# [−]Struct nalgebra::Id

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,

`impl<O> Id<O> where`

O: Operator,

## Trait Implementations

`impl<O> PartialOrd<Id<O>> for Id<O> where`

O: Operator,

`impl<O> PartialOrd<Id<O>> for Id<O> where`

O: Operator,

`fn partial_cmp(&self, &Id<O>) -> Option<Ordering>`

`fn partial_cmp(&self, &Id<O>) -> Option<Ordering>`

This method returns an ordering between `self`

and `other`

values if one exists. Read more

```
#[must_use]
fn lt(&self, other: &Rhs) -> bool
```

1.0.0[src]

```
#[must_use]
fn lt(&self, other: &Rhs) -> bool
```

This method tests less than (for `self`

and `other`

) and is used by the `<`

operator. Read more

```
#[must_use]
fn le(&self, other: &Rhs) -> bool
```

1.0.0[src]

```
#[must_use]
fn le(&self, other: &Rhs) -> bool
```

This method tests less than or equal to (for `self`

and `other`

) and is used by the `<=`

operator. Read more

```
#[must_use]
fn gt(&self, other: &Rhs) -> bool
```

1.0.0[src]

```
#[must_use]
fn gt(&self, other: &Rhs) -> bool
```

This method tests greater than (for `self`

and `other`

) and is used by the `>`

operator. Read more

```
#[must_use]
fn ge(&self, other: &Rhs) -> bool
```

1.0.0[src]

```
#[must_use]
fn ge(&self, other: &Rhs) -> bool
```

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,

`impl<O> JoinSemilattice for Id<O> where`

O: Operator,

`impl<E> OrthogonalTransformation<E> for Id<Multiplicative> where`

E: EuclideanSpace,

`impl<E> OrthogonalTransformation<E> for Id<Multiplicative> where`

E: EuclideanSpace,

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

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

`type Output = Id<Additive>`

The resulting type after applying the `+`

operator.

`fn add(self, Id<Additive>) -> Id<Additive>`

`fn add(self, Id<Additive>) -> Id<Additive>`

Performs the `+`

operation.

`impl<O> Debug for Id<O> where`

O: Operator + Debug,

`impl<O> Debug for Id<O> where`

O: Operator + Debug,

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

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

Formats the value using the given formatter. Read more

`impl<O> RelativeEq for Id<O> where`

O: Operator,

`impl<O> RelativeEq for Id<O> where`

O: Operator,

`fn default_max_relative() -> <Id<O> as AbsDiffEq>::Epsilon`

`fn default_max_relative() -> <Id<O> as AbsDiffEq>::Epsilon`

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

`fn relative_eq(`

&self,

&Id<O>,

<Id<O> as AbsDiffEq>::Epsilon,

<Id<O> as AbsDiffEq>::Epsilon

) -> bool

`fn relative_eq(`

&self,

&Id<O>,

<Id<O> as AbsDiffEq>::Epsilon,

<Id<O> as AbsDiffEq>::Epsilon

) -> bool

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

`fn relative_ne(`

&self,

other: &Self,

epsilon: Self::Epsilon,

max_relative: Self::Epsilon

) -> bool

`fn relative_ne(`

&self,

other: &Self,

epsilon: Self::Epsilon,

max_relative: Self::Epsilon

) -> bool

The inverse of `ApproxEq::relative_eq`

.

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

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

`fn div_assign(&mut self, Id<Multiplicative>)`

`fn div_assign(&mut self, Id<Multiplicative>)`

Performs the `/=`

operation.

`impl<O> AbstractGroup<O> 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> AbstractLoop<O> for Id<O> where`

O: Operator,

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

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

`fn add_assign(&mut self, Id<Additive>)`

`fn add_assign(&mut self, Id<Additive>)`

Performs the `+=`

operation.

`impl<O> AbsDiffEq for Id<O> where`

O: Operator,

`impl<O> AbsDiffEq for Id<O> where`

O: Operator,

`type Epsilon = Id<O>`

Used for specifying relative comparisons.

