Struct nalgebra::geometry::Similarity

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#[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.

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§isometry: Isometry<T, R, D>

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

Implementations§

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

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

Creates a new similarity from its rotational and translational parts.

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

Creates a new similarity from its rotational and translational parts.

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

The scaling factor of this similarity transformation.

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

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pub fn scaling(&self) -> T

The scaling factor of this similarity transformation.

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

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pub fn from_scaling(scaling: T) -> Self

Creates a new similarity that applies only a scaling factor.

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pub fn inverse(&self) -> Self

Inverts self.

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pub fn inverse_mut(&mut self)

Inverts self in-place.

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

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

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

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

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

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

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

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

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

Appends to self the given translation in-place.

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

Appends to self the given rotation in-place.

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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.

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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.

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

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pub fn to_homogeneous( &self ) -> OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>

Converts this similarity into its equivalent homogeneous transformation matrix.

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

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

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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);
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impl<T: SimdRealField> Similarity<T, Rotation2<T>, 2>

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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);
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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());
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impl<T: SimdRealField> Similarity<T, UnitComplex<T>, 2>

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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);
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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());
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impl<T: SimdRealField> Similarity<T, Rotation3<T>, 3>

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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);
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pub fn cast<To: Scalar>(self) -> Similarity<To, Rotation3<To>, 3>
where Similarity<To, Rotation3<To>, 3>: 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());
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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);
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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.

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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);
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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);
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impl<T: SimdRealField> Similarity<T, UnitQuaternion<T>, 3>

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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);
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pub fn cast<To: Scalar>(self) -> Similarity<To, UnitQuaternion<To>, 3>
where Similarity<To, UnitQuaternion<To>, 3>: 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());
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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);
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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.

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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);
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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§

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

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type Epsilon = <T as AbsDiffEq>::Epsilon

Used for specifying relative comparisons.
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fn default_epsilon() -> Self::Epsilon

The default tolerance to use when testing values that are close together. Read more
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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.
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fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of AbsDiffEq::abs_diff_eq.
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impl<T: Clone, R: Clone, const D: usize> Clone for Similarity<T, R, D>

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

Returns a copy of the value. Read more
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fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source. Read more
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impl<T: Debug, R: Debug, const D: usize> Debug for Similarity<T, R, D>

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

Formats the value using the given formatter. Read more
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impl<T: SimdRealField, R, const D: usize> Default for Similarity<T, R, D>

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fn default() -> Self

Returns the “default value” for a type. Read more
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impl<T, R, const D: usize> Display for Similarity<T, R, D>
where T: RealField + Display, R: AbstractRotation<T, D> + Display,

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

Formats the value using the given formatter. Read more
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impl<'a, 'b, T: SimdRealField, R, const D: usize> Div<&'b Isometry<T, R, D>> for &'a Similarity<T, R, D>

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type Output = Similarity<T, R, D>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b Isometry<T, R, D>) -> Self::Output

Performs the / operation. Read more
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impl<'b, T: SimdRealField, R, const D: usize> Div<&'b Isometry<T, R, D>> for Similarity<T, R, D>

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type Output = Similarity<T, R, D>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b Isometry<T, R, D>) -> Self::Output

Performs the / operation. Read more
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impl<'a, 'b, T: SimdRealField, const D: usize> Div<&'b Rotation<T, D>> for &'a Similarity<T, Rotation<T, D>, D>

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

The resulting type after applying the / operator.
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fn div(self, rhs: &'b Rotation<T, D>) -> Self::Output

Performs the / operation. Read more
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impl<'b, T: SimdRealField, const D: usize> Div<&'b Rotation<T, D>> for Similarity<T, Rotation<T, D>, D>

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

The resulting type after applying the / operator.
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fn div(self, rhs: &'b Rotation<T, D>) -> Self::Output

Performs the / operation. Read more
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impl<'a, 'b, T: SimdRealField, R, const D: usize> Div<&'b Similarity<T, R, D>> for &'a Isometry<T, R, D>

