Struct nalgebra::Id [−][src]
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.
Implementations
impl<O> Id<O> where
O: Operator,
[src]
O: Operator,
Trait Implementations
impl<O> AbsDiffEq<Id<O>> for Id<O> where
O: Operator,
[src]
O: Operator,
type Epsilon = Id<O>
Used for specifying relative comparisons.
pub fn default_epsilon() -> <Id<O> as AbsDiffEq<Id<O>>>::Epsilon
[src]
pub fn abs_diff_eq(&self, &Id<O>, <Id<O> as AbsDiffEq<Id<O>>>::Epsilon) -> bool
[src]
pub fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool
[src]
impl<O> AbstractGroup<O> for Id<O> where
O: Operator,
[src]
O: Operator,
impl<O> AbstractGroupAbelian<O> for Id<O> where
O: Operator,
[src]
O: Operator,
pub fn prop_is_commutative_approx(args: (Self, Self)) -> bool where
Self: RelativeEq<Self>,
[src]
Self: RelativeEq<Self>,
pub fn prop_is_commutative(args: (Self, Self)) -> bool where
Self: Eq,
[src]
Self: Eq,
impl<O> AbstractLoop<O> for Id<O> where
O: Operator,
[src]
O: Operator,
impl<O> AbstractMagma<O> for Id<O> where
O: Operator,
[src]
O: Operator,
impl<O> AbstractMonoid<O> for Id<O> where
O: Operator,
[src]
O: Operator,
pub fn prop_operating_identity_element_is_noop_approx(args: (Self,)) -> bool where
Self: RelativeEq<Self>,
[src]
Self: RelativeEq<Self>,
pub fn prop_operating_identity_element_is_noop(args: (Self,)) -> bool where
Self: Eq,
[src]
Self: Eq,
impl<O> AbstractQuasigroup<O> for Id<O> where
O: Operator,
[src]
O: Operator,
pub fn prop_inv_is_latin_square_approx(args: (Self, Self)) -> bool where
Self: RelativeEq<Self>,
[src]
Self: RelativeEq<Self>,
pub fn prop_inv_is_latin_square(args: (Self, Self)) -> bool where
Self: Eq,
[src]
Self: Eq,
impl<O> AbstractSemigroup<O> for Id<O> where
O: Operator,
[src]
O: Operator,
pub fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
Self: RelativeEq<Self>,
[src]
Self: RelativeEq<Self>,
pub fn prop_is_associative(args: (Self, Self, Self)) -> bool where
Self: Eq,
[src]
Self: Eq,
impl Add<Id<Additive>> for Id<Additive>
[src]
type Output = Id<Additive>
The resulting type after applying the +
operator.
pub fn add(self, Id<Additive>) -> Id<Additive>
[src]
impl AddAssign<Id<Additive>> for Id<Additive>
[src]
pub fn add_assign(&mut self, Id<Additive>)
[src]
impl<E> AffineTransformation<E> for Id<Multiplicative> where
E: EuclideanSpace,
[src]
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.