`fn default_epsilon() -> <Id<O> as AbsDiffEq>::Epsilon`

`fn default_epsilon() -> <Id<O> as AbsDiffEq>::Epsilon`

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

`fn abs_diff_eq(&self, &Id<O>, <Id<O> as AbsDiffEq>::Epsilon) -> bool`

`fn abs_diff_eq(&self, &Id<O>, <Id<O> as AbsDiffEq>::Epsilon) -> bool`

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

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

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

The inverse of `ApproxEq::abs_diff_eq`

.

`impl<O> Display for Id<O> where`

O: Operator,

`impl<O> Display for Id<O> where`

O: Operator,

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

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

Formats the value using the given formatter. Read more

`impl<O> Inverse<O> for Id<O> where`

O: Operator,

`impl<O> Inverse<O> for Id<O> where`

O: Operator,

`fn inverse(&self) -> Id<O>`

`fn inverse(&self) -> Id<O>`

Returns the inverse of `self`

, relative to the operator `O`

.

`fn inverse_mut(&mut self)`

`fn inverse_mut(&mut self)`

In-place inversin of `self`

.

`impl<O> MeetSemilattice for Id<O> where`

O: Operator,

`impl<O> MeetSemilattice for Id<O> where`

O: Operator,

`impl<E> Scaling<E> for Id<Multiplicative> where`

E: EuclideanSpace,

`impl<E> Scaling<E> for Id<Multiplicative> where`

E: EuclideanSpace,

`fn to_real(&self) -> <E as EuclideanSpace>::Real`

`fn to_real(&self) -> <E as EuclideanSpace>::Real`

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

.

`fn from_real(r: <E as EuclideanSpace>::Real) -> Option<Self>`

`fn from_real(r: <E as EuclideanSpace>::Real) -> 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

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

`fn powf(&self, n: <E as EuclideanSpace>::Real) -> 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

`fn scale_between(`

a: &<E as EuclideanSpace>::Coordinates,

b: &<E as EuclideanSpace>::Coordinates

) -> Option<Self>

`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> Eq for Id<O> where`

O: Operator,

`impl<O> Eq for Id<O> where`

O: Operator,

`impl<E> Isometry<E> for Id<Multiplicative> where`

E: EuclideanSpace,

`impl<E> Isometry<E> for Id<Multiplicative> where`

E: EuclideanSpace,

`impl<E> Similarity<E> for Id<Multiplicative> where`

E: EuclideanSpace,

`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.

`fn translation(`

&self

) -> <Id<Multiplicative> as AffineTransformation<E>>::Translation

`fn translation(`

&self

) -> <Id<Multiplicative> as AffineTransformation<E>>::Translation

The pure translational component of this similarity transformation.

`fn rotation(&self) -> <Id<Multiplicative> as AffineTransformation<E>>::Rotation`

`fn rotation(&self) -> <Id<Multiplicative> as AffineTransformation<E>>::Rotation`

The pure rotational component of this similarity transformation.

`fn scaling(&self) -> <Id<Multiplicative> as Similarity<E>>::Scaling`

`fn scaling(&self) -> <Id<Multiplicative> as Similarity<E>>::Scaling`

The pure scaling component of this similarity transformation.

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

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

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

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

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

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

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

`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

`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

`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`

`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`

`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`

`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

`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

`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<E> AffineTransformation<E> for Id<Multiplicative> where`

E: EuclideanSpace,

`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.

`fn decompose(`

&self

) -> (Id<Multiplicative>, Id<Multiplicative>, Id<Multiplicative>, Id<Multiplicative>)

`fn decompose(`

&self

) -> (Id<Multiplicative>, Id<Multiplicative>, Id<Multiplicative>, Id<Multiplicative>)

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

`fn append_translation(`

&self,

&<Id<Multiplicative> as AffineTransformation<E>>::Translation

) -> Id<Multiplicative>

`fn append_translation(`

&self,

&<Id<Multiplicative> as AffineTransformation<E>>::Translation

) -> Id<Multiplicative>

Appends a translation to this similarity.

`fn prepend_translation(`

&self,

&<Id<Multiplicative> as AffineTransformation<E>>::Translation

) -> Id<Multiplicative>

`fn prepend_translation(`

&self,

&<Id<Multiplicative> as AffineTransformation<E>>::Translation

) -> Id<Multiplicative>

Prepends a translation to this similarity.