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type Output = Similarity<T, R, D>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b Similarity<T, R, D>) -> Self::Output

Performs the / operation. Read more
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impl<'a, 'b, T: SimdRealField, R, const D: usize> Div<&'b Similarity<T, R, D>> for &'a Similarity<T, R, D>

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type Output = Similarity<T, R, D>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b Similarity<T, R, D>) -> Self::Output

Performs the / operation. Read more
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impl<'b, T: SimdRealField, R, const D: usize> Div<&'b Similarity<T, R, D>> for Isometry<T, R, D>

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type Output = Similarity<T, R, D>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b Similarity<T, R, D>) -> Self::Output

Performs the / operation. Read more
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impl<'b, T: SimdRealField, R, const D: usize> Div<&'b Similarity<T, R, D>> for Similarity<T, R, D>

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type Output = Similarity<T, R, D>

The resulting type after applying the / operator.
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fn div(self, rhs: &'b Similarity<T, R, D>) -> Self::Output

Performs the / operation. Read more
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impl<'a, 'b, T: SimdRealField, const D: usize> Div<&'b Similarity<T, Rotation<T, D>, D>> for &'a Rotation<T, D>

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

The resulting type after applying the / operator.
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fn div(self, right: &'b Similarity<T, Rotation<T, D>, D>) -> Self::Output

Performs the / operation. Read more
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impl<'b, T: SimdRealField, const D: usize> Div<&'b Similarity<T, Rotation<T, D>, D>> for Rotation<T, D>

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

The resulting type after applying the / operator.
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fn div(self, right: &'b Similarity<T, Rotation<T, D>, D>) -> Self::Output

Performs the / operation. Read more
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impl<'a, 'b, T: SimdRealField> Div<&'b Similarity<T, Unit<Quaternion<T>>, 3>> for &'a UnitQuaternion<T>

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

The resulting type after applying the / operator.
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fn div(self, right: &'b Similarity<T, UnitQuaternion<T>, 3>) -> Self::Output

Performs the / operation. Read more
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impl<'b, T: SimdRealField> Div<&'b Similarity<T, Unit<Quaternion<T>>, 3>> for UnitQuaternion<T>

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

The resulting type after applying the / operator.
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fn div(self, right: &'b Similarity<T, UnitQuaternion<T>, 3>) -> Self::Output

Performs the / operation. Read more
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impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for &'a Similarity<T, UnitComplex<T>, 2>

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

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the / operation. Read more
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impl<'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>

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

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the / operation. Read more
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impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for &'a Similarity<T, UnitQuaternion<T>, 3>

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

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>

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

The resulting type after applying the / operator.
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fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<'a, T: SimdRealField, R, const D: usize> Div<Isometry<T, R, D>> for &'a Similarity<T, R, D>

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type Output = Similarity<T, R, D>

The resulting type after applying the / operator.
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fn div(self, rhs: Isometry<T, R, D>) -> Self::Output

Performs the / operation. Read more
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impl<T: SimdRealField, R, const D: usize> Div<Isometry<T, R, D>> for Similarity<T, R, D>

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type Output = Similarity<T, R, D>

The resulting type after applying the / operator.
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fn div(self, rhs: Isometry<T, R, D>) -> Self::Output

Performs the / operation. Read more
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impl<'a, T: SimdRealField, const D: usize> Div<Rotation<T, D>> for &'a Similarity<T, Rotation<T, D>, D>

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

The resulting type after applying the / operator.
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fn div(self, rhs: Rotation<T, D>) -> Self::Output

Performs the / operation. Read more
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impl<T: SimdRealField, const D: usize> Div<Rotation<T, D>> for Similarity<T, Rotation<T, D>, D>

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

The resulting type after applying the / operator.
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fn div(self, rhs: Rotation<T, D>) -> Self::Output

Performs the / operation. Read more
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impl<'a, T: SimdRealField, R, const D: usize> Div<Similarity<T, R, D>> for &'a Isometry<T, R, D>

