Struct nalgebra::geometry::Similarity

#[repr(C)]
pub struct Similarity<N: Real, D: DimName, R> where
    DefaultAllocator: Allocator<N, D>,  {
    pub isometry: Isometry<N, D, R>,
    // some fields omitted
}

A similarity, i.e., an uniform scaling, followed by a rotation, followed by a translation.

Fields

isometry: Isometry<N, D, R>

The part of this similarity that does not include the scaling factor.

Methods

impl<N: Real, D: DimName, R> Similarity<N, D, R> where     R: Rotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

pub fn from_parts(     translation: Translation<N, D>,     rotation: R,     scaling: N ) -> Similarity<N, D, R>

Creates a new similarity from its rotational and translational parts.

pub fn from_isometry(     isometry: Isometry<N, D, R>,     scaling: N ) -> Similarity<N, D, R>

Creates a new similarity from its rotational and translational parts.

pub fn from_scaling(scaling: N) -> Similarity<N, D, R>

Creates a new similarity that applies only a scaling factor.

pub fn inverse(&self) -> Similarity<N, D, R>

Inverts self.

pub fn inverse_mut(&mut self)

Inverts self in-place.

pub fn set_scaling(&mut self, scaling: N)

The scaling factor of this similarity transformation.

pub fn scaling(&self) -> N

The scaling factor of this similarity transformation.

pub fn prepend_scaling(&self, scaling: N) -> Self

The similarity transformation that applies a scaling factor scaling before self.

pub fn append_scaling(&self, scaling: N) -> Self

The similarity transformation that applies a scaling factor scaling after self.

pub fn prepend_scaling_mut(&mut self, scaling: N)

Sets self to the similarity transformation that applies a scaling factor scaling before self.

pub fn append_scaling_mut(&mut self, scaling: N)

Sets self to the similarity transformation that applies a scaling factor scaling after self.

pub fn append_translation_mut(&mut self, t: &Translation<N, D>)

Appends to self the given translation in-place.

pub fn append_rotation_mut(&mut self, r: &R)

Appends to self the given rotation in-place.

pub fn append_rotation_wrt_point_mut(&mut self, r: &R, p: &Point<N, D>)

Appends in-place to self a rotation centered at the point p, i.e., the rotation that lets p invariant.

pub fn append_rotation_wrt_center_mut(&mut self, r: &R)

Appends in-place to self a rotation centered at the point with coordinates self.translation.

impl<N: Real, D: DimName, R> Similarity<N, D, R> where     DefaultAllocator: Allocator<N, D>,

pub fn to_homogeneous(&self) -> MatrixN<N, DimNameSum<D, U1>> where     D: DimNameAdd<U1>,     R: SubsetOf<MatrixN<N, DimNameSum<D, U1>>>,     DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,

Converts this similarity into its equivalent homogeneous transformation matrix.

impl<N: Real, D: DimName, R> Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

pub fn identity() -> Self

Creates a new identity similarity.

impl<N: Real, D: DimName, R> Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

pub fn rotation_wrt_point(r: R, p: Point<N, D>, scaling: N) -> Self

The similarity that applies tha scaling factor scaling, followed by the rotation r with its axis passing through the point p.

impl<N: Real> Similarity<N, U2, Rotation2<N>>

pub fn new(translation: Vector2<N>, angle: N, scaling: N) -> Self

Creates a new similarity from a translation and a rotation angle.

impl<N: Real> Similarity<N, U2, UnitComplex<N>>

pub fn new(translation: Vector2<N>, angle: N, scaling: N) -> Self

Creates a new similarity from a translation and a rotation angle.

impl<N: Real> Similarity<N, U3, Rotation3<N>>

pub fn new(translation: Vector3<N>, axisangle: Vector3<N>, scaling: N) -> Self

Creates a new similarity from a translation, rotation axis-angle, and scaling factor.

pub fn new_observer_frame(     eye: &Point3<N>,     target: &Point3<N>,     up: &Vector3<N>,     scaling: N ) -> Self

Creates an similarity that corresponds to the a scaling factor and a local frame of an observer standing at the point eye and looking toward target.

It maps the view direction target - eye to the positive z axis and the origin to the eye.

Arguments

• eye - The observer position.
• target - The target position.
• up - Vertical direction. The only requirement of this parameter is to not be collinear to eye - at. Non-collinearity is not checked.

pub fn look_at_rh(     eye: &Point3<N>,     target: &Point3<N>,     up: &Vector3<N>,     scaling: N ) -> Self

Builds a right-handed look-at view matrix including scaling factor.

This conforms to the common notion of right handed look-at matrix from the computer graphics community.

Arguments

• eye - The eye position.
• target - The target position.
• up - A vector approximately aligned with required the vertical axis. The only requirement of this parameter is to not be collinear to target - eye.

pub fn look_at_lh(     eye: &Point3<N>,     target: &Point3<N>,     up: &Vector3<N>,     scaling: N ) -> Self

Builds a left-handed look-at view matrix including a scaling factor.

This conforms to the common notion of left handed look-at matrix from the computer graphics community.

