Similarity in nalgebra::geometry - Rust
Description: A similarity, i.e., an uniform scaling, followed by a rotation, followed by a translation.
Keywords: rust, rustlang, rust-lang, Similarity

# Struct nalgebra::geometry::Similarity

source ·

    #[repr(C)]pub struct Similarity<T, R, const D: usize> {
        pub isometry: Isometry<T, R, D>,
        /* private fields */
    }

Expand description

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

## Fields§

§`isometry: Isometry<T, R, D>`

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

## Implementations§

source§

### impl<T: Scalar + Zero, R, const D: usize> Similarity<T, R, D>where
R: AbstractRotation<T, D>,

source

#### pub fn from_parts(translation: Translation<T, D>, rotation: R, scaling: T) -> Self

Creates a new similarity from its rotational and translational parts.

source

#### pub fn from_isometry(isometry: Isometry<T, R, D>, scaling: T) -> Self

Creates a new similarity from its rotational and translational parts.

source

#### pub fn set_scaling(&mut self, scaling: T)

The scaling factor of this similarity transformation.

source§

### impl<T: Scalar, R, const D: usize> Similarity<T, R, D>

source

#### pub fn scaling(&self) -> T

The scaling factor of this similarity transformation.

source§

### impl<T: SimdRealField, R, const D: usize> Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

source

#### pub fn from_scaling(scaling: T) -> Self

Creates a new similarity that applies only a scaling factor.

source

#### pub fn inverse(&self) -> Self

Inverts `self`.

source

#### pub fn inverse_mut(&mut self)

Inverts `self` in-place.

source

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

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

source

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

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

source

#### pub fn prepend_scaling_mut(&mut self, scaling: T)

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

source

#### pub fn append_scaling_mut(&mut self, scaling: T)

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

source

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

Appends to `self` the given translation in-place.

source

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

Appends to `self` the given rotation in-place.

source

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

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

source

#### 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`.

source

#### pub fn transform_point(&self, pt: &Point<T, D>) -> Point<T, 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);

source

#### pub fn transform_vector(&self, v: &SVector<T, D>) -> SVector<T, D>

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);

source

#### pub fn inverse_transform_point(&self, pt: &Point<T, D>) -> Point<T, 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);

source

#### pub fn inverse_transform_vector(&self, v: &SVector<T, D>) -> SVector<T, D>

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);

source§

### impl<T: SimdRealField, R, const D: usize> Similarity<T, R, D>

source

#### pub fn to_homogeneous(
&self
) -> OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>where
Const<D>: DimNameAdd<U1>,
R: SubsetOf<OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

Converts this similarity into its equivalent homogeneous transformation matrix.

source§

### impl<T: SimdRealField, R, const D: usize> Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

source

#### pub fn identity() -> Self

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);

source§

### impl<T: SimdRealField, R, const D: usize> Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

source

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

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);

source§

### impl<T: SimdRealField> Similarity<T, Rotation2<T>, 2>where
T::Element: SimdRealField,

source

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

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);

source

#### pub fn cast<To: Scalar>(self) -> Similarity<To, Rotation2<To>, 2>where
Similarity<To, Rotation2<To>, 2>: SupersetOf<Self>,

Cast the components of `self` to another type.

##### Example

    let sim = SimilarityMatrix2::<f64>::identity();
    let sim2 = sim.cast::<f32>();
    assert_eq!(sim2, SimilarityMatrix2::<f32>::identity());

source§

### impl<T: SimdRealField> Similarity<T, UnitComplex<T>, 2>where
T::Element: SimdRealField,

source

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

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);

source

#### pub fn cast<To: Scalar>(self) -> Similarity<To, UnitComplex<To>, 2>where
Similarity<To, UnitComplex<To>, 2>: SupersetOf<Self>,

Cast the components of `self` to another type.

##### Example

    let sim = Similarity2::<f64>::identity();
    let sim2 = sim.cast::<f32>();
    assert_eq!(sim2, Similarity2::<f32>::identity());

source§

### impl<T: SimdRealField> Similarity<T, Rotation3<T>, { _ }>where
T::Element: SimdRealField,

source

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

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);

source

#### pub fn cast<To: Scalar>(self) -> Similarity<To, Rotation3<To>, { _ }>where
Similarity<To, Rotation3<To>, { _ }>: SupersetOf<Self>,

Cast the components of `self` to another type.

##### Example

    let sim = Similarity3::<f64>::identity();
    let sim2 = sim.cast::<f32>();
    assert_eq!(sim2, Similarity3::<f32>::identity());

source

#### pub fn face_towards(
eye: &Point3<T>,
target: &Point3<T>,
up: &Vector3<T>,
scaling: T
) -> Self

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);

source

#### pub fn new_observer_frames(
eye: &Point3<T>,
target: &Point3<T>,
up: &Vector3<T>,
scaling: T
) -> Self

👎Deprecated: renamed to `face_towards`

Deprecated: Use `SimilarityMatrix3::face_towards` instead.

source

#### pub fn look_at_rh(
eye: &Point3<T>,
target: &Point3<T>,
up: &Vector3<T>,
scaling: T
) -> 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`.

##### 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);

source

#### pub fn look_at_lh(
eye: &Point3<T>,
target: &Point3<T>,
up: &Vector3<T>,
scaling: T
) -> 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`.

##### 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);

source§

### impl<T: SimdRealField> Similarity<T, UnitQuaternion<T>, { _ }>where
T::Element: SimdRealField,

source

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

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);

source

#### pub fn cast<To: Scalar>(self) -> Similarity<To, UnitQuaternion<To>, { _ }>where
Similarity<To, UnitQuaternion<To>, { _ }>: SupersetOf<Self>,

Cast the components of `self` to another type.