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type Output = Similarity<T, R, D>

The resulting type after applying the / operator.
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fn div(self, rhs: Similarity<T, R, D>) -> Self::Output

Performs the / operation. Read more
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impl<'a, T: SimdRealField, R, const D: usize> Div<Similarity<T, R, D>> for &'a Similarity<T, R, D>

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type Output = Similarity<T, R, D>

The resulting type after applying the / operator.
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fn div(self, rhs: Similarity<T, R, D>) -> Self::Output

Performs the / operation. Read more
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impl<T: SimdRealField, R, const D: usize> Div<Similarity<T, R, D>> for Isometry<T, R, D>

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type Output = Similarity<T, R, D>

The resulting type after applying the / operator.
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fn div(self, rhs: Similarity<T, R, D>) -> Self::Output

Performs the / operation. Read more
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impl<'a, T: SimdRealField, const D: usize> Div<Similarity<T, Rotation<T, D>, D>> for &'a Rotation<T, D>

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

The resulting type after applying the / operator.
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fn div(self, right: Similarity<T, Rotation<T, D>, D>) -> Self::Output

Performs the / operation. Read more
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impl<T: SimdRealField, const D: usize> Div<Similarity<T, Rotation<T, D>, D>> for Rotation<T, D>

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

The resulting type after applying the / operator.
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fn div(self, right: Similarity<T, Rotation<T, D>, D>) -> Self::Output

Performs the / operation. Read more
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impl<'a, T: SimdRealField> Div<Similarity<T, Unit<Quaternion<T>>, 3>> for &'a UnitQuaternion<T>

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

The resulting type after applying the / operator.
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fn div(self, right: Similarity<T, UnitQuaternion<T>, 3>) -> Self::Output

Performs the / operation. Read more
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impl<T: SimdRealField> Div<Similarity<T, Unit<Quaternion<T>>, 3>> for UnitQuaternion<T>

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

The resulting type after applying the / operator.
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fn div(self, right: Similarity<T, UnitQuaternion<T>, 3>) -> Self::Output

Performs the / operation. Read more
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impl<'a, T: SimdRealField> Div<Unit<Complex<T>>> for &'a Similarity<T, UnitComplex<T>, 2>

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

The resulting type after applying the / operator.
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fn div(self, rhs: UnitComplex<T>) -> Self::Output

Performs the / operation. Read more
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impl<T: SimdRealField> Div<Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>

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

The resulting type after applying the / operator.
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fn div(self, rhs: UnitComplex<T>) -> Self::Output

Performs the / operation. Read more
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impl<'a, T: SimdRealField> Div<Unit<Quaternion<T>>> for &'a Similarity<T, UnitQuaternion<T>, 3>

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

The resulting type after applying the / operator.
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fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<T: SimdRealField> Div<Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>

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

The resulting type after applying the / operator.
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fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the / operation. Read more
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impl<T: SimdRealField, R, const D: usize> Div for Similarity<T, R, D>

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type Output = Similarity<T, R, D>

The resulting type after applying the / operator.
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fn div(self, rhs: Similarity<T, R, D>) -> Self::Output

Performs the / operation. Read more
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impl<'b, T: SimdRealField, R, const D: usize> DivAssign<&'b Isometry<T, R, D>> for Similarity<T, R, D>

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

Performs the /= operation. Read more
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impl<'b, T, const D: usize> DivAssign<&'b Rotation<T, D>> for Similarity<T, Rotation<T, D>, D>

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

Performs the /= operation. Read more
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impl<'b, T: SimdRealField, R, const D: usize> DivAssign<&'b Similarity<T, R, D>> for Similarity<T, R, D>

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

Performs the /= operation. Read more
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impl<'b, T> DivAssign<&'b Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>

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

Performs the /= operation. Read more
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impl<'b, T> DivAssign<&'b Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>

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

Performs the /= operation. Read more
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impl<T: SimdRealField, R, const D: usize> DivAssign<Isometry<T, R, D>> for Similarity<T, R, D>