Arguments

• eye - The eye position.
• target - The target position.
• up - A vector approximately aligned with required the vertical axis. The only requirement of this parameter is to not be collinear to target - eye.

impl<N: Real> Similarity<N, U3, UnitQuaternion<N>>

pub fn new(translation: Vector3<N>, axisangle: Vector3<N>, scaling: N) -> Self

Creates a new similarity from a translation, rotation axis-angle, and scaling factor.

pub fn new_observer_frame(     eye: &Point3<N>,     target: &Point3<N>,     up: &Vector3<N>,     scaling: N ) -> Self

Creates an similarity that corresponds to the a scaling factor and a local frame of an observer standing at the point eye and looking toward target.

It maps the view direction target - eye to the positive z axis and the origin to the eye.

Arguments

• eye - The observer position.
• target - The target position.
• up - Vertical direction. The only requirement of this parameter is to not be collinear to eye - at. Non-collinearity is not checked.

pub fn look_at_rh(     eye: &Point3<N>,     target: &Point3<N>,     up: &Vector3<N>,     scaling: N ) -> Self

Builds a right-handed look-at view matrix including scaling factor.

This conforms to the common notion of right handed look-at matrix from the computer graphics community.

Arguments

• eye - The eye position.
• target - The target position.
• up - A vector approximately aligned with required the vertical axis. The only requirement of this parameter is to not be collinear to target - eye.

pub fn look_at_lh(     eye: &Point3<N>,     target: &Point3<N>,     up: &Vector3<N>,     scaling: N ) -> Self

Builds a left-handed look-at view matrix including a scaling factor.

This conforms to the common notion of left handed look-at matrix from the computer graphics community.

Arguments

• eye - The eye position.
• target - The target position.
• up - A vector approximately aligned with required the vertical axis. The only requirement of this parameter is to not be collinear to target - eye.

Trait Implementations

impl<N1, N2, D: DimName, R> SubsetOf<Similarity<N2, D, R>> for Rotation<N1, D> where     N1: Real,     N2: Real + SupersetOf<N1>,     R: AlgaRotation<Point<N2, D>> + SupersetOf<Rotation<N1, D>>,     DefaultAllocator: Allocator<N1, D, D> + Allocator<N2, D>,

fn to_superset(&self) -> Similarity<N2, D, R>

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

fn is_in_subset(sim: &Similarity<N2, D, R>) -> bool

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

unsafe fn from_superset_unchecked(sim: &Similarity<N2, D, R>) -> Self

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

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

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

impl<N1, N2, R> SubsetOf<Similarity<N2, U3, R>> for UnitQuaternion<N1> where     N1: Real,     N2: Real + SupersetOf<N1>,     R: AlgaRotation<Point3<N2>> + SupersetOf<UnitQuaternion<N1>>,

fn to_superset(&self) -> Similarity<N2, U3, R>

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

fn is_in_subset(sim: &Similarity<N2, U3, R>) -> bool

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

unsafe fn from_superset_unchecked(sim: &Similarity<N2, U3, R>) -> Self

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

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

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

impl<N: Real> Mul<Similarity<N, U2, UnitComplex<N>>> for UnitComplex<N> where     DefaultAllocator: Allocator<N, U2, U1>,

type Output = Similarity<N, U2, UnitComplex<N>>

The resulting type after applying the * operator.

fn mul(self, rhs: Similarity<N, U2, UnitComplex<N>>) -> Self::Output

Performs the * operation.

impl<'a, N: Real> Mul<Similarity<N, U2, UnitComplex<N>>> for &'a UnitComplex<N> where     DefaultAllocator: Allocator<N, U2, U1>,

type Output = Similarity<N, U2, UnitComplex<N>>

The resulting type after applying the * operator.

fn mul(self, rhs: Similarity<N, U2, UnitComplex<N>>) -> Self::Output

Performs the * operation.

impl<'b, N: Real> Mul<&'b Similarity<N, U2, UnitComplex<N>>> for UnitComplex<N> where     DefaultAllocator: Allocator<N, U2, U1>,

type Output = Similarity<N, U2, UnitComplex<N>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Similarity<N, U2, UnitComplex<N>>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N: Real> Mul<&'b Similarity<N, U2, UnitComplex<N>>> for &'a UnitComplex<N> where     DefaultAllocator: Allocator<N, U2, U1>,

type Output = Similarity<N, U2, UnitComplex<N>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Similarity<N, U2, UnitComplex<N>>) -> Self::Output

Performs the * operation.

impl<N1, N2, R> SubsetOf<Similarity<N2, U2, R>> for UnitComplex<N1> where     N1: Real,     N2: Real + SupersetOf<N1>,     R: AlgaRotation<Point2<N2>> + SupersetOf<UnitComplex<N1>>,

fn to_superset(&self) -> Similarity<N2, U2, R>

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

fn is_in_subset(sim: &Similarity<N2, U2, R>) -> bool

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

unsafe fn from_superset_unchecked(sim: &Similarity<N2, U2, R>) -> Self

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

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

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

impl<N1, N2, D: DimName, R> SubsetOf<Similarity<N2, D, R>> for Translation<N1, D> where     N1: Real,     N2: Real + SupersetOf<N1>,     R: Rotation<Point<N2, D>>,     DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>,

fn to_superset(&self) -> Similarity<N2, D, R>

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

fn is_in_subset(sim: &Similarity<N2, D, R>) -> bool

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

unsafe fn from_superset_unchecked(sim: &Similarity<N2, D, R>) -> Self

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

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

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

impl<N1, N2, D: DimName, R1, R2> SubsetOf<Similarity<N2, D, R2>> for Isometry<N1, D, R1> where     N1: Real,     N2: Real + SupersetOf<N1>,     R1: Rotation<Point<N1, D>> + SubsetOf<R2>,     R2: Rotation<Point<N2, D>>,     DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>,

fn to_superset(&self) -> Similarity<N2, D, R2>

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

fn is_in_subset(sim: &Similarity<N2, D, R2>) -> bool

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

unsafe fn from_superset_unchecked(sim: &Similarity<N2, D, R2>) -> Self

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

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

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

impl<N: Debug + Real, D: Debug + DimName, R: Debug> Debug for Similarity<N, D, R> where     DefaultAllocator: Allocator<N, D>,