`fn append_rotation(`

&self,

&<Id<Multiplicative> as AffineTransformation<E>>::Rotation

) -> Id<Multiplicative>

`fn append_rotation(`

&self,

&<Id<Multiplicative> as AffineTransformation<E>>::Rotation

) -> Id<Multiplicative>

Appends a rotation to this similarity.

`fn prepend_rotation(`

&self,

&<Id<Multiplicative> as AffineTransformation<E>>::Rotation

) -> Id<Multiplicative>

`fn prepend_rotation(`

&self,

&<Id<Multiplicative> as AffineTransformation<E>>::Rotation

) -> Id<Multiplicative>

Prepends a rotation to this similarity.

`fn append_scaling(`

&self,

&<Id<Multiplicative> as AffineTransformation<E>>::NonUniformScaling

) -> Id<Multiplicative>

`fn append_scaling(`

&self,

&<Id<Multiplicative> as AffineTransformation<E>>::NonUniformScaling

) -> Id<Multiplicative>

Appends a scaling factor to this similarity.

`fn prepend_scaling(`

&self,

&<Id<Multiplicative> as AffineTransformation<E>>::NonUniformScaling

) -> Id<Multiplicative>

`fn prepend_scaling(`

&self,

&<Id<Multiplicative> as AffineTransformation<E>>::NonUniformScaling

) -> Id<Multiplicative>

Prepends a scaling factor to this similarity.

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

`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<E> ProjectiveTransformation<E> for Id<Multiplicative> where`

E: EuclideanSpace,

`impl<E> ProjectiveTransformation<E> for Id<Multiplicative> where`

E: EuclideanSpace,

`fn inverse_transform_point(&self, pt: &E) -> E`

`fn inverse_transform_point(&self, pt: &E) -> E`

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

`fn inverse_transform_vector(`

&self,

v: &<E as EuclideanSpace>::Coordinates

) -> <E as EuclideanSpace>::Coordinates

`fn inverse_transform_vector(`

&self,

v: &<E as EuclideanSpace>::Coordinates

) -> <E as EuclideanSpace>::Coordinates

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,

`impl<E> Transformation<E> for Id<Multiplicative> where`

E: EuclideanSpace,

`fn transform_point(&self, pt: &E) -> E`

`fn transform_point(&self, pt: &E) -> E`

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

`fn transform_vector(`

&self,

v: &<E as EuclideanSpace>::Coordinates

) -> <E as EuclideanSpace>::Coordinates

`fn transform_vector(`

&self,

v: &<E as EuclideanSpace>::Coordinates

) -> <E as EuclideanSpace>::Coordinates

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

`impl<O> AbstractQuasigroup<O> for Id<O> where`

O: Operator,

`impl<O> AbstractQuasigroup<O> for Id<O> where`

O: Operator,

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

Self: RelativeEq,

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

Self: RelativeEq,

Returns `true`

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

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

Self: Eq,

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

Self: Eq,

Returns `true`

if latin squareness holds for the given arguments.

`impl<O> AbstractMagma<O> for Id<O> where`

O: Operator,

`impl<O> AbstractMagma<O> for Id<O> where`

O: Operator,

`fn operate(&self, &Id<O>) -> Id<O>`

`fn operate(&self, &Id<O>) -> Id<O>`

Performs an operation.

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

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

Performs specific operation.

