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

The resulting type after applying the / operator.

Performs the / operation.

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

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

Performs the *= operation.

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

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This method tests for !=.

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

Returns a copy of the value. Read more

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Performs copy-assignment from source. Read more

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

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> ApproxEq 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

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

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

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

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

The inverse of ApproxEq::relative_eq.

The inverse of ApproxEq::ulps_eq.

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, 

impl AddAssign<Id<Multiplicative>> for Id<Multiplicative>

Performs the += operation.

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> 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 Add<Id<Multiplicative>> for Id<Multiplicative>

The resulting type after applying the + operator.

Performs the + operation.

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

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

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

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

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

Formats the value using the given formatter.

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

Formats the value using the given formatter. Read more

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

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

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

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

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

impl One for Id<Multiplicative>

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

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

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

Performs an operation.

Performs specific operation.

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

The resulting type after applying the * operator.

Performs the * operation.

impl Zero for Id<Multiplicative>

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

Returns true if self is equal to the additive identity.

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

The identity element.

Specific identity.

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

Performs the /= operation.

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

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<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