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

Formats the value using the given formatter.

impl<N: Real + Hash, D: DimName + Hash, R: Hash> Hash for Similarity<N, D, R> where     DefaultAllocator: Allocator<N, D>,     Owned<N, D>: Hash,

fn hash<H: Hasher>(&self, state: &mut H)

Feeds this value into the given [Hasher].

fn hash_slice<H>(data: &[Self], state: &mut H) where     H: Hasher,

Feeds a slice of this type into the given [Hasher].

impl<N: Real, D: DimName + Copy, R: Rotation<Point<N, D>> + Copy> Copy for Similarity<N, D, R> where     DefaultAllocator: Allocator<N, D>,     Owned<N, D>: Copy,

impl<N: Real, D: DimName, R: Rotation<Point<N, D>> + Clone> Clone for Similarity<N, D, R> where     DefaultAllocator: Allocator<N, D>,

fn clone(&self) -> Self

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<N: Real, D: DimName, R> Eq for Similarity<N, D, R> where     R: Rotation<Point<N, D>> + Eq,     DefaultAllocator: Allocator<N, D>,

impl<N: Real, D: DimName, R> PartialEq for Similarity<N, D, R> where     R: Rotation<Point<N, D>> + PartialEq,     DefaultAllocator: Allocator<N, D>,

fn eq(&self, right: &Similarity<N, D, R>) -> bool

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

fn ne(&self, other: &Rhs) -> bool

This method tests for !=.

impl<N: Real, D: DimName, R> AbsDiffEq for Similarity<N, D, R> where     R: Rotation<Point<N, D>> + AbsDiffEq<Epsilon = N::Epsilon>,     DefaultAllocator: Allocator<N, D>,     N::Epsilon: Copy,

type Epsilon = N::Epsilon

Used for specifying relative comparisons.

fn default_epsilon() -> Self::Epsilon

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

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

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

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

The inverse of ApproxEq::abs_diff_eq.

impl<N: Real, D: DimName, R> RelativeEq for Similarity<N, D, R> where     R: Rotation<Point<N, D>> + RelativeEq<Epsilon = N::Epsilon>,     DefaultAllocator: Allocator<N, D>,     N::Epsilon: Copy,

fn default_max_relative() -> Self::Epsilon

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

fn relative_eq(     &self,     other: &Self,     epsilon: Self::Epsilon,     max_relative: Self::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

The inverse of ApproxEq::relative_eq.

impl<N: Real, D: DimName, R> UlpsEq for Similarity<N, D, R> where     R: Rotation<Point<N, D>> + UlpsEq<Epsilon = N::Epsilon>,     DefaultAllocator: Allocator<N, D>,     N::Epsilon: Copy,

fn default_max_ulps() -> u32

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

fn ulps_eq(&self, other: &Self, epsilon: Self::Epsilon, max_ulps: 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

The inverse of ApproxEq::ulps_eq.

impl<N, D: DimName, R> Display for Similarity<N, D, R> where     N: Real + Display,     R: Rotation<Point<N, D>> + Display,     DefaultAllocator: Allocator<N, D> + Allocator<usize, D>,

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

Formats the value using the given formatter.

impl<N: Real, D: DimName, R> One for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

fn one() -> Self

Creates a new identity similarity.

fn is_one(&self) -> bool where     Self: PartialEq<Self>,

Returns true if self is equal to the multiplicative identity.

impl<N: Real, D: DimName, R> Distribution<Similarity<N, D, R>> for Standard where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,     Standard: Distribution<N> + Distribution<R>,

fn sample<'a, G: Rng + ?Sized>(&self, rng: &mut G) -> Similarity<N, D, R>

Generate a random value of T, using rng as the source of randomness.

Important traits for DistIter<'a, D, R, T>

impl<'a, D, R, T> Iterator for DistIter<'a, D, R, T> where
    D: Distribution<T>,
    R: Rng + 'a,  type Item = T;

fn sample_iter<R>(&'a self, rng: &'a mut R) -> DistIter<'a, Self, R, T> where     R: Rng,

Create an iterator that generates random values of T, using rng as the source of randomness.

impl<N: Real, D: DimName, R> Mul<Similarity<N, D, R>> for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(self, rhs: Similarity<N, D, R>) -> Self::Output

Performs the * operation.

impl<'a, N: Real, D: DimName, R> Mul<Similarity<N, D, R>> for &'a Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(self, rhs: Similarity<N, D, R>) -> Self::Output

Performs the * operation.

impl<'b, N: Real, D: DimName, R> Mul<&'b Similarity<N, D, R>> for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Similarity<N, D, R>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N: Real, D: DimName, R> Mul<&'b Similarity<N, D, R>> for &'a Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Similarity<N, D, R>) -> Self::Output

Performs the * operation.