`impl<E> Rotation<E> for Id<Multiplicative> where`

E: EuclideanSpace,

`impl<E> Rotation<E> for Id<Multiplicative> where`

E: EuclideanSpace,

`fn powf(&self, <E as EuclideanSpace>::Real) -> Option<Id<Multiplicative>>`

`fn powf(&self, <E as EuclideanSpace>::Real) -> Option<Id<Multiplicative>>`

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

`fn rotation_between(`

a: &<E as EuclideanSpace>::Coordinates,

b: &<E as EuclideanSpace>::Coordinates

) -> Option<Id<Multiplicative>>

`fn rotation_between(`

a: &<E as EuclideanSpace>::Coordinates,

b: &<E as EuclideanSpace>::Coordinates

) -> Option<Id<Multiplicative>>

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

`fn scaled_rotation_between(`

a: &<E as EuclideanSpace>::Coordinates,

b: &<E as EuclideanSpace>::Coordinates,

<E as EuclideanSpace>::Real

) -> Option<Id<Multiplicative>>

`fn scaled_rotation_between(`

a: &<E as EuclideanSpace>::Coordinates,

b: &<E as EuclideanSpace>::Coordinates,

<E as EuclideanSpace>::Real

) -> Option<Id<Multiplicative>>

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,

`impl<O> Lattice for Id<O> where`

O: Operator,

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

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

Returns the infimum and the supremum simultaneously.

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

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

Return the minimum of `self`

and `other`

if they are comparable.

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

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

Return the maximum of `self`

and `other`

if they are comparable.

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

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

Sorts two values in increasing order using a partial ordering.

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

`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<E> DirectIsometry<E> for Id<Multiplicative> where`

E: EuclideanSpace,

`impl<E> DirectIsometry<E> for Id<Multiplicative> where`

E: EuclideanSpace,

`impl<O> Identity<O> for Id<O> where`

O: Operator,

`impl<O> Identity<O> for Id<O> where`

O: Operator,

`impl<O> Copy for Id<O> where`

O: Operator,

`impl<O> Copy for Id<O> where`

O: Operator,

`impl<O> PartialEq<Id<O>> for Id<O> where`

O: Operator,

`impl<O> PartialEq<Id<O>> for Id<O> where`

O: Operator,

`fn eq(&self, &Id<O>) -> bool`

`fn eq(&self, &Id<O>) -> bool`

This method tests for `self`

and `other`

values to be equal, and is used by `==`

. Read more

```
#[must_use]
fn ne(&self, other: &Rhs) -> bool
```

1.0.0[src]

```
#[must_use]
fn ne(&self, other: &Rhs) -> bool
```

This method tests for `!=`

.

`impl<O> AbstractGroupAbelian<O> for Id<O> where`

O: Operator,

`impl<O> AbstractGroupAbelian<O> for Id<O> where`

O: Operator,

`fn prop_is_commutative_approx(args: (Self, Self)) -> bool where`

Self: RelativeEq,

`fn prop_is_commutative_approx(args: (Self, Self)) -> bool where`

Self: RelativeEq,

Returns `true`

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

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

Self: Eq,

`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,

`impl<O> AbstractMonoid<O> for Id<O> where`

O: Operator,

`fn prop_operating_identity_element_is_noop_approx(args: (Self,)) -> bool where`

Self: RelativeEq,

`fn prop_operating_identity_element_is_noop_approx(args: (Self,)) -> bool where`

Self: RelativeEq,

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

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

Self: Eq,

`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> AbstractSemigroup<O> for Id<O> where`

O: Operator,

`impl<O> AbstractSemigroup<O> for Id<O> where`

O: Operator,

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

Self: RelativeEq,

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

Self: RelativeEq,

Returns `true`

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

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

Self: Eq,

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

Self: Eq,

Returns `true`

if associativity holds for the given arguments.

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

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

`fn mul_assign(&mut self, Id<Multiplicative>)`

`fn mul_assign(&mut self, Id<Multiplicative>)`

Performs the `*=`

operation.

`impl Zero for Id<Additive>`

`impl Zero for Id<Additive>`

`fn zero() -> Id<Additive>`

`fn zero() -> Id<Additive>`

Returns the additive identity element of `Self`

, `0`

. Read more

`fn is_zero(&self) -> bool`

`fn is_zero(&self) -> bool`

Returns `true`

if `self`

is equal to the additive identity.

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

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

`type Output = Id<Multiplicative>`

The resulting type after applying the `*`

operator.

`fn mul(self, Id<Multiplicative>) -> Id<Multiplicative>`

`fn mul(self, Id<Multiplicative>) -> Id<Multiplicative>`

Performs the `*`

operation.