pub fn decompose(
&self
) -> (Id<Multiplicative>, Id<Multiplicative>, Id<Multiplicative>, Id<Multiplicative>)
[src]
&self
) -> (Id<Multiplicative>, Id<Multiplicative>, Id<Multiplicative>, Id<Multiplicative>)
pub fn append_translation(
&self,
&<Id<Multiplicative> as AffineTransformation<E>>::Translation
) -> Id<Multiplicative>
[src]
&self,
&<Id<Multiplicative> as AffineTransformation<E>>::Translation
) -> Id<Multiplicative>
pub fn prepend_translation(
&self,
&<Id<Multiplicative> as AffineTransformation<E>>::Translation
) -> Id<Multiplicative>
[src]
&self,
&<Id<Multiplicative> as AffineTransformation<E>>::Translation
) -> Id<Multiplicative>
pub fn append_rotation(
&self,
&<Id<Multiplicative> as AffineTransformation<E>>::Rotation
) -> Id<Multiplicative>
[src]
&self,
&<Id<Multiplicative> as AffineTransformation<E>>::Rotation
) -> Id<Multiplicative>
pub fn prepend_rotation(
&self,
&<Id<Multiplicative> as AffineTransformation<E>>::Rotation
) -> Id<Multiplicative>
[src]
&self,
&<Id<Multiplicative> as AffineTransformation<E>>::Rotation
) -> Id<Multiplicative>
pub fn append_scaling(
&self,
&<Id<Multiplicative> as AffineTransformation<E>>::NonUniformScaling
) -> Id<Multiplicative>
[src]
&self,
&<Id<Multiplicative> as AffineTransformation<E>>::NonUniformScaling
) -> Id<Multiplicative>
pub fn prepend_scaling(
&self,
&<Id<Multiplicative> as AffineTransformation<E>>::NonUniformScaling
) -> Id<Multiplicative>
[src]
&self,
&<Id<Multiplicative> as AffineTransformation<E>>::NonUniformScaling
) -> Id<Multiplicative>
pub fn append_rotation_wrt_point(
&self,
r: &Self::Rotation,
p: &E
) -> Option<Self>
[src]
&self,
r: &Self::Rotation,
p: &E
) -> Option<Self>
impl<O> Clone for Id<O> where
O: Operator,
[src]
O: Operator,
impl<O> Copy for Id<O> where
O: Operator,
[src]
O: Operator,
impl<O> Debug for Id<O> where
O: Operator + Debug,
[src]
O: Operator + Debug,
impl<E> DirectIsometry<E> for Id<Multiplicative> where
E: EuclideanSpace,
[src]
E: EuclideanSpace,
impl<O> Display for Id<O> where
O: Operator,
[src]
O: Operator,
impl Div<Id<Multiplicative>> for Id<Multiplicative>
[src]
type Output = Id<Multiplicative>
The resulting type after applying the /
operator.
pub fn div(self, Id<Multiplicative>) -> Id<Multiplicative>
[src]
impl DivAssign<Id<Multiplicative>> for Id<Multiplicative>
[src]
pub fn div_assign(&mut self, Id<Multiplicative>)
[src]
impl<O> Eq for Id<O> where
O: Operator,
[src]
O: Operator,
impl<O> Identity<O> for Id<O> where
O: Operator,
[src]
O: Operator,
impl<E> Isometry<E> for Id<Multiplicative> where
E: EuclideanSpace,
[src]
E: EuclideanSpace,
impl<O> JoinSemilattice for Id<O> where
O: Operator,
[src]
O: Operator,
impl<O> Lattice for Id<O> where
O: Operator,
[src]
O: Operator,
pub fn meet_join(&self, other: &Self) -> (Self, Self)
[src]
pub fn partial_min(&'a self, other: &'a Self) -> Option<&'a Self>
[src]
pub fn partial_max(&'a self, other: &'a Self) -> Option<&'a Self>
[src]
pub fn partial_sort2(&'a self, other: &'a Self) -> Option<(&'a Self, &'a Self)>
[src]
pub fn partial_clamp(&'a self, min: &'a Self, max: &'a Self) -> Option<&'a Self>
[src]
impl<O> MeetSemilattice for Id<O> where
O: Operator,
[src]
O: Operator,
impl Mul<Id<Multiplicative>> for Id<Multiplicative>
[src]
type Output = Id<Multiplicative>
The resulting type after applying the *
operator.