impl<N: Real, D: DimName, R> Div<Similarity<N, D, R>> for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

fn div(self, rhs: Similarity<N, D, R>) -> Self::Output

Performs the / operation.

impl<'a, N: Real, D: DimName, R> Div<Similarity<N, D, R>> for &'a Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

fn div(self, rhs: Similarity<N, D, R>) -> Self::Output

Performs the / operation.

impl<'b, N: Real, D: DimName, R> Div<&'b Similarity<N, D, R>> for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

fn div(self, rhs: &'b Similarity<N, D, R>) -> Self::Output

Performs the / operation.

impl<'a, 'b, N: Real, D: DimName, R> Div<&'b Similarity<N, D, R>> for &'a Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

fn div(self, rhs: &'b Similarity<N, D, R>) -> Self::Output

Performs the / operation.

impl<N: Real, D: DimName, R> MulAssign<Translation<N, D>> for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

fn mul_assign(&mut self, rhs: Translation<N, D>)

Performs the *= operation.

impl<'b, N: Real, D: DimName, R> MulAssign<&'b Translation<N, D>> for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

fn mul_assign(&mut self, rhs: &'b Translation<N, D>)

Performs the *= operation.

impl<N: Real, D: DimName, R> MulAssign<Similarity<N, D, R>> for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

fn mul_assign(&mut self, rhs: Similarity<N, D, R>)

Performs the *= operation.

impl<'b, N: Real, D: DimName, R> MulAssign<&'b Similarity<N, D, R>> for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

fn mul_assign(&mut self, rhs: &'b Similarity<N, D, R>)

Performs the *= operation.

impl<N: Real, D: DimName, R> DivAssign<Similarity<N, D, R>> for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

fn div_assign(&mut self, rhs: Similarity<N, D, R>)

Performs the /= operation.

impl<'b, N: Real, D: DimName, R> DivAssign<&'b Similarity<N, D, R>> for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

fn div_assign(&mut self, rhs: &'b Similarity<N, D, R>)

Performs the /= operation.

impl<N: Real, D: DimName, R> MulAssign<Isometry<N, D, R>> for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

fn mul_assign(&mut self, rhs: Isometry<N, D, R>)

Performs the *= operation.

impl<'b, N: Real, D: DimName, R> MulAssign<&'b Isometry<N, D, R>> for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

fn mul_assign(&mut self, rhs: &'b Isometry<N, D, R>)

Performs the *= operation.

impl<N: Real, D: DimName, R> DivAssign<Isometry<N, D, R>> for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

fn div_assign(&mut self, rhs: Isometry<N, D, R>)

Performs the /= operation.

impl<'b, N: Real, D: DimName, R> DivAssign<&'b Isometry<N, D, R>> for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

fn div_assign(&mut self, rhs: &'b Isometry<N, D, R>)

Performs the /= operation.

impl<N: Real, D: DimName, R> MulAssign<R> for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

fn mul_assign(&mut self, rhs: R)

Performs the *= operation.

impl<'b, N: Real, D: DimName, R> MulAssign<&'b R> for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

fn mul_assign(&mut self, rhs: &'b R)

Performs the *= operation.

impl<N: Real, D: DimName, R> DivAssign<R> for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

fn div_assign(&mut self, rhs: R)

Performs the /= operation.

impl<'b, N: Real, D: DimName, R> DivAssign<&'b R> for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

fn div_assign(&mut self, rhs: &'b R)

Performs the /= operation.

impl<N: Real, D: DimName, R> Mul<R> for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(self, rhs: R) -> Self::Output

Performs the * operation.

impl<'a, N: Real, D: DimName, R> Mul<R> for &'a Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(self, rhs: R) -> Self::Output

Performs the * operation.

impl<'b, N: Real, D: DimName, R> Mul<&'b R> for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b R) -> Self::Output

Performs the * operation.

impl<'a, 'b, N: Real, D: DimName, R> Mul<&'b R> for &'a Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b R) -> Self::Output

Performs the * operation.

impl<N: Real, D: DimName, R> Div<R> for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

fn div(self, rhs: R) -> Self::Output

Performs the / operation.

impl<'a, N: Real, D: DimName, R> Div<R> for &'a Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

fn div(self, rhs: R) -> Self::Output

Performs the / operation.

impl<'b, N: Real, D: DimName, R> Div<&'b R> for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

fn div(self, rhs: &'b R) -> Self::Output

Performs the / operation.

impl<'a, 'b, N: Real, D: DimName, R> Div<&'b R> for &'a Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

fn div(self, rhs: &'b R) -> Self::Output

Performs the / operation.

impl<N: Real, D: DimName, R> Mul<Isometry<N, D, R>> for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(self, rhs: Isometry<N, D, R>) -> Self::Output

Performs the * operation.

impl<'a, N: Real, D: DimName, R> Mul<Isometry<N, D, R>> for &'a Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(self, rhs: Isometry<N, D, R>) -> Self::Output

Performs the * operation.

impl<'b, N: Real, D: DimName, R> Mul<&'b Isometry<N, D, R>> for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Isometry<N, D, R>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N: Real, D: DimName, R> Mul<&'b Isometry<N, D, R>> for &'a Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Isometry<N, D, R>) -> Self::Output

Performs the * operation.

impl<N: Real, D: DimName, R> Div<Isometry<N, D, R>> for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

fn div(self, rhs: Isometry<N, D, R>) -> Self::Output

Performs the / operation.

