative comparisons.

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

A test for equality that uses the absolute difference to compute the approximate equality of two numbers. Read more

The inverse of ApproxEq::abs_diff_eq.

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

Formats the value using the given formatter. Read more

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

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

In-place inversin of self.

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

Returns the meet (aka. infimum) of two values.

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

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

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

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

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

The pure translational component of this similarity transformation.

The pure rotational component of this similarity transformation.

The pure scaling component 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<E> AffineTransformation<E> for Id<Multiplicative> where
    E: EuclideanSpace, 

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.

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

Appends a translation to this similarity.

Prepends a translation to this similarity.

Appends a rotation to this similarity.

Prepends a rotation to this similarity.

Appends a scaling factor to this similarity.

Prepends a scaling factor to this similarity.

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, 

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

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

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

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

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

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

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, 

Performs an operation.

Performs specific operation.

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

Raises this rotation to a power. If this is a simple rotation, the result must be equivalent to multiplying the rotation angle by n. Read more

Computes a simple rotation that makes the angle between a and b equal to zero, i.e., b.angle(a * delta_rotation(a, b)) = 0. If a and b are collinear, the computed rotation may not be unique. Returns None if no such simple rotation exists in the subgroup represented by Self. Read more

Computes the rotation between a and b and raises it to the power n. Read more

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

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, 

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

The identity element.

Specific identity.

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

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

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

This method tests for !=.

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

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, 

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, 

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

Performs the *= operation.

impl Zero for Id<Additive>

Returns the additive identity element of Self, 0. Read more

Returns true if self is equal to the additive identity.

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

The resulting type after applying the * operator.

Performs the * operation.

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

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

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

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

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, 

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

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

The inverse of ApproxEq::ulps_eq.

impl One for Id<Multiplicative>

Returns the multiplicative identity element of Self, 1. Read more

Returns true if self is equal to the multiplicative identity. Read more

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

Returns a copy of the value. Read more

Performs copy-assignment from source. Read more

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

Converts this translation to a vector.

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. Read more

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).

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

The resulting type after applying the / operator.

Performs the / operation.

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> From for T
[src]

Performs the conversion.

impl<T> ToString for T where
    T: Display + ?Sized
[src]

Converts the given value to a String. Read more

impl<T, U> Into for T where
    U: From<T>, 
[src]

Performs the conversion.

impl<T> ToOwned for T where
    T: Clone
[src]

Creates owned data from borrowed data, usually by cloning. Read more

🔬 This is a nightly-only experimental API. (toowned_clone_into)

recently added

Uses borrowed data to replace owned data, usually by cloning. Read more

impl<T, U> TryFrom for T where
    T: From<U>, 
[src]

🔬 This is a nightly-only experimental API. (try_from)

The type returned in the event of a conversion error.

🔬 This is a nightly-only experimental API. (try_from)

Performs the conversion.

impl<T> Borrow for T where
    T: ?Sized
[src]

Immutably borrows from an owned value. Read more

impl<T> Any for T where
    T: 'static + ?Sized
[src]

🔬 This is a nightly-only experimental API. (get_type_id)

this method will likely be replaced by an associated static

Gets the TypeId of self. Read more

impl<T, U> TryInto for T where
    U: TryFrom<T>, 
[src]

🔬 This is a nightly-only experimental API. (try_from)

The type returned in the event of a conversion error.

🔬 This is a nightly-only experimental API. (try_from)

Performs the conversion.

impl<T> BorrowMut for T where
    T: ?Sized
[src]

Mutably borrows from an owned value. Read more

impl<T> Same for 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>, 

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

Checks if self is actually part of its subset T (and can be converted to it).

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

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

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<Real = R>,
    R: Real,
    <E as EuclideanSpace>::Coordinates: ClosedMul<R>,
    <E as EuclideanSpace>::Coordinates: ClosedDiv<R>,
    <E as EuclideanSpace>::Coordinates: ClosedNeg, 

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

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

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, 

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

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

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, 

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.

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

Appends a translation to this similarity.

Prepends a translation to this similarity.

Appends a rotation to this similarity.

Prepends a rotation to this similarity.

Appends a scaling factor to this similarity.

Prepends a scaling factor to this similarity.

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, 

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

The pure translational component of this similarity transformation.

The pure rotational component of this similarity transformation.

The pure scaling component 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, 

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