pub fn mul(self, Id<Multiplicative>) -> Id<Multiplicative>
[src]
impl MulAssign<Id<Multiplicative>> for Id<Multiplicative>
[src]
pub fn mul_assign(&mut self, Id<Multiplicative>)
[src]
impl One for Id<Multiplicative>
[src]
pub fn one() -> Id<Multiplicative>
[src]
pub fn set_one(&mut self)
[src]
pub fn is_one(&self) -> bool where
Self: PartialEq<Self>,
[src]
Self: PartialEq<Self>,
impl<E> OrthogonalTransformation<E> for Id<Multiplicative> where
E: EuclideanSpace,
[src]
E: EuclideanSpace,
impl<O> PartialEq<Id<O>> for Id<O> where
O: Operator,
[src]
O: Operator,
impl<O> PartialOrd<Id<O>> for Id<O> where
O: Operator,
[src]
O: Operator,
pub fn partial_cmp(&self, &Id<O>) -> Option<Ordering>
[src]
#[must_use]pub fn lt(&self, other: &Rhs) -> bool
1.0.0[src]
#[must_use]pub fn le(&self, other: &Rhs) -> bool
1.0.0[src]
#[must_use]pub fn gt(&self, other: &Rhs) -> bool
1.0.0[src]
#[must_use]pub fn ge(&self, other: &Rhs) -> bool
1.0.0[src]
impl<E> ProjectiveTransformation<E> for Id<Multiplicative> where
E: EuclideanSpace,
[src]
E: EuclideanSpace,
pub fn inverse_transform_point(&self, pt: &E) -> E
[src]
pub fn inverse_transform_vector(
&self,
v: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates
[src]
&self,
v: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates
impl<O> RelativeEq<Id<O>> for Id<O> where
O: Operator,
[src]
O: Operator,
pub fn default_max_relative() -> <Id<O> as AbsDiffEq<Id<O>>>::Epsilon
[src]
pub fn relative_eq(
&self,
&Id<O>,
<Id<O> as AbsDiffEq<Id<O>>>::Epsilon,
<Id<O> as AbsDiffEq<Id<O>>>::Epsilon
) -> bool
[src]
&self,
&Id<O>,
<Id<O> as AbsDiffEq<Id<O>>>::Epsilon,
<Id<O> as AbsDiffEq<Id<O>>>::Epsilon
) -> bool
pub fn relative_ne(
&self,
other: &Rhs,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool
[src]
&self,
other: &Rhs,
epsilon: Self::Epsilon,
max_relative: Self::Epsilon
) -> bool
impl<E> Rotation<E> for Id<Multiplicative> where
E: EuclideanSpace,
[src]
E: EuclideanSpace,
pub fn powf(
&self,
<E as EuclideanSpace>::RealField
) -> Option<Id<Multiplicative>>
[src]
&self,
<E as EuclideanSpace>::RealField
) -> Option<Id<Multiplicative>>
pub fn rotation_between(
a: &<E as EuclideanSpace>::Coordinates,
b: &<E as EuclideanSpace>::Coordinates
) -> Option<Id<Multiplicative>>
[src]
a: &<E as EuclideanSpace>::Coordinates,
b: &<E as EuclideanSpace>::Coordinates
) -> Option<Id<Multiplicative>>
pub fn scaled_rotation_between(
a: &<E as EuclideanSpace>::Coordinates,
b: &<E as EuclideanSpace>::Coordinates,
<E as EuclideanSpace>::RealField
) -> Option<Id<Multiplicative>>
[src]
a: &<E as EuclideanSpace>::Coordinates,
b: &<E as EuclideanSpace>::Coordinates,
<E as EuclideanSpace>::RealField
) -> Option<Id<Multiplicative>>
impl<E> Scaling<E> for Id<Multiplicative> where
E: EuclideanSpace,
[src]
E: EuclideanSpace,
pub fn to_real(&self) -> <E as EuclideanSpace>::RealField
[src]
pub fn from_real(r: <E as EuclideanSpace>::RealField) -> Option<Self>
[src]
pub fn powf(&self, n: <E as EuclideanSpace>::RealField) -> Option<Self>
[src]
pub fn scale_between(
a: &<E as EuclideanSpace>::Coordinates,
b: &<E as EuclideanSpace>::Coordinates
) -> Option<Self>
[src]
a: &<E as EuclideanSpace>::Coordinates,
b: &<E as EuclideanSpace>::Coordinates
) -> Option<Self>
impl<E> Similarity<E> for Id<Multiplicative> where
E: EuclideanSpace,
[src]
E: EuclideanSpace,
type Scaling = Id<Multiplicative>
The type of the pure (uniform) scaling part of this similarity transformation.
