Struct na::geometry::Similarity

#[repr(C)]
pub struct Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    DefaultAllocator: Allocator<N, D, U1>,  {
    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, D, R> Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

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) -> Similarity<N, D, R>

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

pub fn append_scaling(&self, scaling: N) -> Similarity<N, D, R>

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.

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

Transform the given point by this similarity.

This is the same as the multiplication self * pt.

Example

let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
let translation = Vector3::new(1.0, 2.0, 3.0);
let sim = Similarity3::new(translation, axisangle, 3.0);
let transformed_point = sim.transform_point(&Point3::new(4.0, 5.0, 6.0));
assert_relative_eq!(transformed_point, Point3::new(19.0, 17.0, -9.0), epsilon = 1.0e-5);

pub fn transform_vector(
    &self,
    v: &Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>
) -> Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>

Transform the given vector by this similarity, ignoring the translational component.

This is the same as the multiplication self * t.

Example

let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
let translation = Vector3::new(1.0, 2.0, 3.0);
let sim = Similarity3::new(translation, axisangle, 3.0);
let transformed_vector = sim.transform_vector(&Vector3::new(4.0, 5.0, 6.0));
assert_relative_eq!(transformed_vector, Vector3::new(18.0, 15.0, -12.0), epsilon = 1.0e-5);

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

Transform the given point by the inverse of this similarity. This may be cheaper than inverting the similarity and then transforming the given point.

Example

let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
let translation = Vector3::new(1.0, 2.0, 3.0);
let sim = Similarity3::new(translation, axisangle, 2.0);
let transformed_point = sim.inverse_transform_point(&Point3::new(4.0, 5.0, 6.0));
assert_relative_eq!(transformed_point, Point3::new(-1.5, 1.5, 1.5), epsilon = 1.0e-5);

pub fn inverse_transform_vector(
    &self,
    v: &Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>
) -> Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>

Transform the given vector by the inverse of this similarity, ignoring the translational component. This may be cheaper than inverting the similarity and then transforming the given vector.

Example

let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
let translation = Vector3::new(1.0, 2.0, 3.0);
let sim = Similarity3::new(translation, axisangle, 2.0);
let transformed_vector = sim.inverse_transform_vector(&Vector3::new(4.0, 5.0, 6.0));
assert_relative_eq!(transformed_vector, Vector3::new(-3.0, 2.5, 2.0), epsilon = 1.0e-5);

impl<N, D, R> Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    DefaultAllocator: Allocator<N, D, U1>, 

pub fn to_homogeneous(
    &self
) -> Matrix<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer> where
    D: DimNameAdd<U1>,
    R: SubsetOf<Matrix<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

Converts this similarity into its equivalent homogeneous transformation matrix.

impl<N, D, R> Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

pub fn identity() -> Similarity<N, D, R>

Creates a new identity similarity.

Example

let sim = Similarity2::identity();
let pt = Point2::new(1.0, 2.0);
assert_eq!(sim * pt, pt);

let sim = Similarity3::identity();
let pt = Point3::new(1.0, 2.0, 3.0);
assert_eq!(sim * pt, pt);

impl<N, D, R> Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

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

Example

let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
let pt = Point2::new(3.0, 2.0);
let sim = Similarity2::rotation_wrt_point(rot, pt, 4.0);

assert_relative_eq!(sim * Point2::new(1.0, 2.0), Point2::new(-3.0, 3.0), epsilon = 1.0e-6);

impl<N> Similarity<N, U2, Rotation<N, U2>> where
    N: RealField, 

pub fn new(
    translation: Matrix<N, U2, U1, <DefaultAllocator as Allocator<N, U2, U1>>::Buffer>,
    angle: N,
    scaling: N
) -> Similarity<N, U2, Rotation<N, U2>>

Creates a new similarity from a translation, a rotation, and an uniform scaling factor.

Example

let sim = SimilarityMatrix2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2, 3.0);

assert_relative_eq!(sim * Point2::new(2.0, 4.0), Point2::new(-11.0, 8.0), epsilon = 1.0e-6);

impl<N> Similarity<N, U2, Unit<Complex<N>>> where
    N: RealField, 

pub fn new(
    translation: Matrix<N, U2, U1, <DefaultAllocator as Allocator<N, U2, U1>>::Buffer>,
    angle: N,
    scaling: N
) -> Similarity<N, U2, Unit<Complex<N>>>

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

Example

let sim = Similarity2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2, 3.0);

assert_relative_eq!(sim * Point2::new(2.0, 4.0), Point2::new(-11.0, 8.0), epsilon = 1.0e-6);

impl<N> Similarity<N, U3, Rotation<N, U3>> where
    N: RealField, 

pub fn new(
    translation: Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>,
    axisangle: Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>,
    scaling: N
) -> Similarity<N, U3, Rotation<N, U3>>

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

Example

let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
let translation = Vector3::new(1.0, 2.0, 3.0);
// Point and vector being transformed in the tests.
let pt = Point3::new(4.0, 5.0, 6.0);
let vec = Vector3::new(4.0, 5.0, 6.0);

// Similarity with its rotation part represented as a UnitQuaternion
let sim = Similarity3::new(translation, axisangle, 3.0);
assert_relative_eq!(sim * pt, Point3::new(19.0, 17.0, -9.0), epsilon = 1.0e-5);
assert_relative_eq!(sim * vec, Vector3::new(18.0, 15.0, -12.0), epsilon = 1.0e-5);

// Similarity with its rotation part represented as a Rotation3 (a 3x3 rotation matrix).
let sim = SimilarityMatrix3::new(translation, axisangle, 3.0);
assert_relative_eq!(sim * pt, Point3::new(19.0, 17.0, -9.0), epsilon = 1.0e-5);
assert_relative_eq!(sim * vec, Vector3::new(18.0, 15.0, -12.0), epsilon = 1.0e-5);

pub fn face_towards(
    eye: &Point<N, U3>,
    target: &Point<N, U3>,
    up: &Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>,
    scaling: N
) -> Similarity<N, U3, Rotation<N, U3>>

Creates an similarity that corresponds to 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.