##### Example

    let sim = Similarity3::<f64>::identity();
    let sim2 = sim.cast::<f32>();
    assert_eq!(sim2, Similarity3::<f32>::identity());

source

#### pub fn face_towards(
eye: &Point3<T>,
target: &Point3<T>,
up: &Vector3<T>,
scaling: T
) -> Self

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);

source

#### pub fn new_observer_frames(
eye: &Point3<T>,
target: &Point3<T>,
up: &Vector3<T>,
scaling: T
) -> Self

👎Deprecated: renamed to `face_towards`

Deprecated: Use `SimilarityMatrix3::face_towards` instead.

source

#### pub fn look_at_rh(
eye: &Point3<T>,
target: &Point3<T>,
up: &Vector3<T>,
scaling: T
) -> 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`.

##### 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);

source

#### pub fn look_at_lh(
eye: &Point3<T>,
target: &Point3<T>,
up: &Vector3<T>,
scaling: T
) -> 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`.

##### 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§

source§

### impl<T: RealField, R, const D: usize> AbsDiffEq<Similarity<T, R, D>> for Similarity<T, R, D>where
R: AbstractRotation<T, D> + AbsDiffEq<Epsilon = T::Epsilon>,
T::Epsilon: Clone,

§

#### type Epsilon = <T as AbsDiffEq<T>>::Epsilon

Used for specifying relative comparisons.
source§

#### fn default_epsilon() -> Self::Epsilon

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

#### 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. Read more
source§

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

The inverse of `AbsDiffEq::abs_diff_eq`.
source§

### impl<T: Clone, R: Clone, const D: usize> Clone for Similarity<T, R, D>

source§

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

Returns a copy of the value. Read more
1.0.0 · source§

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

Performs copy-assignment from `source`. Read more
source§

### impl<T: Debug, R: Debug, const D: usize> Debug for Similarity<T, R, D>

source§

#### fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter. Read more
source§

### impl<T: SimdRealField, R, const D: usize> Default for Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

source§

#### fn default() -> Self

Returns the “default value” for a type. Read more
source§

### impl<T, R, const D: usize> Display for Similarity<T, R, D>where
T: RealField + Display,
R: AbstractRotation<T, D> + Display,

source§

#### fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter. Read more
source§

### impl<'a, 'b, T: SimdRealField, R, const D: usize> Div<&'b Isometry<T, R, D>> for &'a Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Similarity<T, R, D>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: &'b Isometry<T, R, D>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'b, T: SimdRealField, R, const D: usize> Div<&'b Isometry<T, R, D>> for Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Similarity<T, R, D>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: &'b Isometry<T, R, D>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'a, 'b, T: SimdRealField, const D: usize> Div<&'b Rotation<T, D>> for &'a Similarity<T, Rotation<T, D>, D>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Rotation<T, D>, D>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: &'b Rotation<T, D>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'b, T: SimdRealField, const D: usize> Div<&'b Rotation<T, D>> for Similarity<T, Rotation<T, D>, D>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Rotation<T, D>, D>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: &'b Rotation<T, D>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'a, 'b, T: SimdRealField, R, const D: usize> Div<&'b Similarity<T, R, D>> for &'a Isometry<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Similarity<T, R, D>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: &'b Similarity<T, R, D>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'a, 'b, T: SimdRealField, R, const D: usize> Div<&'b Similarity<T, R, D>> for &'a Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Similarity<T, R, D>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: &'b Similarity<T, R, D>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'b, T: SimdRealField, R, const D: usize> Div<&'b Similarity<T, R, D>> for Isometry<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Similarity<T, R, D>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: &'b Similarity<T, R, D>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'b, T: SimdRealField, R, const D: usize> Div<&'b Similarity<T, R, D>> for Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Similarity<T, R, D>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: &'b Similarity<T, R, D>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'a, 'b, T: SimdRealField, const D: usize> Div<&'b Similarity<T, Rotation<T, D>, D>> for &'a Rotation<T, D>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Rotation<T, D>, D>

The resulting type after applying the `/` operator.
source§

#### fn div(self, right: &'b Similarity<T, Rotation<T, D>, D>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'b, T: SimdRealField, const D: usize> Div<&'b Similarity<T, Rotation<T, D>, D>> for Rotation<T, D>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Rotation<T, D>, D>

The resulting type after applying the `/` operator.
source§

#### fn div(self, right: &'b Similarity<T, Rotation<T, D>, D>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'a, 'b, T: SimdRealField> Div<&'b Similarity<T, Unit<Quaternion<T>>, 3>> for &'a UnitQuaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `/` operator.
source§

#### fn div(self, right: &'b Similarity<T, UnitQuaternion<T>, 3>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'b, T: SimdRealField> Div<&'b Similarity<T, Unit<Quaternion<T>>, 3>> for UnitQuaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `/` operator.
source§

#### fn div(self, right: &'b Similarity<T, UnitQuaternion<T>, 3>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for &'a Similarity<T, UnitComplex<T>, 2>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Complex<T>>, 2>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Complex<T>>, 2>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for &'a Similarity<T, UnitQuaternion<T>, 3>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'a, T: SimdRealField, R, const D: usize> Div<Isometry<T, R, D>> for &'a Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Similarity<T, R, D>

The resulting type after applying the `/` operator.
source§

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

Performs the `/` operation. Read more
source§

### impl<T: SimdRealField, R, const D: usize> Div<Isometry<T, R, D>> for Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Similarity<T, R, D>

The resulting type after applying the `/` operator.
source§

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

Performs the `/` operation. Read more
source§

### impl<'a, T: SimdRealField, const D: usize> Div<Rotation<T, D>> for &'a Similarity<T, Rotation<T, D>, D>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Rotation<T, D>, D>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: Rotation<T, D>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<T: SimdRealField, const D: usize> Div<Rotation<T, D>> for Similarity<T, Rotation<T, D>, D>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Rotation<T, D>, D>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: Rotation<T, D>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'a, T: SimdRealField, R, const D: usize> Div<Similarity<T, R, D>> for &'a Isometry<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Similarity<T, R, D>