impl<'a, N: Real, D: DimName, R> Div<Isometry<N, D, R>> for &'a Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

fn div(self, rhs: Isometry<N, D, R>) -> Self::Output

Performs the / operation.

impl<'b, N: Real, D: DimName, R> Div<&'b Isometry<N, D, R>> for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

fn div(self, rhs: &'b Isometry<N, D, R>) -> Self::Output

Performs the / operation.

impl<'a, 'b, N: Real, D: DimName, R> Div<&'b Isometry<N, D, R>> for &'a Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

fn div(self, rhs: &'b Isometry<N, D, R>) -> Self::Output

Performs the / operation.

impl<N: Real, D: DimName, R> Mul<Similarity<N, D, R>> for Isometry<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(self, rhs: Similarity<N, D, R>) -> Self::Output

Performs the * operation.

impl<'a, N: Real, D: DimName, R> Mul<Similarity<N, D, R>> for &'a Isometry<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(self, rhs: Similarity<N, D, R>) -> Self::Output

Performs the * operation.

impl<'b, N: Real, D: DimName, R> Mul<&'b Similarity<N, D, R>> for Isometry<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Similarity<N, D, R>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N: Real, D: DimName, R> Mul<&'b Similarity<N, D, R>> for &'a Isometry<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Similarity<N, D, R>) -> Self::Output

Performs the * operation.

impl<N: Real, D: DimName, R> Div<Similarity<N, D, R>> for Isometry<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

fn div(self, rhs: Similarity<N, D, R>) -> Self::Output

Performs the / operation.

impl<'a, N: Real, D: DimName, R> Div<Similarity<N, D, R>> for &'a Isometry<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

fn div(self, rhs: Similarity<N, D, R>) -> Self::Output

Performs the / operation.

impl<'b, N: Real, D: DimName, R> Div<&'b Similarity<N, D, R>> for Isometry<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

fn div(self, rhs: &'b Similarity<N, D, R>) -> Self::Output

Performs the / operation.

impl<'a, 'b, N: Real, D: DimName, R> Div<&'b Similarity<N, D, R>> for &'a Isometry<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

fn div(self, rhs: &'b Similarity<N, D, R>) -> Self::Output

Performs the / operation.

impl<N: Real, D: DimName, R> Mul<Point<N, D>> for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Point<N, D>

The resulting type after applying the * operator.

fn mul(self, right: Point<N, D>) -> Self::Output

Performs the * operation.

impl<'a, N: Real, D: DimName, R> Mul<Point<N, D>> for &'a Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Point<N, D>

The resulting type after applying the * operator.

fn mul(self, right: Point<N, D>) -> Self::Output

Performs the * operation.

impl<'b, N: Real, D: DimName, R> Mul<&'b Point<N, D>> for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Point<N, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<N, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N: Real, D: DimName, R> Mul<&'b Point<N, D>> for &'a Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Point<N, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<N, D>) -> Self::Output

Performs the * operation.

impl<N: Real, D: DimName, R> Mul<VectorN<N, D>> for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = VectorN<N, D>

The resulting type after applying the * operator.

fn mul(self, right: VectorN<N, D>) -> Self::Output

Performs the * operation.

impl<'a, N: Real, D: DimName, R> Mul<VectorN<N, D>> for &'a Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = VectorN<N, D>

The resulting type after applying the * operator.

fn mul(self, right: VectorN<N, D>) -> Self::Output

Performs the * operation.

impl<'b, N: Real, D: DimName, R> Mul<&'b VectorN<N, D>> for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = VectorN<N, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b VectorN<N, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N: Real, D: DimName, R> Mul<&'b VectorN<N, D>> for &'a Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = VectorN<N, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b VectorN<N, D>) -> Self::Output

Performs the * operation.

impl<N: Real, D: DimName, R> Mul<Translation<N, D>> for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(self, right: Translation<N, D>) -> Self::Output

Performs the * operation.

impl<'a, N: Real, D: DimName, R> Mul<Translation<N, D>> for &'a Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(self, right: Translation<N, D>) -> Self::Output

Performs the * operation.

impl<'b, N: Real, D: DimName, R> Mul<&'b Translation<N, D>> for Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(self, right: &'b Translation<N, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N: Real, D: DimName, R> Mul<&'b Translation<N, D>> for &'a Similarity<N, D, R> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(self, right: &'b Translation<N, D>) -> Self::Output

Performs the * operation.

impl<N: Real, D: DimName, R> Mul<Similarity<N, D, R>> for Translation<N, D> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(self, right: Similarity<N, D, R>) -> Self::Output

Performs the * operation.

impl<'a, N: Real, D: DimName, R> Mul<Similarity<N, D, R>> for &'a Translation<N, D> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(self, right: Similarity<N, D, R>) -> Self::Output

Performs the * operation.

impl<'b, N: Real, D: DimName, R> Mul<&'b Similarity<N, D, R>> for Translation<N, D> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(self, right: &'b Similarity<N, D, R>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N: Real, D: DimName, R> Mul<&'b Similarity<N, D, R>> for &'a Translation<N, D> where     R: AlgaRotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(self, right: &'b Similarity<N, D, R>) -> Self::Output

Performs the * operation.

impl<N: Real, D: DimName> Mul<Similarity<N, D, Rotation<N, D>>> for Rotation<N, D> where     DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>,

type Output = Similarity<N, D, Rotation<N, D>>

The resulting type after applying the * operator.