Example

let eye = Point3::new(1.0, 2.0, 3.0);
let target = Point3::new(2.0, 2.0, 3.0);
let up = Vector3::y();

// Similarity with its rotation part represented as a UnitQuaternion
let sim = Similarity3::face_towards(&eye, &target, &up, 3.0);
assert_eq!(sim * Point3::origin(), eye);
assert_relative_eq!(sim * Vector3::z(), Vector3::x() * 3.0, epsilon = 1.0e-6);

// Similarity with its rotation part represented as Rotation3 (a 3x3 rotation matrix).
let sim = SimilarityMatrix3::face_towards(&eye, &target, &up, 3.0);
assert_eq!(sim * Point3::origin(), eye);
assert_relative_eq!(sim * Vector3::z(), Vector3::x() * 3.0, epsilon = 1.0e-6);

pub fn new_observer_frames(
    eye: &Point<N, U3>,
    target: &Point<N, U3>,
    up: &Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>,
    scaling: N
) -> Similarity<N, U3, Rotation<N, U3>>

Deprecated:

renamed to face_towards

Deprecated: Use [SimilarityMatrix3::face_towards] instead.

pub fn look_at_rh(
    eye: &Point<N, U3>,
    target: &Point<N, U3>,
    up: &Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>,
    scaling: N
) -> Similarity<N, U3, Rotation<N, U3>>

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.

Example

let eye = Point3::new(1.0, 2.0, 3.0);
let target = Point3::new(2.0, 2.0, 3.0);
let up = Vector3::y();

// Similarity with its rotation part represented as a UnitQuaternion
let iso = Similarity3::look_at_rh(&eye, &target, &up, 3.0);
assert_relative_eq!(iso * Vector3::x(), -Vector3::z() * 3.0, epsilon = 1.0e-6);

// Similarity with its rotation part represented as Rotation3 (a 3x3 rotation matrix).
let iso = SimilarityMatrix3::look_at_rh(&eye, &target, &up, 3.0);
assert_relative_eq!(iso * Vector3::x(), -Vector3::z() * 3.0, epsilon = 1.0e-6);

pub fn look_at_lh(
    eye: &Point<N, U3>,
    target: &Point<N, U3>,
    up: &Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>,
    scaling: N
) -> Similarity<N, U3, Rotation<N, U3>>

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.

Example

let eye = Point3::new(1.0, 2.0, 3.0);
let target = Point3::new(2.0, 2.0, 3.0);
let up = Vector3::y();

// Similarity with its rotation part represented as a UnitQuaternion
let sim = Similarity3::look_at_lh(&eye, &target, &up, 3.0);
assert_relative_eq!(sim * Vector3::x(), Vector3::z() * 3.0, epsilon = 1.0e-6);

// Similarity with its rotation part represented as Rotation3 (a 3x3 rotation matrix).
let sim = SimilarityMatrix3::look_at_lh(&eye, &target, &up, 3.0);
assert_relative_eq!(sim * Vector3::x(), Vector3::z() * 3.0, epsilon = 1.0e-6);

impl<N> Similarity<N, U3, Unit<Quaternion<N>>> where
    N: RealField, 

pub fn new(
    translation: Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>,
    axisangle: Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>,
    scaling: N
) -> Similarity<N, U3, Unit<Quaternion<N>>>

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

Example

let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;
let translation = Vector3::new(1.0, 2.0, 3.0);
// Point and vector being transformed in the tests.
let pt = Point3::new(4.0, 5.0, 6.0);
let vec = Vector3::new(4.0, 5.0, 6.0);

// Similarity with its rotation part represented as a UnitQuaternion
let sim = Similarity3::new(translation, axisangle, 3.0);
assert_relative_eq!(sim * pt, Point3::new(19.0, 17.0, -9.0), epsilon = 1.0e-5);
assert_relative_eq!(sim * vec, Vector3::new(18.0, 15.0, -12.0), epsilon = 1.0e-5);

// Similarity with its rotation part represented as a Rotation3 (a 3x3 rotation matrix).
let sim = SimilarityMatrix3::new(translation, axisangle, 3.0);
assert_relative_eq!(sim * pt, Point3::new(19.0, 17.0, -9.0), epsilon = 1.0e-5);
assert_relative_eq!(sim * vec, Vector3::new(18.0, 15.0, -12.0), epsilon = 1.0e-5);

pub fn face_towards(
    eye: &Point<N, U3>,
    target: &Point<N, U3>,
    up: &Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>,
    scaling: N
) -> Similarity<N, U3, Unit<Quaternion<N>>>

Creates an similarity that corresponds to 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.