`impl<O, T> SubsetOf<T> for Id<O> where`

O: Operator,

T: Identity<O> + PartialEq<T>,

`impl<O, T> SubsetOf<T> for Id<O> where`

O: Operator,

T: Identity<O> + PartialEq<T>,

`fn to_superset(&self) -> T`

`fn to_superset(&self) -> T`

The inclusion map: converts `self`

to the equivalent element of its superset.

`fn is_in_subset(t: &T) -> bool`

`fn is_in_subset(t: &T) -> bool`

Checks if `element`

is actually part of the subset `Self`

(and can be converted to it).

`unsafe fn from_superset_unchecked(&T) -> Id<O>`

`unsafe fn from_superset_unchecked(&T) -> Id<O>`

Use with care! Same as `self.to_superset`

but without any property checks. Always succeeds.

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

`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<O> UlpsEq for Id<O> where`

O: Operator,

`impl<O> UlpsEq for Id<O> where`

O: Operator,

`fn default_max_ulps() -> u32`

`fn default_max_ulps() -> u32`

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

`fn ulps_eq(&self, &Id<O>, <Id<O> as AbsDiffEq>::Epsilon, u32) -> bool`

`fn ulps_eq(&self, &Id<O>, <Id<O> as AbsDiffEq>::Epsilon, u32) -> bool`

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

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

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

The inverse of `ApproxEq::ulps_eq`

.

`impl One for Id<Multiplicative>`

`impl One for Id<Multiplicative>`

`fn one() -> Id<Multiplicative>`

`fn one() -> Id<Multiplicative>`

Returns the multiplicative identity element of `Self`

, `1`

. Read more

`fn is_one(&self) -> bool where`

Self: PartialEq<Self>,

[src]

`fn is_one(&self) -> bool where`

Self: PartialEq<Self>,

Returns `true`

if `self`

is equal to the multiplicative identity. Read more

`impl<O> Clone for Id<O> where`

O: Operator,

`impl<O> Clone for Id<O> where`

O: Operator,

`fn clone(&self) -> Id<O>`

`fn clone(&self) -> Id<O>`

Returns a copy of the value. Read more

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

1.0.0[src]

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

Performs copy-assignment from `source`

. Read more

`impl<E> Translation<E> for Id<Multiplicative> where`

E: EuclideanSpace,

`impl<E> Translation<E> for Id<Multiplicative> where`

E: EuclideanSpace,

`fn to_vector(&self) -> <E as EuclideanSpace>::Coordinates`

`fn to_vector(&self) -> <E as EuclideanSpace>::Coordinates`

Converts this translation to a vector.

`fn from_vector(`

v: <E as EuclideanSpace>::Coordinates

) -> Option<Id<Multiplicative>>

`fn from_vector(`

v: <E as EuclideanSpace>::Coordinates

) -> Option<Id<Multiplicative>>

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

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

`fn powf(&self, n: <E as EuclideanSpace>::Real) -> 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

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

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

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

## Auto Trait Implementations

## Blanket Implementations

`impl<T> From for T`

[src]

`impl<T> From for T`

`impl<T> ToString for T where`

T: Display + ?Sized,

[src]

`impl<T> ToString for T where`

T: Display + ?Sized,

`impl<T, U> Into for T where`

U: From<T>,

[src]

`impl<T, U> Into for T where`

U: From<T>,

`impl<T> ToOwned for T where`

T: Clone,

[src]

`impl<T> ToOwned for T where`

T: Clone,

`type Owned = T`

`fn to_owned(&self) -> T`

[src]

`fn to_owned(&self) -> T`

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

`fn clone_into(&self, target: &mut T)`

[src]

`fn clone_into(&self, target: &mut T)`

## 🔬 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]

`impl<T, U> TryFrom for T where`

T: From<U>,

`type Error = !`

`try_from`

)The type returned in the event of a conversion error.

`fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>`

[src]

`fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>`

`try_from`

)Performs the conversion.

`impl<T> Borrow for T where`

T: ?Sized,

[src]

`impl<T> Borrow for T where`

T: ?Sized,

`impl<T> Any for T where`

T: 'static + ?Sized,

[src]

`impl<T> Any for T where`

T: 'static + ?Sized,

`fn get_type_id(&self) -> TypeId`

[src]

`fn get_type_id(&self) -> TypeId`

## 🔬 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]

`impl<T, U> TryInto for T where`

U: TryFrom<T>,

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

`try_from`

)The type returned in the event of a conversion error.

`fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>`

[src]

`fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>`

`try_from`

)Performs the conversion.

`impl<T> BorrowMut for T where`

T: ?Sized,

[src]

`impl<T> BorrowMut for T where`

T: ?Sized,

`fn borrow_mut(&mut self) -> &mut T`

[src]

`fn borrow_mut(&mut self) -> &mut T`

Mutably borrows from an owned value. Read more

`impl<T> Same for T`

`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> 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> 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<T, Right> ClosedDiv for T where`

T: Div<Right, Output = T> + DivAssign<Right>,

`impl<SS, SP> SupersetOf for SP where`

SS: SubsetOf<SP>,

`impl<SS, SP> SupersetOf for SP where`

SS: SubsetOf<SP>,

`fn to_subset(&self) -> Option<SS>`

`fn to_subset(&self) -> Option<SS>`

The inverse inclusion map: attempts to construct `self`

from the equivalent element of its superset. Read more

`fn is_in_subset(&self) -> bool`

`fn is_in_subset(&self) -> bool`

Checks if `self`

is actually part of its subset `T`

(and can be converted to it).

`unsafe fn to_subset_unchecked(&self) -> SS`

`unsafe fn to_subset_unchecked(&self) -> SS`

Use with care! Same as `self.to_subset`

but without any property checks. Always succeeds.

`fn from_subset(element: &SS) -> SP`

`fn from_subset(element: &SS) -> SP`

The inclusion map: converts `self`

to the equivalent element of its superset.

`impl<T> AdditiveMagma for T where`

T: AbstractMagma<Additive>,

`impl<T> AdditiveMagma for T where`

T: AbstractMagma<Additive>,

`impl<T> AdditiveSemigroup for T where`

T: AbstractSemigroup<Additive> + ClosedAdd<T> + AdditiveMagma,

`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> AdditiveMonoid for T where`

T: AbstractMonoid<Additive> + AdditiveSemigroup + Zero,

`impl<T> MultiplicativeMagma for T where`

T: AbstractMagma<Multiplicative>,

`impl<T> MultiplicativeMagma for T where`

T: AbstractMagma<Multiplicative>,

`impl<T> MultiplicativeQuasigroup for T where`

T: AbstractQuasigroup<Multiplicative> + ClosedDiv<T> + MultiplicativeMagma,

`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> MultiplicativeLoop for T where`

T: AbstractLoop<Multiplicative> + MultiplicativeQuasigroup + One,

`impl<T> MultiplicativeSemigroup for T where`

T: AbstractSemigroup<Multiplicative> + ClosedMul<T> + MultiplicativeMagma,

`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> MultiplicativeMonoid for T where`

T: AbstractMonoid<Multiplicative> + MultiplicativeSemigroup + One,

`impl<T> MultiplicativeGroup for T where`

T: AbstractGroup<Multiplicative> + MultiplicativeLoop + MultiplicativeMonoid,

`impl<T> MultiplicativeGroup for T where`

T: AbstractGroup<Multiplicative> + MultiplicativeLoop + MultiplicativeMonoid,

`impl<T> MultiplicativeGroupAbelian for T where`

T: AbstractGroupAbelian<Multiplicative> + MultiplicativeGroup,

`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,

`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,

`fn transform_point(&self, pt: &E) -> E`

`fn transform_point(&self, pt: &E) -> E`

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

`fn transform_vector(`

&self,

v: &<E as EuclideanSpace>::Coordinates

) -> <E as EuclideanSpace>::Coordinates

`fn transform_vector(`

&self,

v: &<E as EuclideanSpace>::Coordinates

) -> <E as EuclideanSpace>::Coordinates

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,

`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,

`fn inverse_transform_point(&self, pt: &E) -> E`

`fn inverse_transform_point(&self, pt: &E) -> E`

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

`fn inverse_transform_vector(`

&self,

v: &<E as EuclideanSpace>::Coordinates

) -> <E as EuclideanSpace>::Coordinates

`fn inverse_transform_vector(`

&self,

v: &<E as EuclideanSpace>::Coordinates

) -> <E as EuclideanSpace>::Coordinates

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,

`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 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.