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

Performs the /= operation. Read more
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impl<T, const D: usize> DivAssign<Rotation<T, D>> for Similarity<T, Rotation<T, D>, D>

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

Performs the /= operation. Read more
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impl<T> DivAssign<Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>

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

Performs the /= operation. Read more
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impl<T> DivAssign<Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>

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

Performs the /= operation. Read more
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impl<T: SimdRealField, R, const D: usize> DivAssign for Similarity<T, R, D>

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

Performs the /= operation. Read more
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impl<T, R, const D: usize> From<[Similarity<<T as SimdValue>::Element, <R as SimdValue>::Element, D>; 16]> for Similarity<T, R, D>

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

Converts to this type from the input type.
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impl<T, R, const D: usize> From<[Similarity<<T as SimdValue>::Element, <R as SimdValue>::Element, D>; 2]> for Similarity<T, R, D>

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

Converts to this type from the input type.
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impl<T, R, const D: usize> From<[Similarity<<T as SimdValue>::Element, <R as SimdValue>::Element, D>; 4]> for Similarity<T, R, D>

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

Converts to this type from the input type.
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impl<T, R, const D: usize> From<[Similarity<<T as SimdValue>::Element, <R as SimdValue>::Element, D>; 8]> for Similarity<T, R, D>

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

Converts to this type from the input type.
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impl<T: SimdRealField, R, const D: usize> From<Similarity<T, R, D>> for OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>

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

Converts to this type from the input type.
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impl From<Similarity<f32, Unit<Complex<f32>>, 2>> for Mat3

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fn from(iso: Similarity2<f32>) -> Mat3

Converts to this type from the input type.
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impl From<Similarity<f32, Unit<Quaternion<f32>>, 3>> for Mat4

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fn from(iso: Similarity3<f32>) -> Mat4

Converts to this type from the input type.
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impl From<Similarity<f64, Unit<Complex<f64>>, 2>> for DMat3

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fn from(iso: Similarity2<f64>) -> DMat3

Converts to this type from the input type.
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impl From<Similarity<f64, Unit<Quaternion<f64>>, 3>> for DMat4

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fn from(iso: Similarity3<f64>) -> DMat4

Converts to this type from the input type.
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impl<T: Scalar + Hash, R: Hash, const D: usize> Hash for Similarity<T, R, D>
where Owned<T, Const<D>>: Hash,

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

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type Output = Similarity<T, R, D>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Isometry<T, R, D>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField, R, const D: usize> Mul<&'b Isometry<T, R, D>> for Similarity<T, R, D>

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type Output = Similarity<T, R, D>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Isometry<T, R, D>) -> Self::Output

Performs the * operation. Read more
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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>

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

The resulting type after applying the * operator.
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fn mul(self, right: &'b SVector<T, D>) -> Self::Output

Performs the * operation. Read more
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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>

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

The resulting type after applying the * operator.
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fn mul(self, right: &'b SVector<T, D>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T: SimdRealField, R, const D: usize> Mul<&'b OPoint<T, Const<D>>> for &'a Similarity<T, R, D>

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

The resulting type after applying the * operator.
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fn mul(self, right: &'b Point<T, D>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField, R, const D: usize> Mul<&'b OPoint<T, Const<D>>> for Similarity<T, R, D>

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

The resulting type after applying the * operator.
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fn mul(self, right: &'b Point<T, D>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T: SimdRealField, const D: usize> Mul<&'b Rotation<T, D>> for &'a Similarity<T, Rotation<T, D>, D>

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

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Rotation<T, D>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField, const D: usize> Mul<&'b Rotation<T, D>> for Similarity<T, Rotation<T, D>, D>

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

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Rotation<T, D>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T: SimdRealField, R, const D: usize> Mul<&'b Similarity<T, R, D>> for &'a Isometry<T, R, D>