Example

let eye = Point3::new(1.0, 2.0, 3.0);
let target = Point3::new(2.0, 2.0, 3.0);
let up = Vector3::y();

// Similarity with its rotation part represented as a UnitQuaternion
let sim = Similarity3::face_towards(&eye, &target, &up, 3.0);
assert_eq!(sim * Point3::origin(), eye);
assert_relative_eq!(sim * Vector3::z(), Vector3::x() * 3.0, epsilon = 1.0e-6);

// Similarity with its rotation part represented as Rotation3 (a 3x3 rotation matrix).
let sim = SimilarityMatrix3::face_towards(&eye, &target, &up, 3.0);
assert_eq!(sim * Point3::origin(), eye);
assert_relative_eq!(sim * Vector3::z(), Vector3::x() * 3.0, epsilon = 1.0e-6);

pub fn new_observer_frames(
    eye: &Point<N, U3>,
    target: &Point<N, U3>,
    up: &Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>,
    scaling: N
) -> Similarity<N, U3, Unit<Quaternion<N>>>

Deprecated:

renamed to face_towards

Deprecated: Use [SimilarityMatrix3::face_towards] instead.

pub fn look_at_rh(
    eye: &Point<N, U3>,
    target: &Point<N, U3>,
    up: &Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>,
    scaling: N
) -> Similarity<N, U3, Unit<Quaternion<N>>>

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.

Example

let eye = Point3::new(1.0, 2.0, 3.0);
let target = Point3::new(2.0, 2.0, 3.0);
let up = Vector3::y();

// Similarity with its rotation part represented as a UnitQuaternion
let iso = Similarity3::look_at_rh(&eye, &target, &up, 3.0);
assert_relative_eq!(iso * Vector3::x(), -Vector3::z() * 3.0, epsilon = 1.0e-6);

// Similarity with its rotation part represented as Rotation3 (a 3x3 rotation matrix).
let iso = SimilarityMatrix3::look_at_rh(&eye, &target, &up, 3.0);
assert_relative_eq!(iso * Vector3::x(), -Vector3::z() * 3.0, epsilon = 1.0e-6);

pub fn look_at_lh(
    eye: &Point<N, U3>,
    target: &Point<N, U3>,
    up: &Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>,
    scaling: N
) -> Similarity<N, U3, Unit<Quaternion<N>>>

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.

Example

let eye = Point3::new(1.0, 2.0, 3.0);
let target = Point3::new(2.0, 2.0, 3.0);
let up = Vector3::y();

// Similarity with its rotation part represented as a UnitQuaternion
let sim = Similarity3::look_at_lh(&eye, &target, &up, 3.0);
assert_relative_eq!(sim * Vector3::x(), Vector3::z() * 3.0, epsilon = 1.0e-6);

// Similarity with its rotation part represented as Rotation3 (a 3x3 rotation matrix).
let sim = SimilarityMatrix3::look_at_lh(&eye, &target, &up, 3.0);
assert_relative_eq!(sim * Vector3::x(), Vector3::z() * 3.0, epsilon = 1.0e-6);

Trait Implementations

impl<N, D, R> MulAssign<Similarity<N, D, R>> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

Performs the *= operation.

impl<N, D, C, R> MulAssign<Similarity<N, D, R>> for Transform<N, D, C> where
    C: TCategory,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + RealField,
    R: SubsetOf<Matrix<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

Performs the *= operation.

impl<'b, N, D, R> MulAssign<&'b Translation<N, D>> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

Performs the *= operation.

impl<N, D, R> MulAssign<R> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

fn mul_assign(&mut self, rhs: R)

Performs the *= operation.

impl<N, D, R> MulAssign<Translation<N, D>> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

Performs the *= operation.

impl<'b, N, D, C, R> MulAssign<&'b Similarity<N, D, R>> for Transform<N, D, C> where
    C: TCategory,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + RealField,
    R: SubsetOf<Matrix<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

Performs the *= operation.

impl<'b, N, D, R> MulAssign<&'b R> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

Performs the *= operation.

impl<'b, N, D, R> MulAssign<&'b Similarity<N, D, R>> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

Performs the *= operation.

impl<'b, N, D, R> MulAssign<&'b Isometry<N, D, R>> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

Performs the *= operation.

impl<N, D, R> MulAssign<Isometry<N, D, R>> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

Performs the *= operation.

impl<N, D, R> TwoSidedInverse<Multiplicative> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

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

fn two_sided_inverse_mut(&mut self)

In-place inversion of self, relative to the operator O.

impl<N, D, R> AbstractSemigroup<Multiplicative> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

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, D, R> Transformation<Point<N, D>> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

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: &Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>
) -> Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>

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

impl<N, D, R> Clone for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Clone + Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<N, D, R> PartialEq<Similarity<N, D, R>> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>> + PartialEq<R>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

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

#[must_use]

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

This method tests for !=.

impl<N, D, R> AbstractGroup<Multiplicative> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

impl<N, D, R> RelativeEq<Similarity<N, D, R>> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>> + RelativeEq<R, Epsilon = <N as AbsDiffEq<N>>::Epsilon>,
    DefaultAllocator: Allocator<N, D, U1>,
    <N as AbsDiffEq<N>>::Epsilon: Copy, 

fn default_max_relative(
) -> <Similarity<N, D, R> as AbsDiffEq<Similarity<N, D, R>>>::Epsilon

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

fn relative_eq(
    &self,
    other: &Similarity<N, D, R>,
    epsilon: <Similarity<N, D, R> as AbsDiffEq<Similarity<N, D, R>>>::Epsilon,
    max_relative: <Similarity<N, D, R> as AbsDiffEq<Similarity<N, D, R>>>::Epsilon
) -> bool

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

fn relative_ne(
    &self,
    other: &Rhs,
    epsilon: Self::Epsilon,
    max_relative: Self::Epsilon
) -> bool

The inverse of ApproxEq::relative_eq.

impl<N, D, R> DivAssign<Similarity<N, D, R>> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

Performs the /= operation.