fn mul(self, right: Similarity<N, D, Rotation<N, D>>) -> Self::Output

Performs the * operation.

impl<'a, N: Real, D: DimName> Mul<Similarity<N, D, Rotation<N, D>>> for &'a Rotation<N, D> where     DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>,

type Output = Similarity<N, D, Rotation<N, D>>

The resulting type after applying the * operator.

fn mul(self, right: Similarity<N, D, Rotation<N, D>>) -> Self::Output

Performs the * operation.

impl<'b, N: Real, D: DimName> Mul<&'b Similarity<N, D, Rotation<N, D>>> for Rotation<N, D> where     DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>,

type Output = Similarity<N, D, Rotation<N, D>>

The resulting type after applying the * operator.

fn mul(self, right: &'b Similarity<N, D, Rotation<N, D>>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N: Real, D: DimName> Mul<&'b Similarity<N, D, Rotation<N, D>>> for &'a Rotation<N, D> where     DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>,

type Output = Similarity<N, D, Rotation<N, D>>

The resulting type after applying the * operator.

fn mul(self, right: &'b Similarity<N, D, Rotation<N, D>>) -> Self::Output

Performs the * operation.

impl<N: Real, D: DimName> Div<Similarity<N, D, Rotation<N, D>>> for Rotation<N, D> where     DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>,

type Output = Similarity<N, D, Rotation<N, D>>

The resulting type after applying the / operator.

fn div(self, right: Similarity<N, D, Rotation<N, D>>) -> Self::Output

Performs the / operation.

impl<'a, N: Real, D: DimName> Div<Similarity<N, D, Rotation<N, D>>> for &'a Rotation<N, D> where     DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>,

type Output = Similarity<N, D, Rotation<N, D>>

The resulting type after applying the / operator.

fn div(self, right: Similarity<N, D, Rotation<N, D>>) -> Self::Output

Performs the / operation.

impl<'b, N: Real, D: DimName> Div<&'b Similarity<N, D, Rotation<N, D>>> for Rotation<N, D> where     DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>,

type Output = Similarity<N, D, Rotation<N, D>>

The resulting type after applying the / operator.

fn div(self, right: &'b Similarity<N, D, Rotation<N, D>>) -> Self::Output

Performs the / operation.

impl<'a, 'b, N: Real, D: DimName> Div<&'b Similarity<N, D, Rotation<N, D>>> for &'a Rotation<N, D> where     DefaultAllocator: Allocator<N, D, D> + Allocator<N, D, U1>,

type Output = Similarity<N, D, Rotation<N, D>>

The resulting type after applying the / operator.

fn div(self, right: &'b Similarity<N, D, Rotation<N, D>>) -> Self::Output

Performs the / operation.

impl<N: Real> Mul<Similarity<N, U3, UnitQuaternion<N>>> for UnitQuaternion<N> where     DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>,

type Output = Similarity<N, U3, UnitQuaternion<N>>

The resulting type after applying the * operator.

fn mul(self, right: Similarity<N, U3, UnitQuaternion<N>>) -> Self::Output

Performs the * operation.

impl<'a, N: Real> Mul<Similarity<N, U3, UnitQuaternion<N>>> for &'a UnitQuaternion<N> where     DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>,

type Output = Similarity<N, U3, UnitQuaternion<N>>

The resulting type after applying the * operator.

fn mul(self, right: Similarity<N, U3, UnitQuaternion<N>>) -> Self::Output

Performs the * operation.

impl<'b, N: Real> Mul<&'b Similarity<N, U3, UnitQuaternion<N>>> for UnitQuaternion<N> where     DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>,

type Output = Similarity<N, U3, UnitQuaternion<N>>

The resulting type after applying the * operator.

fn mul(self, right: &'b Similarity<N, U3, UnitQuaternion<N>>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N: Real> Mul<&'b Similarity<N, U3, UnitQuaternion<N>>> for &'a UnitQuaternion<N> where     DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>,

type Output = Similarity<N, U3, UnitQuaternion<N>>

The resulting type after applying the * operator.

fn mul(self, right: &'b Similarity<N, U3, UnitQuaternion<N>>) -> Self::Output

Performs the * operation.

impl<N: Real> Div<Similarity<N, U3, UnitQuaternion<N>>> for UnitQuaternion<N> where     DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>,

type Output = Similarity<N, U3, UnitQuaternion<N>>

The resulting type after applying the / operator.

fn div(self, right: Similarity<N, U3, UnitQuaternion<N>>) -> Self::Output

Performs the / operation.

impl<'a, N: Real> Div<Similarity<N, U3, UnitQuaternion<N>>> for &'a UnitQuaternion<N> where     DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>,

type Output = Similarity<N, U3, UnitQuaternion<N>>

The resulting type after applying the / operator.

fn div(self, right: Similarity<N, U3, UnitQuaternion<N>>) -> Self::Output

Performs the / operation.

impl<'b, N: Real> Div<&'b Similarity<N, U3, UnitQuaternion<N>>> for UnitQuaternion<N> where     DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>,

type Output = Similarity<N, U3, UnitQuaternion<N>>

The resulting type after applying the / operator.

fn div(self, right: &'b Similarity<N, U3, UnitQuaternion<N>>) -> Self::Output

Performs the / operation.

impl<'a, 'b, N: Real> Div<&'b Similarity<N, U3, UnitQuaternion<N>>> for &'a UnitQuaternion<N> where     DefaultAllocator: Allocator<N, U4, U1> + Allocator<N, U3, U1>,

type Output = Similarity<N, U3, UnitQuaternion<N>>

The resulting type after applying the / operator.