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type Output = Similarity<T, R, D>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Similarity<T, R, D>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T: SimdRealField, R, const D: usize> Mul<&'b Similarity<T, R, D>> for &'a Similarity<T, R, D>

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type Output = Similarity<T, R, D>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Similarity<T, R, D>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T, C, R, const D: usize> Mul<&'b Similarity<T, R, D>> for &'a Transform<T, C, D>

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

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Similarity<T, R, D>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T: SimdRealField, R, const D: usize> Mul<&'b Similarity<T, R, D>> for &'a Translation<T, D>

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type Output = Similarity<T, R, D>

The resulting type after applying the * operator.
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fn mul(self, right: &'b Similarity<T, R, D>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField, R, const D: usize> Mul<&'b Similarity<T, R, D>> for Isometry<T, R, D>

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type Output = Similarity<T, R, D>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Similarity<T, R, D>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField, R, const D: usize> Mul<&'b Similarity<T, R, D>> for Similarity<T, R, D>

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type Output = Similarity<T, R, D>

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Similarity<T, R, D>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T, C, R, const D: usize> Mul<&'b Similarity<T, R, D>> for Transform<T, C, D>

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

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Similarity<T, R, D>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField, R, const D: usize> Mul<&'b Similarity<T, R, D>> for Translation<T, D>

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type Output = Similarity<T, R, D>

The resulting type after applying the * operator.
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fn mul(self, right: &'b Similarity<T, R, D>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T: SimdRealField, const D: usize> Mul<&'b Similarity<T, Rotation<T, D>, D>> for &'a Rotation<T, D>

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

The resulting type after applying the * operator.
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fn mul(self, right: &'b Similarity<T, Rotation<T, D>, D>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField, const D: usize> Mul<&'b Similarity<T, Rotation<T, D>, D>> for Rotation<T, D>

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

The resulting type after applying the * operator.
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fn mul(self, right: &'b Similarity<T, Rotation<T, D>, D>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T: SimdRealField> Mul<&'b Similarity<T, Unit<Complex<T>>, 2>> for &'a UnitComplex<T>

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

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Similarity<T, UnitComplex<T>, 2>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField> Mul<&'b Similarity<T, Unit<Complex<T>>, 2>> for UnitComplex<T>

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

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Similarity<T, UnitComplex<T>, 2>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T: SimdRealField> Mul<&'b Similarity<T, Unit<Quaternion<T>>, 3>> for &'a UnitQuaternion<T>

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

The resulting type after applying the * operator.
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fn mul(self, right: &'b Similarity<T, UnitQuaternion<T>, 3>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField> Mul<&'b Similarity<T, Unit<Quaternion<T>>, 3>> for UnitQuaternion<T>

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

The resulting type after applying the * operator.
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fn mul(self, right: &'b Similarity<T, UnitQuaternion<T>, 3>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T, C, R, const D: usize> Mul<&'b Transform<T, C, D>> for &'a Similarity<T, R, D>

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

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Transform<T, C, D>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T, C, R, const D: usize> Mul<&'b Transform<T, C, D>> for Similarity<T, R, D>

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

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b Transform<T, C, D>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T: SimdRealField, R, const D: usize> Mul<&'b Translation<T, D>> for &'a Similarity<T, R, D>

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type Output = Similarity<T, R, D>

The resulting type after applying the * operator.
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fn mul(self, right: &'b Translation<T, D>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField, R, const D: usize> Mul<&'b Translation<T, D>> for Similarity<T, R, D>

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type Output = Similarity<T, R, D>

The resulting type after applying the * operator.
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fn mul(self, right: &'b Translation<T, D>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for &'a Similarity<T, UnitComplex<T>, 2>

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

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>

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

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for &'a Similarity<T, UnitQuaternion<T>, 3>

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

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>

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

The resulting type after applying the * operator.
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fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField, R, const D: usize> Mul<Isometry<T, R, D>> for &'a Similarity<T, R, D>

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type Output = Similarity<T, R, D>