impl<N, D, R> DivAssign<Isometry<N, D, R>> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

Performs the /= operation.

impl<'b, N, D, R> DivAssign<&'b R> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

Performs the /= operation.

impl<'b, N, D, R> DivAssign<&'b Isometry<N, D, R>> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

Performs the /= operation.

impl<'b, N, D, R> DivAssign<&'b Similarity<N, D, R>> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

Performs the /= operation.

impl<N, D, R> DivAssign<R> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

fn div_assign(&mut self, rhs: R)

Performs the /= operation.

impl<N, D, R> Similarity<Point<N, D>> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

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<N, D, R> Debug for Similarity<N, D, R> where
    D: DimName + Debug,
    N: Debug + RealField,
    R: Debug,
    DefaultAllocator: Allocator<N, D, U1>, 

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

Formats the value using the given formatter.

impl<N, D, R> Display for Similarity<N, D, R> where
    D: DimName,
    N: RealField + Display,
    R: Rotation<Point<N, D>> + Display,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<usize, D, U1>, 

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

Formats the value using the given formatter.

impl<N, D, R> AbstractMonoid<Multiplicative> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

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, D, R> AffineTransformation<Point<N, D>> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

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: &<Similarity<N, D, R> as AffineTransformation<Point<N, D>>>::Translation
) -> Similarity<N, D, R>

Appends a translation to this similarity.

fn prepend_translation(
    &self,
    t: &<Similarity<N, D, R> as AffineTransformation<Point<N, D>>>::Translation
) -> Similarity<N, D, R>

Prepends a translation to this similarity.

fn append_rotation(
    &self,
    r: &<Similarity<N, D, R> as AffineTransformation<Point<N, D>>>::Rotation
) -> Similarity<N, D, R>

Appends a rotation to this similarity.

fn prepend_rotation(
    &self,
    r: &<Similarity<N, D, R> as AffineTransformation<Point<N, D>>>::Rotation
) -> Similarity<N, D, R>

Prepends a rotation to this similarity.

fn append_scaling(
    &self,
    s: &<Similarity<N, D, R> as AffineTransformation<Point<N, D>>>::NonUniformScaling
) -> Similarity<N, D, R>

Appends a scaling factor to this similarity.

fn prepend_scaling(
    &self,
    s: &<Similarity<N, D, R> as AffineTransformation<Point<N, D>>>::NonUniformScaling
) -> Similarity<N, D, R>

Prepends a scaling factor to this similarity.

fn append_rotation_wrt_point(
    &self,
    r: &<Similarity<N, D, R> as AffineTransformation<Point<N, D>>>::Rotation,
    p: &Point<N, D>
) -> Option<Similarity<N, D, R>>

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

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

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>
) -> Similarity<N1, D, R>

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, R1, R2> SubsetOf<Similarity<N2, D, R2>> for Similarity<N1, D, R1> where
    D: DimName,
    N1: RealField + SubsetOf<N2>,
    N2: RealField + SupersetOf<N1>,
    R1: Rotation<Point<N1, D>> + SubsetOf<R2>,
    R2: Rotation<Point<N2, D>>,
    DefaultAllocator: Allocator<N1, D, U1>,
    DefaultAllocator: Allocator<N2, D, U1>, 

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>
) -> Similarity<N1, D, R1>

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 Unit<Quaternion<N1>> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    R: Rotation<Point<N2, U3>> + SupersetOf<Unit<Quaternion<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>
) -> Unit<Quaternion<N1>>

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, R1, R2> SubsetOf<Similarity<N2, D, R2>> for Isometry<N1, D, R1> where
    D: DimName,
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    R1: Rotation<Point<N1, D>> + SubsetOf<R2>,
    R2: Rotation<Point<N2, D>>,
    DefaultAllocator: Allocator<N1, D, U1>,
    DefaultAllocator: Allocator<N2, D, U1>, 

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>
) -> Isometry<N1, D, R1>

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<Similarity<N2, D, R>> for Translation<N1, D> where
    D: DimName,
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    R: Rotation<Point<N2, D>>,
    DefaultAllocator: Allocator<N1, D, U1>,
    DefaultAllocator: Allocator<N2, D, U1>, 

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>
) -> Translation<N1, D>

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<Matrix<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>> for Similarity<N1, D, R> where
    D: DimNameAdd<U1> + DimMin<D, Output = D>,
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    R: Rotation<Point<N1, D>> + SubsetOf<Matrix<N1, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N1, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>> + SubsetOf<Matrix<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>>,
    DefaultAllocator: Allocator<N1, D, U1>,
    DefaultAllocator: Allocator<N1, D, D>,
    DefaultAllocator: Allocator<N1, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<(usize, usize), D, U1>,
    DefaultAllocator: Allocator<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N2, D, D>,
    DefaultAllocator: Allocator<N2, D, U1>, 

fn to_superset(
    &self
) -> Matrix<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>

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

fn is_in_subset(
    m: &Matrix<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>
) -> bool

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

unsafe fn from_superset_unchecked(
    m: &Matrix<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>
) -> Similarity<N1, D, R>

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<Similarity<N2, D, R>> for Rotation<N1, D> where
    D: DimName,
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    R: Rotation<Point<N2, D>> + SupersetOf<Rotation<N1, D>>,
    DefaultAllocator: Allocator<N1, D, D>,
    DefaultAllocator: Allocator<N2, D, U1>, 

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>) -> Rotation<N1, D>

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, U2, R>> for Unit<Complex<N1>> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    R: Rotation<Point<N2, U2>> + SupersetOf<Unit<Complex<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>
) -> Unit<Complex<N1>>

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, R> Hash for Similarity<N, D, R> where
    D: DimName + Hash,
    N: Hash + RealField,
    R: Hash,
    DefaultAllocator: Allocator<N, D, U1>,
    <DefaultAllocator as Allocator<N, D, U1>>::Buffer: Hash, 

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

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, D, R> One for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

fn one() -> Similarity<N, D, R>

Creates a new identity similarity.