The resulting type after applying the `/` operator.
source§

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

Performs the `/` operation. Read more
source§

### impl<'a, T: SimdRealField, R, const D: usize> Div<Similarity<T, R, D>> for &'a Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Similarity<T, R, D>

The resulting type after applying the `/` operator.
source§

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

Performs the `/` operation. Read more
source§

### impl<T: SimdRealField, R, const D: usize> Div<Similarity<T, R, D>> for Isometry<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Similarity<T, R, D>

The resulting type after applying the `/` operator.
source§

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

Performs the `/` operation. Read more
source§

### impl<T: SimdRealField, R, const D: usize> Div<Similarity<T, R, D>> for Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Similarity<T, R, D>

The resulting type after applying the `/` operator.
source§

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

Performs the `/` operation. Read more
source§

### impl<'a, T: SimdRealField, const D: usize> Div<Similarity<T, Rotation<T, D>, D>> for &'a Rotation<T, D>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Rotation<T, D>, D>

The resulting type after applying the `/` operator.
source§

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

Performs the `/` operation. Read more
source§

### impl<T: SimdRealField, const D: usize> Div<Similarity<T, Rotation<T, D>, D>> for Rotation<T, D>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Rotation<T, D>, D>

The resulting type after applying the `/` operator.
source§

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

Performs the `/` operation. Read more
source§

### impl<'a, T: SimdRealField> Div<Similarity<T, Unit<Quaternion<T>>, 3>> for &'a UnitQuaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `/` operator.
source§

#### fn div(self, right: Similarity<T, UnitQuaternion<T>, 3>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<T: SimdRealField> Div<Similarity<T, Unit<Quaternion<T>>, 3>> for UnitQuaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `/` operator.
source§

#### fn div(self, right: Similarity<T, UnitQuaternion<T>, 3>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'a, T: SimdRealField> Div<Unit<Complex<T>>> for &'a Similarity<T, UnitComplex<T>, 2>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Complex<T>>, 2>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitComplex<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<T: SimdRealField> Div<Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Complex<T>>, 2>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitComplex<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'a, T: SimdRealField> Div<Unit<Quaternion<T>>> for &'a Similarity<T, UnitQuaternion<T>, 3>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<T: SimdRealField> Div<Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `/` operator.
source§

#### fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the `/` operation. Read more
source§

### impl<'b, T: SimdRealField, R, const D: usize> DivAssign<&'b Isometry<T, R, D>> for Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

source§

#### fn div_assign(&mut self, rhs: &'b Isometry<T, R, D>)

Performs the `/=` operation. Read more
source§

### impl<'b, T, const D: usize> DivAssign<&'b Rotation<T, D>> for Similarity<T, Rotation<T, D>, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

source§

#### fn div_assign(&mut self, rhs: &'b Rotation<T, D>)

Performs the `/=` operation. Read more
source§

### impl<'b, T: SimdRealField, R, const D: usize> DivAssign<&'b Similarity<T, R, D>> for Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

source§

#### fn div_assign(&mut self, rhs: &'b Similarity<T, R, D>)

Performs the `/=` operation. Read more
source§

### impl<'b, T> DivAssign<&'b Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

source§

#### fn div_assign(&mut self, rhs: &'b UnitComplex<T>)

Performs the `/=` operation. Read more
source§

### impl<'b, T> DivAssign<&'b Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

source§

#### fn div_assign(&mut self, rhs: &'b UnitQuaternion<T>)

Performs the `/=` operation. Read more
source§

### impl<T: SimdRealField, R, const D: usize> DivAssign<Isometry<T, R, D>> for Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

source§

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

Performs the `/=` operation. Read more
source§

### impl<T, const D: usize> DivAssign<Rotation<T, D>> for Similarity<T, Rotation<T, D>, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

source§

#### fn div_assign(&mut self, rhs: Rotation<T, D>)

Performs the `/=` operation. Read more
source§

### impl<T: SimdRealField, R, const D: usize> DivAssign<Similarity<T, R, D>> for Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

source§

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

Performs the `/=` operation. Read more
source§

### impl<T> DivAssign<Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

source§

#### fn div_assign(&mut self, rhs: UnitComplex<T>)

Performs the `/=` operation. Read more
source§

### impl<T> DivAssign<Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

source§

#### fn div_assign(&mut self, rhs: UnitQuaternion<T>)

Performs the `/=` operation. Read more
source§

### impl<T, R, const D: usize> From<[Similarity<<T as SimdValue>::Element, <R as SimdValue>::Element, D>; 16]> for Similarity<T, R, D>where
T: From<[<T as SimdValue>::Element; 16]> + Scalar + Zero + PrimitiveSimdValue,
R: SimdValue + AbstractRotation<T, D> + From<[<R as SimdValue>::Element; 16]>,
R::Element: AbstractRotation<T::Element, D> + Scalar + Zero + Copy,
T::Element: Scalar + Zero + Copy,

source§

#### fn from(arr: [Similarity<T::Element, R::Element, D>; 16]) -> Self

Converts to this type from the input type.
source§

### impl<T, R, const D: usize> From<[Similarity<<T as SimdValue>::Element, <R as SimdValue>::Element, D>; 2]> for Similarity<T, R, D>where
T: From<[<T as SimdValue>::Element; 2]> + Scalar + Zero + PrimitiveSimdValue,
R: SimdValue + AbstractRotation<T, D> + From<[<R as SimdValue>::Element; 2]>,
R::Element: AbstractRotation<T::Element, D> + Scalar + Zero + Copy,
T::Element: Scalar + Zero + Copy,