fn div(self, right: &'b Similarity<N, U3, UnitQuaternion<N>>) -> Self::Output

Performs the / operation.

impl<N: Real, D: DimName, R> Identity<Multiplicative> for Similarity<N, D, R> where     R: Rotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

fn identity() -> Self

The identity element.

fn id(O) -> Self

Specific identity.

impl<N: Real, D: DimName, R> Inverse<Multiplicative> for Similarity<N, D, R> where     R: Rotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

fn inverse(&self) -> Self

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

fn inverse_mut(&mut self)

In-place inversin of self.

impl<N: Real, D: DimName, R> AbstractMagma<Multiplicative> for Similarity<N, D, R> where     R: Rotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

fn operate(&self, rhs: &Self) -> Self

Performs an operation.

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

Performs specific operation.

impl<N: Real, D: DimName, R> AbstractSemigroup<Multiplicative> for Similarity<N, D, R> where     R: Rotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

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.

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

Returns true if associativity holds for the given arguments.

impl<N: Real, D: DimName, R> AbstractMonoid<Multiplicative> for Similarity<N, D, R> where     R: Rotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

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.

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.

impl<N: Real, D: DimName, R> AbstractQuasigroup<Multiplicative> for Similarity<N, D, R> where     R: Rotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

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.

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

Returns true if latin squareness holds for the given arguments.

impl<N: Real, D: DimName, R> AbstractLoop<Multiplicative> for Similarity<N, D, R> where     R: Rotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

impl<N: Real, D: DimName, R> AbstractGroup<Multiplicative> for Similarity<N, D, R> where     R: Rotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

impl<N: Real, D: DimName, R> Transformation<Point<N, D>> for Similarity<N, D, R> where     R: Rotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

fn transform_point(&self, pt: &Point<N, D>) -> Point<N, D>

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

fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D>

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

impl<N: Real, D: DimName, R> ProjectiveTransformation<Point<N, D>> for Similarity<N, D, R> where     R: Rotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

fn inverse_transform_point(&self, pt: &Point<N, D>) -> Point<N, D>

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

fn inverse_transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, D>

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

impl<N: Real, D: DimName, R> AffineTransformation<Point<N, D>> for Similarity<N, D, R> where     R: Rotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type NonUniformScaling = N

Type of the non-uniform scaling to be applied.

type Rotation = R

Type of the first rotation to be applied.

type Translation = Translation<N, D>

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

fn decompose(&self) -> (Translation<N, D>, R, N, R)

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

fn append_translation(&self, t: &Self::Translation) -> Self

Appends a translation to this similarity.

fn prepend_translation(&self, t: &Self::Translation) -> Self

Prepends a translation to this similarity.

fn append_rotation(&self, r: &Self::Rotation) -> Self

Appends a rotation to this similarity.

fn prepend_rotation(&self, r: &Self::Rotation) -> Self

Prepends a rotation to this similarity.

fn append_scaling(&self, s: &Self::NonUniformScaling) -> Self

Appends a scaling factor to this similarity.

fn prepend_scaling(&self, s: &Self::NonUniformScaling) -> Self

Prepends a scaling factor to this similarity.

fn append_rotation_wrt_point(     &self,     r: &Self::Rotation,     p: &Point<N, D> ) -> Option<Self>

Appends to this similarity a rotation centered at the point p, i.e., this point is left invariant.

impl<N: Real, D: DimName, R> AlgaSimilarity<Point<N, D>> for Similarity<N, D, R> where     R: Rotation<Point<N, D>>,     DefaultAllocator: Allocator<N, D>,

type Scaling = N

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

fn translation(&self) -> Translation<N, D>

The pure translational component of this similarity transformation.

fn rotation(&self) -> R

The pure rotational component of this similarity transformation.

fn scaling(&self) -> N

The pure scaling component of this similarity transformation.

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

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

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

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

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

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

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

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

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

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

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

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

impl<N1, N2, D: DimName, R1, R2> SubsetOf<Similarity<N2, D, R2>> for Similarity<N1, D, R1> where     N1: Real + SubsetOf<N2>,     N2: Real + SupersetOf<N1>,     R1: Rotation<Point<N1, D>> + SubsetOf<R2>,     R2: Rotation<Point<N2, D>>,     DefaultAllocator: Allocator<N1, D> + Allocator<N2, D>,

fn to_superset(&self) -> Similarity<N2, D, R2>

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

fn is_in_subset(sim: &Similarity<N2, D, R2>) -> bool

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

unsafe fn from_superset_unchecked(sim: &Similarity<N2, D, R2>) -> Self

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

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

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

impl<N1, N2, D, R, C> SubsetOf<Transform<N2, D, C>> for Similarity<N1, D, R> where     N1: Real,     N2: Real + SupersetOf<N1>,     C: SuperTCategoryOf<TAffine>,     R: Rotation<Point<N1, D>> + SubsetOf<MatrixN<N1, DimNameSum<D, U1>>> + SubsetOf<MatrixN<N2, DimNameSum<D, U1>>>,     D: DimNameAdd<U1> + DimMin<D, Output = D>,     DefaultAllocator: Allocator<N1, D> + Allocator<N1, D, D> + Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<(usize, usize), D> + Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N2, D, D> + Allocator<N2, D>,