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

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

Returns true if self is equal to the multiplicative identity.

impl<N, D, R> From<Similarity<N, D, R>> for Matrix<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer> where
    D: DimName + DimNameAdd<U1>,
    N: RealField,
    R: SubsetOf<Matrix<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

fn from(
    sim: Similarity<N, D, R>
) -> Matrix<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>

Performs the conversion.

impl<N, D, R> AbstractQuasigroup<Multiplicative> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

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, D, R> Eq for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>> + Eq,
    DefaultAllocator: Allocator<N, D, U1>, 

impl<'a, N> Mul<Similarity<N, U3, Unit<Quaternion<N>>>> for &'a Unit<Quaternion<N>> where
    N: RealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Similarity<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the * operator.

fn mul(
    self,
    right: Similarity<N, U3, Unit<Quaternion<N>>>
) -> <&'a Unit<Quaternion<N>> as Mul<Similarity<N, U3, Unit<Quaternion<N>>>>>::Output

Performs the * operation.

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

type Output = Point<N, D>

The resulting type after applying the * operator.

fn mul(
    self,
    right: &'b Point<N, D>
) -> <&'a Similarity<N, D, R> as Mul<&'b Point<N, D>>>::Output

Performs the * operation.

impl<N, D, R> Mul<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>

The resulting type after applying the * operator.

fn mul(
    self,
    right: Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>
) -> <Similarity<N, D, R> as Mul<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>>::Output

Performs the * operation.

impl<'b, N, D, C, R> Mul<&'b Transform<N, D, C>> for Similarity<N, D, R> where
    C: TCategoryMul<TAffine>,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + RealField,
    R: SubsetOf<Matrix<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, <D as DimNameAdd<U1>>::Output>, 

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

The resulting type after applying the * operator.

fn mul(
    self,
    rhs: &'b Transform<N, D, C>
) -> <Similarity<N, D, R> as Mul<&'b Transform<N, D, C>>>::Output

Performs the * operation.

impl<'a, N, D, R> Mul<Translation<N, D>> for &'a Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(
    self,
    right: Translation<N, D>
) -> <&'a Similarity<N, D, R> as Mul<Translation<N, D>>>::Output

Performs the * operation.

impl<'a, 'b, N> Mul<&'b Similarity<N, U2, Unit<Complex<N>>>> for &'a Unit<Complex<N>> where
    N: RealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Similarity<N, U2, Unit<Complex<N>>>

The resulting type after applying the * operator.

fn mul(
    self,
    rhs: &'b Similarity<N, U2, Unit<Complex<N>>>
) -> <&'a Unit<Complex<N>> as Mul<&'b Similarity<N, U2, Unit<Complex<N>>>>>::Output

Performs the * operation.

impl<'b, N, D, R> Mul<&'b Similarity<N, D, R>> for Isometry<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b, N, D, C, R> Mul<&'b Transform<N, D, C>> for &'a Similarity<N, D, R> where
    C: TCategoryMul<TAffine>,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + RealField,
    R: SubsetOf<Matrix<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, <D as DimNameAdd<U1>>::Output>, 

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

The resulting type after applying the * operator.

fn mul(
    self,
    rhs: &'b Transform<N, D, C>
) -> <&'a Similarity<N, D, R> as Mul<&'b Transform<N, D, C>>>::Output

Performs the * operation.

impl<'a, 'b, N, D, R> Mul<&'b Translation<N, D>> for &'a Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(
    self,
    right: &'b Translation<N, D>
) -> <&'a Similarity<N, D, R> as Mul<&'b Translation<N, D>>>::Output

Performs the * operation.

impl<'a, N, D, R> Mul<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>> for &'a Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>

The resulting type after applying the * operator.

fn mul(
    self,
    right: Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>
) -> <&'a Similarity<N, D, R> as Mul<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>>::Output

Performs the * operation.

impl<N, D, R> Mul<R> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N, D, R> Mul<R> for &'a Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(self, rhs: R) -> <&'a Similarity<N, D, R> as Mul<R>>::Output

Performs the * operation.

impl<N, D> Mul<Similarity<N, D, Rotation<N, D>>> for Rotation<N, D> where
    D: DimName,
    N: RealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: 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>>
) -> <Rotation<N, D> as Mul<Similarity<N, D, Rotation<N, D>>>>::Output

Performs the * operation.

impl<N, D, R> Mul<Translation<N, D>> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N, D, R> Mul<Similarity<N, D, R>> for &'a Translation<N, D> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(
    self,
    right: Similarity<N, D, R>
) -> <&'a Translation<N, D> as Mul<Similarity<N, D, R>>>::Output

Performs the * operation.

impl<N, D, R> Mul<Similarity<N, D, R>> for Isometry<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N, D, C, R> Mul<Transform<N, D, C>> for &'a Similarity<N, D, R> where
    C: TCategoryMul<TAffine>,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + RealField,
    R: SubsetOf<Matrix<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, <D as DimNameAdd<U1>>::Output>, 

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

The resulting type after applying the * operator.

fn mul(
    self,
    rhs: Transform<N, D, C>
) -> <&'a Similarity<N, D, R> as Mul<Transform<N, D, C>>>::Output