source§

#### fn from(arr: [Similarity<T::Element, R::Element, D>; 2]) -> Self

Converts to this type from the input type.
source§

### impl<T, R, const D: usize> From<[Similarity<<T as SimdValue>::Element, <R as SimdValue>::Element, D>; 4]> for Similarity<T, R, D>where
T: From<[<T as SimdValue>::Element; 4]> + Scalar + Zero + PrimitiveSimdValue,
R: SimdValue + AbstractRotation<T, D> + From<[<R as SimdValue>::Element; 4]>,
R::Element: AbstractRotation<T::Element, D> + Scalar + Zero + Copy,
T::Element: Scalar + Zero + Copy,

source§

#### fn from(arr: [Similarity<T::Element, R::Element, D>; 4]) -> Self

Converts to this type from the input type.
source§

### impl<T, R, const D: usize> From<[Similarity<<T as SimdValue>::Element, <R as SimdValue>::Element, D>; 8]> for Similarity<T, R, D>where
T: From<[<T as SimdValue>::Element; 8]> + Scalar + Zero + PrimitiveSimdValue,
R: SimdValue + AbstractRotation<T, D> + From<[<R as SimdValue>::Element; 8]>,
R::Element: AbstractRotation<T::Element, D> + Scalar + Zero + Copy,
T::Element: Scalar + Zero + Copy,

source§

#### fn from(arr: [Similarity<T::Element, R::Element, D>; 8]) -> Self

Converts to this type from the input type.
source§

### impl<T: SimdRealField, R, const D: usize> From<Similarity<T, R, D>> for OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>where
Const<D>: DimNameAdd<U1>,
R: SubsetOf<OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

source§

#### fn from(sim: Similarity<T, R, D>) -> Self

Converts to this type from the input type.
source§

### impl<T: Scalar + Hash, R: Hash, const D: usize> Hash for Similarity<T, R, D>where
Owned<T, Const<D>>: Hash,

source§

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

Feeds this value into the given `Hasher`. Read more
1.3.0 · source§

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

Feeds a slice of this type into the given `Hasher`. Read more
source§

### impl<'a, 'b, T: SimdRealField, R, const D: usize> Mul<&'b Isometry<T, R, D>> for &'a Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Similarity<T, R, D>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: &'b Isometry<T, R, D>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'b, T: SimdRealField, R, const D: usize> Mul<&'b Isometry<T, R, D>> for Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Similarity<T, R, D>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: &'b Isometry<T, R, D>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'a, 'b, T: SimdRealField, R, const D: usize> Mul<&'b Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for &'a Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, right: &'b SVector<T, D>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'b, T: SimdRealField, R, const D: usize> Mul<&'b Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, right: &'b SVector<T, D>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'a, 'b, T: SimdRealField, R, const D: usize> Mul<&'b OPoint<T, Const<D>>> for &'a Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = OPoint<T, Const<D>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, right: &'b Point<T, D>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'b, T: SimdRealField, R, const D: usize> Mul<&'b OPoint<T, Const<D>>> for Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = OPoint<T, Const<D>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, right: &'b Point<T, D>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'a, 'b, T: SimdRealField, const D: usize> Mul<&'b Rotation<T, D>> for &'a Similarity<T, Rotation<T, D>, D>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Rotation<T, D>, D>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: &'b Rotation<T, D>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'b, T: SimdRealField, const D: usize> Mul<&'b Rotation<T, D>> for Similarity<T, Rotation<T, D>, D>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Rotation<T, D>, D>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: &'b Rotation<T, D>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'a, 'b, T: SimdRealField, R, const D: usize> Mul<&'b Similarity<T, R, D>> for &'a Isometry<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Similarity<T, R, D>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: &'b Similarity<T, R, D>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'a, 'b, T: SimdRealField, R, const D: usize> Mul<&'b Similarity<T, R, D>> for &'a Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Similarity<T, R, D>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: &'b Similarity<T, R, D>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'a, 'b, T, C, R, const D: usize> Mul<&'b Similarity<T, R, D>> for &'a Transform<T, C, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
R: SubsetOf<OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

§

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

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: &'b Similarity<T, R, D>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'a, 'b, T: SimdRealField, R, const D: usize> Mul<&'b Similarity<T, R, D>> for &'a Translation<T, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Similarity<T, R, D>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, right: &'b Similarity<T, R, D>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'b, T: SimdRealField, R, const D: usize> Mul<&'b Similarity<T, R, D>> for Isometry<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Similarity<T, R, D>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: &'b Similarity<T, R, D>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'b, T: SimdRealField, R, const D: usize> Mul<&'b Similarity<T, R, D>> for Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Similarity<T, R, D>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: &'b Similarity<T, R, D>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'b, T, C, R, const D: usize> Mul<&'b Similarity<T, R, D>> for Transform<T, C, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
R: SubsetOf<OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

§

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

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: &'b Similarity<T, R, D>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'b, T: SimdRealField, R, const D: usize> Mul<&'b Similarity<T, R, D>> for Translation<T, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Similarity<T, R, D>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, right: &'b Similarity<T, R, D>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'a, 'b, T: SimdRealField, const D: usize> Mul<&'b Similarity<T, Rotation<T, D>, D>> for &'a Rotation<T, D>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Rotation<T, D>, D>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, right: &'b Similarity<T, Rotation<T, D>, D>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'b, T: SimdRealField, const D: usize> Mul<&'b Similarity<T, Rotation<T, D>, D>> for Rotation<T, D>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Rotation<T, D>, D>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, right: &'b Similarity<T, Rotation<T, D>, D>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'a, 'b, T: SimdRealField> Mul<&'b Similarity<T, Unit<Complex<T>>, 2>> for &'a UnitComplex<T>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Complex<T>>, 2>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: &'b Similarity<T, UnitComplex<T>, 2>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'b, T: SimdRealField> Mul<&'b Similarity<T, Unit<Complex<T>>, 2>> for UnitComplex<T>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Complex<T>>, 2>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: &'b Similarity<T, UnitComplex<T>, 2>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'a, 'b, T: SimdRealField> Mul<&'b Similarity<T, Unit<Quaternion<T>>, 3>> for &'a UnitQuaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, right: &'b Similarity<T, UnitQuaternion<T>, 3>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'b, T: SimdRealField> Mul<&'b Similarity<T, Unit<Quaternion<T>>, 3>> for UnitQuaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, right: &'b Similarity<T, UnitQuaternion<T>, 3>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'a, 'b, T, C, R, const D: usize> Mul<&'b Transform<T, C, D>> for &'a Similarity<T, R, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
R: SubsetOf<OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