fn to_superset(&self) -> Transform<N2, D, C>

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

fn is_in_subset(t: &Transform<N2, D, C>) -> bool

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

unsafe fn from_superset_unchecked(t: &Transform<N2, D, C>) -> Self

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

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

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

impl<N1, N2, D, R> SubsetOf<MatrixN<N2, DimNameSum<D, U1>>> for Similarity<N1, D, R> where     N1: Real,     N2: Real + SupersetOf<N1>,     R: Rotation<Point<N1, D>> + SubsetOf<MatrixN<N1, DimNameSum<D, U1>>> + SubsetOf<MatrixN<N2, DimNameSum<D, U1>>>,     D: DimNameAdd<U1> + DimMin<D, Output = D>,     DefaultAllocator: Allocator<N1, D> + Allocator<N1, D, D> + Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<(usize, usize), D> + Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N2, D, D> + Allocator<N2, D>,

fn to_superset(&self) -> MatrixN<N2, DimNameSum<D, U1>>

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

fn is_in_subset(m: &MatrixN<N2, DimNameSum<D, U1>>) -> bool

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

unsafe fn from_superset_unchecked(m: &MatrixN<N2, DimNameSum<D, U1>>) -> Self

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

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

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

impl<N, D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>>>> Mul<Similarity<N, D, R>> for Transform<N, D, C> where     N: Scalar + Zero + One + ClosedAdd + ClosedMul + Real,     DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, U1> + Allocator<N, DimNameSum<D, U1>, U1>,

type Output = Transform<N, D, C::Representative>

The resulting type after applying the * operator.

fn mul(self, rhs: Similarity<N, D, R>) -> Self::Output

Performs the * operation.

impl<'a, N, D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>>>> Mul<Similarity<N, D, R>> for &'a Transform<N, D, C> where     N: Scalar + Zero + One + ClosedAdd + ClosedMul + Real,     DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, U1> + Allocator<N, DimNameSum<D, U1>, U1>,

type Output = Transform<N, D, C::Representative>

The resulting type after applying the * operator.

fn mul(self, rhs: Similarity<N, D, R>) -> Self::Output

Performs the * operation.

impl<'b, N, D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>>>> Mul<&'b Similarity<N, D, R>> for Transform<N, D, C> where     N: Scalar + Zero + One + ClosedAdd + ClosedMul + Real,     DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, U1> + Allocator<N, DimNameSum<D, U1>, U1>,

type Output = Transform<N, D, C::Representative>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Similarity<N, D, R>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N, D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>>>> Mul<&'b Similarity<N, D, R>> for &'a Transform<N, D, C> where     N: Scalar + Zero + One + ClosedAdd + ClosedMul + Real,     DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, U1> + Allocator<N, DimNameSum<D, U1>, U1>,

type Output = Transform<N, D, C::Representative>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Similarity<N, D, R>) -> Self::Output

Performs the * operation.

impl<N, D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>>>> Mul<Transform<N, D, C>> for Similarity<N, D, R> where     N: Scalar + Zero + One + ClosedAdd + ClosedMul + Real,     DefaultAllocator: Allocator<N, D, U1> + Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, DimNameSum<D, U1>>,

type Output = Transform<N, D, C::Representative>

The resulting type after applying the * operator.

fn mul(self, rhs: Transform<N, D, C>) -> Self::Output

Performs the * operation.

impl<'a, N, D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>>>> Mul<Transform<N, D, C>> for &'a Similarity<N, D, R> where     N: Scalar + Zero + One + ClosedAdd + ClosedMul + Real,     DefaultAllocator: Allocator<N, D, U1> + Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, DimNameSum<D, U1>>,

type Output = Transform<N, D, C::Representative>

The resulting type after applying the * operator.

fn mul(self, rhs: Transform<N, D, C>) -> Self::Output

Performs the * operation.

impl<'b, N, D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>>>> Mul<&'b Transform<N, D, C>> for Similarity<N, D, R> where     N: Scalar + Zero + One + ClosedAdd + ClosedMul + Real,     DefaultAllocator: Allocator<N, D, U1> + Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, DimNameSum<D, U1>>,

type Output = Transform<N, D, C::Representative>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Transform<N, D, C>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N, D: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>>>> Mul<&'b Transform<N, D, C>> for &'a Similarity<N, D, R> where     N: Scalar + Zero + One + ClosedAdd + ClosedMul + Real,     DefaultAllocator: Allocator<N, D, U1> + Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, DimNameSum<D, U1>>,

type Output = Transform<N, D, C::Representative>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Transform<N, D, C>) -> Self::Output

Performs the * operation.

impl<N, D: DimNameAdd<U1>, C: TCategory, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>>>> MulAssign<Similarity<N, D, R>> for Transform<N, D, C> where     N: Scalar + Zero + One + ClosedAdd + ClosedMul + Real,     DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, U1>,

fn mul_assign(&mut self, rhs: Similarity<N, D, R>)

Performs the *= operation.

impl<'b, N, D: DimNameAdd<U1>, C: TCategory, R: SubsetOf<MatrixN<N, DimNameSum<D, U1>>>> MulAssign<&'b Similarity<N, D, R>> for Transform<N, D, C> where     N: Scalar + Zero + One + ClosedAdd + ClosedMul + Real,     DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D, U1>,

fn mul_assign(&mut self, rhs: &'b Similarity<N, D, R>)

Performs the *= operation.