pub fn translation(
&self
) -> <Id<Multiplicative> as AffineTransformation<E>>::Translation
[src]
&self
) -> <Id<Multiplicative> as AffineTransformation<E>>::Translation
pub fn rotation(
&self
) -> <Id<Multiplicative> as AffineTransformation<E>>::Rotation
[src]
&self
) -> <Id<Multiplicative> as AffineTransformation<E>>::Rotation
pub fn scaling(&self) -> <Id<Multiplicative> as Similarity<E>>::Scaling
[src]
pub fn translate_point(&self, pt: &E) -> E
[src]
pub fn rotate_point(&self, pt: &E) -> E
[src]
pub fn scale_point(&self, pt: &E) -> E
[src]
pub fn rotate_vector(
&self,
pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates
[src]
&self,
pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates
pub fn scale_vector(
&self,
pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates
[src]
&self,
pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates
pub fn inverse_translate_point(&self, pt: &E) -> E
[src]
pub fn inverse_rotate_point(&self, pt: &E) -> E
[src]
pub fn inverse_scale_point(&self, pt: &E) -> E
[src]
pub fn inverse_rotate_vector(
&self,
pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates
[src]
&self,
pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates
pub fn inverse_scale_vector(
&self,
pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates
[src]
&self,
pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates
impl<O, T> SubsetOf<T> for Id<O> where
T: Identity<O> + PartialEq<T>,
O: Operator,
[src]
T: Identity<O> + PartialEq<T>,
O: Operator,
pub fn to_superset(&self) -> T
[src]
pub fn is_in_subset(t: &T) -> bool
[src]
pub unsafe fn from_superset_unchecked(&T) -> Id<O>
[src]
pub fn from_superset(element: &T) -> Option<Self>
[src]
impl<E> Transformation<E> for Id<Multiplicative> where
E: EuclideanSpace,
[src]
E: EuclideanSpace,
pub fn transform_point(&self, pt: &E) -> E
[src]
pub fn transform_vector(
&self,
v: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates
[src]
&self,
v: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates
impl<E> Translation<E> for Id<Multiplicative> where
E: EuclideanSpace,
[src]
E: EuclideanSpace,
pub fn to_vector(&self) -> <E as EuclideanSpace>::Coordinates
[src]
pub fn from_vector(
v: <E as EuclideanSpace>::Coordinates
) -> Option<Id<Multiplicative>>
[src]
v: <E as EuclideanSpace>::Coordinates
) -> Option<Id<Multiplicative>>
pub fn powf(&self, n: <E as EuclideanSpace>::RealField) -> Option<Self>
[src]
pub fn translation_between(a: &E, b: &E) -> Option<Self>
[src]
impl<O> TwoSidedInverse<O> for Id<O> where
O: Operator,
[src]
O: Operator,
pub fn two_sided_inverse(&self) -> Id<O>
[src]
pub fn two_sided_inverse_mut(&mut self)
[src]
impl<O> UlpsEq<Id<O>> for Id<O> where
O: Operator,
[src]
O: Operator,
pub fn default_max_ulps() -> u32
[src]
pub fn ulps_eq(&self, &Id<O>, <Id<O> as AbsDiffEq<Id<O>>>::Epsilon, u32) -> bool
[src]
pub fn ulps_ne(
&self,
other: &Rhs,
epsilon: Self::Epsilon,
max_ulps: u32
) -> bool
[src]
&self,
other: &Rhs,
epsilon: Self::Epsilon,
max_ulps: u32
) -> bool
impl Zero for Id<Additive>
[src]
Auto Trait Implementations
impl<O> RefUnwindSafe for Id<O> where
O: RefUnwindSafe,
O: RefUnwindSafe,
impl<O> Send for Id<O> where
O: Send,
O: Send,
impl<O> Sync for Id<O> where
O: Sync,
O: Sync,
impl<O> Unpin for Id<O> where
O: Unpin,
O: Unpin,
impl<O> UnwindSafe for Id<O> where
O: UnwindSafe,
O: UnwindSafe,