§

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

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: &'b Transform<T, C, D>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'b, T, C, R, const D: usize> Mul<&'b Transform<T, C, D>> for Similarity<T, R, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
R: SubsetOf<OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

§

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

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: &'b Transform<T, C, D>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'a, 'b, T: SimdRealField, R, const D: usize> Mul<&'b Translation<T, D>> for &'a Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Similarity<T, R, D>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, right: &'b Translation<T, D>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'b, T: SimdRealField, R, const D: usize> Mul<&'b Translation<T, D>> for Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Similarity<T, R, D>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, right: &'b Translation<T, D>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for &'a Similarity<T, UnitComplex<T>, 2>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Complex<T>>, 2>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Complex<T>>, 2>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for &'a Similarity<T, UnitQuaternion<T>, 3>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'a, T: SimdRealField, R, const D: usize> Mul<Isometry<T, R, D>> for &'a Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Similarity<T, R, D>

The resulting type after applying the `*` operator.
source§

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

Performs the `*` operation. Read more
source§

### impl<T: SimdRealField, R, const D: usize> Mul<Isometry<T, R, D>> for Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Similarity<T, R, D>

The resulting type after applying the `*` operator.
source§

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

Performs the `*` operation. Read more
source§

### impl<'a, T: SimdRealField, R, const D: usize> Mul<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for &'a Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, right: SVector<T, D>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<T: SimdRealField, R, const D: usize> Mul<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, right: SVector<T, D>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'a, T: SimdRealField, R, const D: usize> Mul<OPoint<T, Const<D>>> for &'a Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = OPoint<T, Const<D>>

The resulting type after applying the `*` operator.
source§

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

Performs the `*` operation. Read more
source§

### impl<T: SimdRealField, R, const D: usize> Mul<OPoint<T, Const<D>>> for Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = OPoint<T, Const<D>>

The resulting type after applying the `*` operator.
source§

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

Performs the `*` operation. Read more
source§

### impl<'a, T: SimdRealField, const D: usize> Mul<Rotation<T, D>> for &'a Similarity<T, Rotation<T, D>, D>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Rotation<T, D>, D>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: Rotation<T, D>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<T: SimdRealField, const D: usize> Mul<Rotation<T, D>> for Similarity<T, Rotation<T, D>, D>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Rotation<T, D>, D>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: Rotation<T, D>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'a, T: SimdRealField, R, const D: usize> Mul<Similarity<T, R, D>> for &'a Isometry<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Similarity<T, R, D>

The resulting type after applying the `*` operator.
source§

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

Performs the `*` operation. Read more
source§

### impl<'a, T: SimdRealField, R, const D: usize> Mul<Similarity<T, R, D>> for &'a Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Similarity<T, R, D>

The resulting type after applying the `*` operator.
source§

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

Performs the `*` operation. Read more
source§

### impl<'a, T, C, R, const D: usize> Mul<Similarity<T, R, D>> for &'a Transform<T, C, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
R: SubsetOf<OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

§

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

The resulting type after applying the `*` operator.
source§

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

Performs the `*` operation. Read more
source§

### impl<'a, T: SimdRealField, R, const D: usize> Mul<Similarity<T, R, D>> for &'a Translation<T, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Similarity<T, R, D>

The resulting type after applying the `*` operator.
source§

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

Performs the `*` operation. Read more
source§

### impl<T: SimdRealField, R, const D: usize> Mul<Similarity<T, R, D>> for Isometry<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Similarity<T, R, D>

The resulting type after applying the `*` operator.
source§

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

Performs the `*` operation. Read more
source§

### impl<T: SimdRealField, R, const D: usize> Mul<Similarity<T, R, D>> for Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Similarity<T, R, D>

The resulting type after applying the `*` operator.
source§

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

Performs the `*` operation. Read more
source§

### impl<T, C, R, const D: usize> Mul<Similarity<T, R, D>> for Transform<T, C, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
R: SubsetOf<OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

§

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

The resulting type after applying the `*` operator.
source§

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

Performs the `*` operation. Read more
source§

### impl<T: SimdRealField, R, const D: usize> Mul<Similarity<T, R, D>> for Translation<T, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Similarity<T, R, D>

The resulting type after applying the `*` operator.
source§

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

Performs the `*` operation. Read more
source§

### impl<'a, T: SimdRealField, const D: usize> Mul<Similarity<T, Rotation<T, D>, D>> for &'a Rotation<T, D>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Rotation<T, D>, D>

The resulting type after applying the `*` operator.
source§

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

Performs the `*` operation. Read more
source§

### impl<T: SimdRealField, const D: usize> Mul<Similarity<T, Rotation<T, D>, D>> for Rotation<T, D>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Rotation<T, D>, D>

The resulting type after applying the `*` operator.
source§

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

Performs the `*` operation. Read more
source§

### impl<'a, T: SimdRealField> Mul<Similarity<T, Unit<Complex<T>>, 2>> for &'a UnitComplex<T>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Complex<T>>, 2>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: Similarity<T, UnitComplex<T>, 2>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<T: SimdRealField> Mul<Similarity<T, Unit<Complex<T>>, 2>> for UnitComplex<T>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Complex<T>>, 2>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: Similarity<T, UnitComplex<T>, 2>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'a, T: SimdRealField> Mul<Similarity<T, Unit<Quaternion<T>>, 3>> for &'a UnitQuaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, right: Similarity<T, UnitQuaternion<T>, 3>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<T: SimdRealField> Mul<Similarity<T, Unit<Quaternion<T>>, 3>> for UnitQuaternion<T>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, right: Similarity<T, UnitQuaternion<T>, 3>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'a, T, C, R, const D: usize> Mul<Transform<T, C, D>> for &'a Similarity<T, R, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
R: SubsetOf<OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