Performs the * operation.

impl<N, D, R> Mul<Point<N, D>> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Point<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, N> Mul<&'b Similarity<N, U2, Unit<Complex<N>>>> for Unit<Complex<N>> where
    N: RealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Similarity<N, U2, Unit<Complex<N>>>

The resulting type after applying the * operator.

fn mul(
    self,
    rhs: &'b Similarity<N, U2, Unit<Complex<N>>>
) -> <Unit<Complex<N>> as Mul<&'b Similarity<N, U2, Unit<Complex<N>>>>>::Output

Performs the * operation.

impl<'a, N, D, R> Mul<Similarity<N, D, R>> for &'a Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(
    self,
    rhs: Similarity<N, D, R>
) -> <&'a Similarity<N, D, R> as Mul<Similarity<N, D, R>>>::Output

Performs the * operation.

impl<N> Mul<Similarity<N, U3, Unit<Quaternion<N>>>> for Unit<Quaternion<N>> where
    N: RealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Similarity<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the * operator.

fn mul(
    self,
    right: Similarity<N, U3, Unit<Quaternion<N>>>
) -> <Unit<Quaternion<N>> as Mul<Similarity<N, U3, Unit<Quaternion<N>>>>>::Output

Performs the * operation.

impl<N> Mul<Similarity<N, U2, Unit<Complex<N>>>> for Unit<Complex<N>> where
    N: RealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Similarity<N, U2, Unit<Complex<N>>>

The resulting type after applying the * operator.

fn mul(
    self,
    rhs: Similarity<N, U2, Unit<Complex<N>>>
) -> <Unit<Complex<N>> as Mul<Similarity<N, U2, Unit<Complex<N>>>>>::Output

Performs the * operation.

impl<'b, N, D, R> Mul<&'b Similarity<N, D, R>> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, N, D, R> Mul<&'b Translation<N, D>> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, N, D, R> Mul<&'b Isometry<N, D, R>> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N, D> Mul<Similarity<N, D, Rotation<N, D>>> for &'a Rotation<N, D> where
    D: DimName,
    N: RealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: 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>>
) -> <&'a Rotation<N, D> as Mul<Similarity<N, D, Rotation<N, D>>>>::Output

Performs the * operation.

impl<'b, N, D, C, R> Mul<&'b Similarity<N, D, R>> for Transform<N, D, C> where
    C: TCategoryMul<TAffine>,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + RealField,
    R: SubsetOf<Matrix<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, U1>, 

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

The resulting type after applying the * operator.

fn mul(
    self,
    rhs: &'b Similarity<N, D, R>
) -> <Transform<N, D, C> as Mul<&'b Similarity<N, D, R>>>::Output

Performs the * operation.

impl<'a, 'b, N, D, R> Mul<&'b Similarity<N, D, R>> for &'a Isometry<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(
    self,
    rhs: &'b Similarity<N, D, R>
) -> <&'a Isometry<N, D, R> as Mul<&'b Similarity<N, D, R>>>::Output

Performs the * operation.

impl<'a, 'b, N, D> Mul<&'b Similarity<N, D, Rotation<N, D>>> for &'a Rotation<N, D> where
    D: DimName,
    N: RealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: 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>>
) -> <&'a Rotation<N, D> as Mul<&'b Similarity<N, D, Rotation<N, D>>>>::Output

Performs the * operation.

impl<'b, N> Mul<&'b Similarity<N, U3, Unit<Quaternion<N>>>> for Unit<Quaternion<N>> where
    N: RealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Similarity<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the * operator.

fn mul(
    self,
    right: &'b Similarity<N, U3, Unit<Quaternion<N>>>
) -> <Unit<Quaternion<N>> as Mul<&'b Similarity<N, U3, Unit<Quaternion<N>>>>>::Output

Performs the * operation.

impl<'a, N, D, R> Mul<Point<N, D>> for &'a Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Point<N, D>

The resulting type after applying the * operator.

fn mul(
    self,
    right: Point<N, D>
) -> <&'a Similarity<N, D, R> as Mul<Point<N, D>>>::Output

Performs the * operation.

impl<'a, 'b, N> Mul<&'b Similarity<N, U3, Unit<Quaternion<N>>>> for &'a Unit<Quaternion<N>> where
    N: RealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Similarity<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the * operator.

fn mul(
    self,
    right: &'b Similarity<N, U3, Unit<Quaternion<N>>>
) -> <&'a Unit<Quaternion<N>> as Mul<&'b Similarity<N, U3, Unit<Quaternion<N>>>>>::Output

Performs the * operation.

impl<'a, N, D, R> Mul<Isometry<N, D, R>> for &'a Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(
    self,
    rhs: Isometry<N, D, R>
) -> <&'a Similarity<N, D, R> as Mul<Isometry<N, D, R>>>::Output

Performs the * operation.

impl<'b, N, D, R> Mul<&'b Point<N, D>> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Point<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b, N, D, R> Mul<&'b Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>> for &'a Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>

The resulting type after applying the * operator.

fn mul(
    self,
    right: &'b Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>
) -> <&'a Similarity<N, D, R> as Mul<&'b Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>>::Output

Performs the * operation.

impl<N, D, R> Mul<Isometry<N, D, R>> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, N, D, R> Mul<&'b Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>

The resulting type after applying the * operator.

fn mul(
    self,
    right: &'b Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>
) -> <Similarity<N, D, R> as Mul<&'b Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>>::Output

Performs the * operation.