`fn decompose(`

&self

) -> (Id<Multiplicative>, Id<Multiplicative>, R, Id<Multiplicative>)

`fn decompose(`

&self

) -> (Id<Multiplicative>, Id<Multiplicative>, R, Id<Multiplicative>)

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

`fn append_translation(&self, &<R as AffineTransformation<E>>::Translation) -> R`

`fn append_translation(&self, &<R as AffineTransformation<E>>::Translation) -> R`

Appends a translation to this similarity.

`fn prepend_translation(&self, &<R as AffineTransformation<E>>::Translation) -> R`

`fn prepend_translation(&self, &<R as AffineTransformation<E>>::Translation) -> R`

Prepends a translation to this similarity.

`fn append_rotation(&self, &<R as AffineTransformation<E>>::Rotation) -> R`

`fn append_rotation(&self, &<R as AffineTransformation<E>>::Rotation) -> R`

Appends a rotation to this similarity.

`fn prepend_rotation(&self, &<R as AffineTransformation<E>>::Rotation) -> R`

`fn prepend_rotation(&self, &<R as AffineTransformation<E>>::Rotation) -> R`

Prepends a rotation to this similarity.

`fn append_scaling(`

&self,

s: &<R as AffineTransformation<E>>::NonUniformScaling

) -> R

`fn append_scaling(`

&self,

s: &<R as AffineTransformation<E>>::NonUniformScaling

) -> R

Appends a scaling factor to this similarity.

`fn prepend_scaling(`

&self,

s: &<R as AffineTransformation<E>>::NonUniformScaling

) -> R

`fn prepend_scaling(`

&self,

s: &<R as AffineTransformation<E>>::NonUniformScaling

) -> R

Prepends a scaling factor to this similarity.

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

`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<Real = R>,

R: Real + SubsetOf<R>,

<E as EuclideanSpace>::Coordinates: ClosedMul<R>,

<E as EuclideanSpace>::Coordinates: ClosedDiv<R>,

<E as EuclideanSpace>::Coordinates: ClosedNeg,

`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,

`type Scaling = R`

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

`fn translation(&self) -> <R as AffineTransformation<E>>::Translation`

`fn translation(&self) -> <R as AffineTransformation<E>>::Translation`

The pure translational component of this similarity transformation.

`fn rotation(&self) -> <R as AffineTransformation<E>>::Rotation`

`fn rotation(&self) -> <R as AffineTransformation<E>>::Rotation`

The pure rotational component of this similarity transformation.

`fn scaling(&self) -> <R as Similarity<E>>::Scaling`

`fn scaling(&self) -> <R as Similarity<E>>::Scaling`

The pure scaling component of this similarity transformation.

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

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

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

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

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

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

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

`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

`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

`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`

`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`

`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`

`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

`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

`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<Real = R>,

R: Real + SubsetOf<R>,

<E as EuclideanSpace>::Coordinates: ClosedMul<R>,

<E as EuclideanSpace>::Coordinates: ClosedDiv<R>,

<E as EuclideanSpace>::Coordinates: ClosedNeg,

`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,

`fn to_real(&self) -> <E as EuclideanSpace>::Real`

`fn to_real(&self) -> <E as EuclideanSpace>::Real`

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

.

`fn from_real(r: <E as EuclideanSpace>::Real) -> Option<R>`

`fn from_real(r: <E as EuclideanSpace>::Real) -> Option<R>`

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

`fn powf(&self, n: <E as EuclideanSpace>::Real) -> Option<R>`

`fn powf(&self, n: <E as EuclideanSpace>::Real) -> Option<R>`

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

`fn scale_between(`

a: &<E as EuclideanSpace>::Coordinates,

b: &<E as EuclideanSpace>::Coordinates

) -> Option<R>

`fn scale_between(`

a: &<E as EuclideanSpace>::Coordinates,

b: &<E as EuclideanSpace>::Coordinates

) -> Option<R>

The scaling required to make `a`

have the same norm as `b`

, i.e., `|b| = |a| * norm_ratio(a, b)`

. Read more