§

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

The resulting type after applying the `*` operator.
source§

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

Performs the `*` operation. Read more
source§

### impl<T, C, R, const D: usize> Mul<Transform<T, C, D>> for Similarity<T, R, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategoryMul<TAffine>,
R: SubsetOf<OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

§

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

The resulting type after applying the `*` operator.
source§

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

Performs the `*` operation. Read more
source§

### impl<'a, T: SimdRealField, R, const D: usize> Mul<Translation<T, D>> for &'a Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Similarity<T, R, D>

The resulting type after applying the `*` operator.
source§

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

Performs the `*` operation. Read more
source§

### impl<T: SimdRealField, R, const D: usize> Mul<Translation<T, D>> for Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

§

#### type Output = Similarity<T, R, D>

The resulting type after applying the `*` operator.
source§

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

Performs the `*` operation. Read more
source§

### impl<'a, T: SimdRealField> Mul<Unit<Complex<T>>> for &'a Similarity<T, UnitComplex<T>, 2>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Complex<T>>, 2>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<T: SimdRealField> Mul<Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Complex<T>>, 2>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'a, T: SimdRealField> Mul<Unit<Quaternion<T>>> for &'a Similarity<T, UnitQuaternion<T>, 3>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<T: SimdRealField> Mul<Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>where
T::Element: SimdRealField,

§

#### type Output = Similarity<T, Unit<Quaternion<T>>, 3>

The resulting type after applying the `*` operator.
source§

#### fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the `*` operation. Read more
source§

### impl<'b, T: SimdRealField, R, const D: usize> MulAssign<&'b Isometry<T, R, D>> for Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

source§

#### fn mul_assign(&mut self, rhs: &'b Isometry<T, R, D>)

Performs the `*=` operation. Read more
source§

### impl<'b, T, const D: usize> MulAssign<&'b Rotation<T, D>> for Similarity<T, Rotation<T, D>, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

source§

#### fn mul_assign(&mut self, rhs: &'b Rotation<T, D>)

Performs the `*=` operation. Read more
source§

### impl<'b, T: SimdRealField, R, const D: usize> MulAssign<&'b Similarity<T, R, D>> for Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

source§

#### fn mul_assign(&mut self, rhs: &'b Similarity<T, R, D>)

Performs the `*=` operation. Read more
source§

### impl<'b, T, C, R, const D: usize> MulAssign<&'b Similarity<T, R, D>> for Transform<T, C, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategory,
R: SubsetOf<OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

source§

#### fn mul_assign(&mut self, rhs: &'b Similarity<T, R, D>)

Performs the `*=` operation. Read more
source§

### impl<'b, T: SimdRealField, R, const D: usize> MulAssign<&'b Translation<T, D>> for Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

source§

#### fn mul_assign(&mut self, rhs: &'b Translation<T, D>)

Performs the `*=` operation. Read more
source§

### impl<'b, T> MulAssign<&'b Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

source§

#### fn mul_assign(&mut self, rhs: &'b UnitComplex<T>)

Performs the `*=` operation. Read more
source§

### impl<'b, T> MulAssign<&'b Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

source§

#### fn mul_assign(&mut self, rhs: &'b UnitQuaternion<T>)

Performs the `*=` operation. Read more
source§

### impl<T: SimdRealField, R, const D: usize> MulAssign<Isometry<T, R, D>> for Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

source§

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

Performs the `*=` operation. Read more
source§

### impl<T, const D: usize> MulAssign<Rotation<T, D>> for Similarity<T, Rotation<T, D>, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

source§

#### fn mul_assign(&mut self, rhs: Rotation<T, D>)

Performs the `*=` operation. Read more
source§

### impl<T: SimdRealField, R, const D: usize> MulAssign<Similarity<T, R, D>> for Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

source§

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

Performs the `*=` operation. Read more
source§

### impl<T, C, R, const D: usize> MulAssign<Similarity<T, R, D>> for Transform<T, C, D>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
Const<D>: DimNameAdd<U1>,
C: TCategory,
R: SubsetOf<OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

source§

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

Performs the `*=` operation. Read more
source§

### impl<T: SimdRealField, R, const D: usize> MulAssign<Translation<T, D>> for Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

source§

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

Performs the `*=` operation. Read more
source§

### impl<T> MulAssign<Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

source§

#### fn mul_assign(&mut self, rhs: UnitComplex<T>)

Performs the `*=` operation. Read more
source§

### impl<T> MulAssign<Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>where
T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
T::Element: SimdRealField,

source§

#### fn mul_assign(&mut self, rhs: UnitQuaternion<T>)

Performs the `*=` operation. Read more
source§

### impl<T: SimdRealField, R, const D: usize> One for Similarity<T, R, D>where
T::Element: SimdRealField,
R: AbstractRotation<T, D>,

source§

#### fn one() -> Self

Creates a new identity similarity.

source§

#### fn set_one(&mut self)

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

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

Returns `true` if `self` is equal to the multiplicative identity. Read more
source§

### impl<T: SimdRealField, R, const D: usize> PartialEq<Similarity<T, R, D>> for Similarity<T, R, D>where
R: AbstractRotation<T, D> + PartialEq,

source§

#### fn eq(&self, right: &Self) -> bool

This method tests for `self` and `other` values to be equal, and is used by `==`. Read more
1.0.0 · source§