impl<'b, N, D, R> Mul<&'b R> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N, D, C, R> Mul<Similarity<N, D, R>> for Transform<N, D, C> where
    C: TCategoryMul<TAffine>,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + RealField,
    R: SubsetOf<Matrix<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, U1>, 

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

The resulting type after applying the * operator.

fn mul(
    self,
    rhs: Similarity<N, D, R>
) -> <Transform<N, D, C> as Mul<Similarity<N, D, R>>>::Output

Performs the * operation.

impl<N, D, C, R> Mul<Transform<N, D, C>> for Similarity<N, D, R> where
    C: TCategoryMul<TAffine>,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + RealField,
    R: SubsetOf<Matrix<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, <D as DimNameAdd<U1>>::Output>, 

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

The resulting type after applying the * operator.

fn mul(
    self,
    rhs: Transform<N, D, C>
) -> <Similarity<N, D, R> as Mul<Transform<N, D, C>>>::Output

Performs the * operation.

impl<'a, N, D, C, R> Mul<Similarity<N, D, R>> for &'a Transform<N, D, C> where
    C: TCategoryMul<TAffine>,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + RealField,
    R: SubsetOf<Matrix<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, U1>, 

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

The resulting type after applying the * operator.

fn mul(
    self,
    rhs: Similarity<N, D, R>
) -> <&'a Transform<N, D, C> as Mul<Similarity<N, D, R>>>::Output

Performs the * operation.

impl<'a, N> Mul<Similarity<N, U2, Unit<Complex<N>>>> for &'a Unit<Complex<N>> where
    N: RealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

type Output = Similarity<N, U2, Unit<Complex<N>>>

The resulting type after applying the * operator.

fn mul(
    self,
    rhs: Similarity<N, U2, Unit<Complex<N>>>
) -> <&'a Unit<Complex<N>> as Mul<Similarity<N, U2, Unit<Complex<N>>>>>::Output

Performs the * operation.

impl<N, D, R> Mul<Similarity<N, D, R>> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N, D, R> Mul<Similarity<N, D, R>> for &'a Isometry<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(
    self,
    rhs: Similarity<N, D, R>
) -> <&'a Isometry<N, D, R> as Mul<Similarity<N, D, R>>>::Output

Performs the * operation.

impl<N, D, R> Mul<Similarity<N, D, R>> for Translation<N, D> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b, N, D, C, R> Mul<&'b Similarity<N, D, R>> for &'a Transform<N, D, C> where
    C: TCategoryMul<TAffine>,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + RealField,
    R: SubsetOf<Matrix<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, U1>, 

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

The resulting type after applying the * operator.

fn mul(
    self,
    rhs: &'b Similarity<N, D, R>
) -> <&'a Transform<N, D, C> as Mul<&'b Similarity<N, D, R>>>::Output

Performs the * operation.

impl<'a, 'b, N, D, R> Mul<&'b Similarity<N, D, R>> for &'a Translation<N, D> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(
    self,
    right: &'b Similarity<N, D, R>
) -> <&'a Translation<N, D> as Mul<&'b Similarity<N, D, R>>>::Output

Performs the * operation.

impl<'b, N, D> Mul<&'b Similarity<N, D, Rotation<N, D>>> for Rotation<N, D> where
    D: DimName,
    N: RealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: 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>>
) -> <Rotation<N, D> as Mul<&'b Similarity<N, D, Rotation<N, D>>>>::Output

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, N, D, R> Mul<&'b Similarity<N, D, R>> for Translation<N, D> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b, N, D, R> Mul<&'b Isometry<N, D, R>> for &'a Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

fn mul(
    self,
    rhs: &'b Isometry<N, D, R>
) -> <&'a Similarity<N, D, R> as Mul<&'b Isometry<N, D, R>>>::Output

Performs the * operation.

impl<N, D, R> UlpsEq<Similarity<N, D, R>> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>> + UlpsEq<R, Epsilon = <N as AbsDiffEq<N>>::Epsilon>,
    DefaultAllocator: Allocator<N, D, U1>,
    <N as AbsDiffEq<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: &Similarity<N, D, R>,
    epsilon: <Similarity<N, D, R> as AbsDiffEq<Similarity<N, D, R>>>::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: &Rhs, epsilon: Self::Epsilon, max_ulps: u32) -> bool

The inverse of ApproxEq::ulps_eq.

impl<N, D, R> Div<Isometry<N, D, R>> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'b, N, D, R> Div<&'b Isometry<N, D, R>> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, N, D> Div<Similarity<N, D, Rotation<N, D>>> for &'a Rotation<N, D> where
    D: DimName,
    N: RealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: 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>>
) -> <&'a Rotation<N, D> as Div<Similarity<N, D, Rotation<N, D>>>>::Output

Performs the / operation.

impl<'a, N, D, R> Div<Similarity<N, D, R>> for &'a Isometry<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

fn div(
    self,
    rhs: Similarity<N, D, R>
) -> <&'a Isometry<N, D, R> as Div<Similarity<N, D, R>>>::Output

Performs the / operation.

impl<N, D> Div<Similarity<N, D, Rotation<N, D>>> for Rotation<N, D> where
    D: DimName,
    N: RealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: 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>>
) -> <Rotation<N, D> as Div<Similarity<N, D, Rotation<N, D>>>>::Output

Performs the / operation.

impl<'a, N, D, R> Div<R> for &'a Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

fn div(self, rhs: R) -> <&'a Similarity<N, D, R> as Div<R>>::Output

Performs the / operation.

impl<'a, N> Div<Similarity<N, U3, Unit<Quaternion<N>>>> for &'a Unit<Quaternion<N>> where
    N: RealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Similarity<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the / operator.