Blanket Implementations
impl<T> AdditiveMagma for T where
T: AbstractMagma<Additive>,
[src]
T: AbstractMagma<Additive>,
impl<T> AdditiveMonoid for T where
T: AbstractMonoid<Additive> + AdditiveSemigroup + Zero,
[src]
T: AbstractMonoid<Additive> + AdditiveSemigroup + Zero,
impl<T> AdditiveSemigroup for T where
T: AbstractSemigroup<Additive> + ClosedAdd<T> + AdditiveMagma,
[src]
T: AbstractSemigroup<Additive> + ClosedAdd<T> + AdditiveMagma,
impl<T> Any for T where
T: 'static + ?Sized,
[src]
T: 'static + ?Sized,
impl<T> Borrow<T> for T where
T: ?Sized,
[src]
T: ?Sized,
impl<T> BorrowMut<T> for T where
T: ?Sized,
[src]
T: ?Sized,
pub fn borrow_mut(&mut self) -> &mut T
[src]
impl<T, Right> ClosedAdd<Right> for T where
T: Add<Right, Output = T> + AddAssign<Right>,
[src]
T: Add<Right, Output = T> + AddAssign<Right>,
impl<T, Right> ClosedDiv<Right> for T where
T: Div<Right, Output = T> + DivAssign<Right>,
[src]
T: Div<Right, Output = T> + DivAssign<Right>,
impl<T, Right> ClosedMul<Right> for T where
T: Mul<Right, Output = T> + MulAssign<Right>,
[src]
T: Mul<Right, Output = T> + MulAssign<Right>,
impl<T> From<T> for T
[src]
impl<T, U> Into<U> for T where
U: From<T>,
[src]
U: From<T>,
impl<T> MultiplicativeGroup for T where
T: AbstractGroup<Multiplicative> + MultiplicativeLoop + MultiplicativeMonoid,
[src]
T: AbstractGroup<Multiplicative> + MultiplicativeLoop + MultiplicativeMonoid,
impl<T> MultiplicativeGroupAbelian for T where
T: AbstractGroupAbelian<Multiplicative> + MultiplicativeGroup,
[src]
T: AbstractGroupAbelian<Multiplicative> + MultiplicativeGroup,
impl<T> MultiplicativeLoop for T where
T: AbstractLoop<Multiplicative> + MultiplicativeQuasigroup + One,
[src]
T: AbstractLoop<Multiplicative> + MultiplicativeQuasigroup + One,
impl<T> MultiplicativeMagma for T where
T: AbstractMagma<Multiplicative>,
[src]
T: AbstractMagma<Multiplicative>,
impl<T> MultiplicativeMonoid for T where
T: AbstractMonoid<Multiplicative> + MultiplicativeSemigroup + One,
[src]
T: AbstractMonoid<Multiplicative> + MultiplicativeSemigroup + One,
impl<T> MultiplicativeQuasigroup for T where
T: AbstractQuasigroup<Multiplicative> + ClosedDiv<T> + MultiplicativeMagma,
[src]
T: AbstractQuasigroup<Multiplicative> + ClosedDiv<T> + MultiplicativeMagma,
impl<T> MultiplicativeSemigroup for T where
T: AbstractSemigroup<Multiplicative> + ClosedMul<T> + MultiplicativeMagma,
[src]
T: AbstractSemigroup<Multiplicative> + ClosedMul<T> + MultiplicativeMagma,
impl<T> Same<T> for T
[src]
type Output = T
Should always be Self
impl<SS, SP> SupersetOf<SS> for SP where
SS: SubsetOf<SP>,
[src]
SS: SubsetOf<SP>,
pub fn to_subset(&self) -> Option<SS>
[src]
pub fn is_in_subset(&self) -> bool
[src]
pub unsafe fn to_subset_unchecked(&self) -> SS
[src]
pub fn from_subset(element: &SS) -> SP
[src]
impl<T> ToOwned for T where
T: Clone,
[src]
T: Clone,
type Owned = T
The resulting type after obtaining ownership.
pub fn to_owned(&self) -> T
[src]
pub fn clone_into(&self, target: &mut T)
[src]
impl<T> ToString for T where
T: Display + ?Sized,
[src]
T: Display + ?Sized,
impl<T, U> TryFrom<U> for T where
U: Into<T>,
[src]
U: Into<T>,
type Error = Infallible
The type returned in the event of a conversion error.
pub fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>
[src]
impl<T, U> TryInto<U> for T where
U: TryFrom<T>,
[src]
U: TryFrom<T>,