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

This method tests for `!=`. The default implementation is almost always sufficient, and should not be overridden without very good reason. Read more
source§

### impl<T: RealField, R, const D: usize> RelativeEq<Similarity<T, R, D>> for Similarity<T, R, D>where
R: AbstractRotation<T, D> + RelativeEq<Epsilon = T::Epsilon>,
T::Epsilon: Clone,

source§

#### fn default_max_relative() -> Self::Epsilon

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

#### 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.
source§

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

The inverse of `RelativeEq::relative_eq`.
source§

### impl<T: SimdRealField, R, const D: usize> SimdValue for Similarity<T, R, D>where
T::Element: SimdRealField,
R: SimdValue<SimdBool = T::SimdBool> + AbstractRotation<T, D>,
R::Element: AbstractRotation<T::Element, D>,

§

#### type Element = Similarity<<T as SimdValue>::Element, <R as SimdValue>::Element, D>

The type of the elements of each lane of this SIMD value.
§

#### type SimdBool = <T as SimdValue>::SimdBool

Type of the result of comparing two SIMD values like `self`.
source§

#### fn lanes() -> usize

The number of lanes of this SIMD value.
source§

#### fn splat(val: Self::Element) -> Self

Initializes an SIMD value with each lanes set to `val`.
source§

#### fn extract(&self, i: usize) -> Self::Element

Extracts the i-th lane of `self`. Read more
source§

#### unsafe fn extract_unchecked(&self, i: usize) -> Self::Element

Extracts the i-th lane of `self` without bound-checking.
source§

#### fn replace(&mut self, i: usize, val: Self::Element)

Replaces the i-th lane of `self` by `val`. Read more
source§

#### unsafe fn replace_unchecked(&mut self, i: usize, val: Self::Element)

Replaces the i-th lane of `self` by `val` without bound-checking.
source§

#### fn select(self, cond: Self::SimdBool, other: Self) -> Self

Merges `self` and `other` depending on the lanes of `cond`. Read more
source§

#### fn map_lanes(self, f: impl Fn(Self::Element) -> Self::Element) -> Selfwhere
Self: Clone,

Applies a function to each lane of `self`. Read more
source§

#### fn zip_map_lanes(
self,
b: Self,
f: impl Fn(Self::Element, Self::Element) -> Self::Element
) -> Selfwhere
Self: Clone,

Applies a function to each lane of `self` paired with the corresponding lane of `b`. Read more
source§

### impl<T1, T2, R, const D: usize> SubsetOf<Matrix<T2, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output, <DefaultAllocator as Allocator<T2, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>>::Buffer>> for Similarity<T1, R, D>where
T1: RealField,
T2: RealField + SupersetOf<T1>,
R: AbstractRotation<T1, D> + SubsetOf<OMatrix<T1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>> + SubsetOf<OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>,
Const<D>: DimNameAdd<U1> + DimMin<Const<D>, Output = Const<D>>,
DefaultAllocator: Allocator<T1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> + Allocator<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> + Allocator<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

source§

#### fn to_superset(
&self
) -> OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>

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

#### fn is_in_subset(
m: &OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
) -> bool

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

#### fn from_superset_unchecked(
m: &OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
) -> Self

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

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

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
source§

### impl<T1, T2, R> SubsetOf<Similarity<T2, R, 2>> for UnitComplex<T1>where
T1: RealField,
T2: RealField + SupersetOf<T1>,
R: AbstractRotation<T2, 2> + SupersetOf<Self>,

source§

#### fn to_superset(&self) -> Similarity<T2, R, 2>

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

#### fn is_in_subset(sim: &Similarity<T2, R, 2>) -> bool

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

#### fn from_superset_unchecked(sim: &Similarity<T2, R, 2>) -> Self

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

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

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
source§

### impl<T1, T2, R> SubsetOf<Similarity<T2, R, 3>> for UnitQuaternion<T1>where
T1: RealField,
T2: RealField + SupersetOf<T1>,
R: AbstractRotation<T2, 3> + SupersetOf<Self>,

source§

#### fn to_superset(&self) -> Similarity<T2, R, 3>

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

#### fn is_in_subset(sim: &Similarity<T2, R, 3>) -> bool

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

#### fn from_superset_unchecked(sim: &Similarity<T2, R, 3>) -> Self

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

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

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
source§

### impl<T1, T2, R, const D: usize> SubsetOf<Similarity<T2, R, D>> for Rotation<T1, D>where
T1: RealField,
T2: RealField + SupersetOf<T1>,
R: AbstractRotation<T2, D> + SupersetOf<Self>,

source§

#### fn to_superset(&self) -> Similarity<T2, R, D>

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

#### fn is_in_subset(sim: &Similarity<T2, R, D>) -> bool

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

#### fn from_superset_unchecked(sim: &Similarity<T2, R, D>) -> Self

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

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

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
source§

### impl<T1, T2, R, const D: usize> SubsetOf<Similarity<T2, R, D>> for Translation<T1, D>where
T1: RealField,
T2: RealField + SupersetOf<T1>,
R: AbstractRotation<T2, D>,

source§

#### fn to_superset(&self) -> Similarity<T2, R, D>

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

#### fn is_in_subset(sim: &Similarity<T2, R, D>) -> bool

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

#### fn from_superset_unchecked(sim: &Similarity<T2, R, D>) -> Self

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

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

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
source§

### impl<T1, T2, R1, R2, const D: usize> SubsetOf<Similarity<T2, R2, D>> for Isometry<T1, R1, D>where
T1: RealField,
T2: RealField + SupersetOf<T1>,
R1: AbstractRotation<T1, D> + SubsetOf<R2>,
R2: AbstractRotation<T2, D>,