fn div(
    self,
    right: Similarity<N, U3, Unit<Quaternion<N>>>
) -> <&'a Unit<Quaternion<N>> as Div<Similarity<N, U3, Unit<Quaternion<N>>>>>::Output

Performs the / operation.

impl<N, D, R> Div<R> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, 'b, N, D, R> Div<&'b Similarity<N, D, R>> for &'a Isometry<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

fn div(
    self,
    rhs: &'b Similarity<N, D, R>
) -> <&'a Isometry<N, D, R> as Div<&'b Similarity<N, D, R>>>::Output

Performs the / operation.

impl<'b, N> Div<&'b Similarity<N, U3, Unit<Quaternion<N>>>> for Unit<Quaternion<N>> where
    N: RealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Similarity<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the / operator.

fn div(
    self,
    right: &'b Similarity<N, U3, Unit<Quaternion<N>>>
) -> <Unit<Quaternion<N>> as Div<&'b Similarity<N, U3, Unit<Quaternion<N>>>>>::Output

Performs the / operation.

impl<'a, N, D, R> Div<Similarity<N, D, R>> for &'a Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

fn div(
    self,
    rhs: Similarity<N, D, R>
) -> <&'a Similarity<N, D, R> as Div<Similarity<N, D, R>>>::Output

Performs the / operation.

impl<'b, N, D> Div<&'b Similarity<N, D, Rotation<N, D>>> for Rotation<N, D> where
    D: DimName,
    N: RealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: 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>>
) -> <Rotation<N, D> as Div<&'b Similarity<N, D, Rotation<N, D>>>>::Output

Performs the / operation.

impl<'b, N, D, R> Div<&'b Similarity<N, D, R>> for Isometry<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<N, D, R> Div<Similarity<N, D, R>> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, 'b, N, D> Div<&'b Similarity<N, D, Rotation<N, D>>> for &'a Rotation<N, D> where
    D: DimName,
    N: RealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: 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>>
) -> <&'a Rotation<N, D> as Div<&'b Similarity<N, D, Rotation<N, D>>>>::Output

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'b, N, D, R> Div<&'b R> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, 'b, N> Div<&'b Similarity<N, U3, Unit<Quaternion<N>>>> for &'a Unit<Quaternion<N>> where
    N: RealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Similarity<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the / operator.

fn div(
    self,
    right: &'b Similarity<N, U3, Unit<Quaternion<N>>>
) -> <&'a Unit<Quaternion<N>> as Div<&'b Similarity<N, U3, Unit<Quaternion<N>>>>>::Output

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<N, D, R> Div<Similarity<N, D, R>> for Isometry<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, 'b, N, D, R> Div<&'b Isometry<N, D, R>> for &'a Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

fn div(
    self,
    rhs: &'b Isometry<N, D, R>
) -> <&'a Similarity<N, D, R> as Div<&'b Isometry<N, D, R>>>::Output

Performs the / operation.

impl<'a, N, D, R> Div<Isometry<N, D, R>> for &'a Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

fn div(
    self,
    rhs: Isometry<N, D, R>
) -> <&'a Similarity<N, D, R> as Div<Isometry<N, D, R>>>::Output

Performs the / operation.

impl<N> Div<Similarity<N, U3, Unit<Quaternion<N>>>> for Unit<Quaternion<N>> where
    N: RealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

type Output = Similarity<N, U3, Unit<Quaternion<N>>>

The resulting type after applying the / operator.

fn div(
    self,
    right: Similarity<N, U3, Unit<Quaternion<N>>>
) -> <Unit<Quaternion<N>> as Div<Similarity<N, U3, Unit<Quaternion<N>>>>>::Output

Performs the / operation.

impl<'b, N, D, R> Div<&'b Similarity<N, D, R>> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<N, D, R> Copy for Similarity<N, D, R> where
    D: DimName + Copy,
    N: RealField,
    R: Copy + Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>,
    <DefaultAllocator as Allocator<N, D, U1>>::Buffer: Copy, 

impl<N, D, R> ProjectiveTransformation<Point<N, D>> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

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

fn inverse_transform_vector(
    &self,
    v: &Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>
) -> Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>

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

impl<N, D, R> AbsDiffEq<Similarity<N, D, R>> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>> + AbsDiffEq<R, Epsilon = <N as AbsDiffEq<N>>::Epsilon>,
    DefaultAllocator: Allocator<N, D, U1>,
    <N as AbsDiffEq<N>>::Epsilon: Copy, 

type Epsilon = <N as AbsDiffEq<N>>::Epsilon

Used for specifying relative comparisons.

fn default_epsilon(
) -> <Similarity<N, D, R> as AbsDiffEq<Similarity<N, D, R>>>::Epsilon

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

fn abs_diff_eq(
    &self,
    other: &Similarity<N, D, R>,
    epsilon: <Similarity<N, D, R> as AbsDiffEq<Similarity<N, D, R>>>::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: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of ApproxEq::abs_diff_eq.

impl<N, D, R> AbstractMagma<Multiplicative> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

fn operate(&self, rhs: &Similarity<N, D, R>) -> Similarity<N, D, R>

Performs an operation.

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

Performs specific operation.

impl<N, D, R> Identity<Multiplicative> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>, 

fn identity() -> Similarity<N, D, R>

The identity element.

fn id(O) -> Self

Specific identity.

impl<N, D, R> AbstractLoop<Multiplicative> for Similarity<N, D, R> where
    D: DimName,
    N: RealField,
    R: Rotation<Point<N, D>>,
    DefaultAllocator: Allocator<N, D, U1>,