source§

#### fn to_superset(&self) -> Similarity<T2, R2, D>

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

#### fn is_in_subset(sim: &Similarity<T2, R2, D>) -> bool

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

#### fn from_superset_unchecked(sim: &Similarity<T2, R2, D>) -> Self

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

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

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
source§

### impl<T1, T2, R1, R2, const D: usize> SubsetOf<Similarity<T2, R2, D>> for Similarity<T1, R1, D>where
T1: RealField + SubsetOf<T2>,
T2: RealField + SupersetOf<T1>,
R1: AbstractRotation<T1, D> + SubsetOf<R2>,
R2: AbstractRotation<T2, D>,

source§

#### fn to_superset(&self) -> Similarity<T2, R2, D>

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

#### fn is_in_subset(sim: &Similarity<T2, R2, D>) -> bool

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

#### fn from_superset_unchecked(sim: &Similarity<T2, R2, D>) -> Self

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

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

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
source§

### impl<T1, T2> SubsetOf<Similarity<T2, Unit<Quaternion<T2>>, 3>> for UnitDualQuaternion<T1>where
T1: RealField,
T2: RealField + SupersetOf<T1>,

source§

#### fn to_superset(&self) -> Similarity3<T2>

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

#### fn is_in_subset(sim: &Similarity3<T2>) -> bool

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

#### fn from_superset_unchecked(sim: &Similarity3<T2>) -> Self

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

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

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
source§

### impl<T1, T2, R, C, const D: usize> SubsetOf<Transform<T2, C, D>> for Similarity<T1, R, D>where
T1: RealField,
T2: RealField + SupersetOf<T1>,
C: SuperTCategoryOf<TAffine>,
R: AbstractRotation<T1, D> + SubsetOf<OMatrix<T1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>> + SubsetOf<OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>,
Const<D>: DimNameAdd<U1> + DimMin<Const<D>, Output = Const<D>>,
DefaultAllocator: Allocator<T1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> + Allocator<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> + Allocator<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

source§

#### fn to_superset(&self) -> Transform<T2, C, D>

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

#### fn is_in_subset(t: &Transform<T2, C, D>) -> bool

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

#### fn from_superset_unchecked(t: &Transform<T2, C, D>) -> Self

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

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

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
source§

### impl<T: RealField, R, const D: usize> UlpsEq<Similarity<T, R, D>> for Similarity<T, R, D>where
R: AbstractRotation<T, D> + UlpsEq<Epsilon = T::Epsilon>,
T::Epsilon: Clone,

source§

#### fn default_max_ulps() -> u32

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

#### 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.
source§

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

The inverse of `UlpsEq::ulps_eq`.
source§

### impl<T: Copy, R: Copy, const D: usize> Copy for Similarity<T, R, D>

source§

### impl<T: SimdRealField, R, const D: usize> Eq for Similarity<T, R, D>where
R: AbstractRotation<T, D> + Eq,

## Auto Trait Implementations§

§

### impl<T, R, const D: usize> RefUnwindSafe for Similarity<T, R, D>where
R: RefUnwindSafe,
T: RefUnwindSafe,

§

### impl<T, R, const D: usize> Send for Similarity<T, R, D>where
R: Send,
T: Send,

§

### impl<T, R, const D: usize> Sync for Similarity<T, R, D>where
R: Sync,
T: Sync,

§

### impl<T, R, const D: usize> Unpin for Similarity<T, R, D>where
R: Unpin,
T: Unpin,

§

### impl<T, R, const D: usize> UnwindSafe for Similarity<T, R, D>where
R: UnwindSafe,
T: UnwindSafe,

## Blanket Implementations§

source§

### impl<T> Any for Twhere
T: 'static + ?Sized,

source§

#### fn type_id(&self) -> TypeId

Gets the `TypeId` of `self`. Read more
source§

### impl<T> Borrow<T> for Twhere
T: ?Sized,

const: unstable · source§

#### fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
source§

### impl<T> BorrowMut<T> for Twhere
T: ?Sized,

const: unstable · source§

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

Mutably borrows from an owned value. Read more
source§

### impl<T> From<T> for T

const: unstable · source§

#### fn from(t: T) -> T

Returns the argument unchanged.

source§

### impl<T, U> Into<U> for Twhere
U: From<T>,

const: unstable · source§

#### fn into(self) -> U

Calls `U::from(self)`.

That is, this conversion is whatever the implementation of `From<T> for U` chooses to do.

source§

### impl<T> Same<T> for T

§

#### type Output = T

Should always be `Self`
source§

### impl<SS, SP> SupersetOf<SS> for SPwhere
SS: SubsetOf<SP>,

source§

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

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
source§

#### fn is_in_subset(&self) -> bool

Checks if `self` is actually part of its subset `T` (and can be converted to it).
source§

#### fn to_subset_unchecked(&self) -> SS

Use with care! Same as `self.to_subset` but without any property checks. Always succeeds.
source§

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

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

### impl<T> ToOwned for Twhere
T: Clone,

§

#### type Owned = T

The resulting type after obtaining ownership.
source§

#### fn to_owned(&self) -> T

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

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

Uses borrowed data to replace owned data, usually by cloning. Read more
source§

### impl<T> ToString for Twhere
T: Display + ?Sized,

source§

#### default fn to_string(&self) -> String

Converts the given value to a `String`. Read more
source§

### impl<T, U> TryFrom<U> for Twhere
U: Into<T>,

§

#### type Error = Infallible

The type returned in the event of a conversion error.
const: unstable · source§

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

Performs the conversion.
source§

### impl<T, U> TryInto<U> for Twhere
U: TryFrom<T>,

§

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

The type returned in the event of a conversion error.
const: unstable · source§

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

Performs the conversion.
source§

### impl<T, Right> ClosedDiv<Right> for Twhere
T: Div<Right, Output = T> + DivAssign<Right>,

source§

### impl<T, Right> ClosedMul<Right> for Twhere
T: Mul<Right, Output = T> + MulAssign<Right>,