The resulting type after applying the * operator.
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fn mul(self, rhs: Isometry<T, R, D>) -> Self::Output

Performs the * operation. Read more
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impl<T: SimdRealField, R, const D: usize> Mul<Isometry<T, R, D>> for Similarity<T, R, D>

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type Output = Similarity<T, R, D>

The resulting type after applying the * operator.
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fn mul(self, rhs: Isometry<T, R, D>) -> Self::Output

Performs the * operation. Read more
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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>

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

The resulting type after applying the * operator.
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fn mul(self, right: SVector<T, D>) -> Self::Output

Performs the * operation. Read more
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impl<T: SimdRealField, R, const D: usize> Mul<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for Similarity<T, R, D>

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

The resulting type after applying the * operator.
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fn mul(self, right: SVector<T, D>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField, R, const D: usize> Mul<OPoint<T, Const<D>>> for &'a Similarity<T, R, D>

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

The resulting type after applying the * operator.
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fn mul(self, right: Point<T, D>) -> Self::Output

Performs the * operation. Read more
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impl<T: SimdRealField, R, const D: usize> Mul<OPoint<T, Const<D>>> for Similarity<T, R, D>

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

The resulting type after applying the * operator.
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fn mul(self, right: Point<T, D>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField, const D: usize> Mul<Rotation<T, D>> for &'a Similarity<T, Rotation<T, D>, D>

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

The resulting type after applying the * operator.
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fn mul(self, rhs: Rotation<T, D>) -> Self::Output

Performs the * operation. Read more
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impl<T: SimdRealField, const D: usize> Mul<Rotation<T, D>> for Similarity<T, Rotation<T, D>, D>

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

The resulting type after applying the * operator.
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fn mul(self, rhs: Rotation<T, D>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField, R, const D: usize> Mul<Similarity<T, R, D>> for &'a Isometry<T, R, D>

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type Output = Similarity<T, R, D>

The resulting type after applying the * operator.
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fn mul(self, rhs: Similarity<T, R, D>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField, R, const D: usize> Mul<Similarity<T, R, D>> for &'a Similarity<T, R, D>

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type Output = Similarity<T, R, D>

The resulting type after applying the * operator.
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fn mul(self, rhs: Similarity<T, R, D>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T, C, R, const D: usize> Mul<Similarity<T, R, D>> for &'a Transform<T, C, D>

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

The resulting type after applying the * operator.
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fn mul(self, rhs: Similarity<T, R, D>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField, R, const D: usize> Mul<Similarity<T, R, D>> for &'a Translation<T, D>

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type Output = Similarity<T, R, D>

The resulting type after applying the * operator.
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fn mul(self, right: Similarity<T, R, D>) -> Self::Output

Performs the * operation. Read more
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impl<T: SimdRealField, R, const D: usize> Mul<Similarity<T, R, D>> for Isometry<T, R, D>

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type Output = Similarity<T, R, D>

The resulting type after applying the * operator.
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fn mul(self, rhs: Similarity<T, R, D>) -> Self::Output

Performs the * operation. Read more
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impl<T, C, R, const D: usize> Mul<Similarity<T, R, D>> for Transform<T, C, D>

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

The resulting type after applying the * operator.
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fn mul(self, rhs: Similarity<T, R, D>) -> Self::Output

Performs the * operation. Read more
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impl<T: SimdRealField, R, const D: usize> Mul<Similarity<T, R, D>> for Translation<T, D>

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type Output = Similarity<T, R, D>

The resulting type after applying the * operator.
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fn mul(self, right: Similarity<T, R, D>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField, const D: usize> Mul<Similarity<T, Rotation<T, D>, D>> for &'a Rotation<T, D>

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

The resulting type after applying the * operator.
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fn mul(self, right: Similarity<T, Rotation<T, D>, D>) -> Self::Output

Performs the * operation. Read more
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impl<T: SimdRealField, const D: usize> Mul<Similarity<T, Rotation<T, D>, D>> for Rotation<T, D>

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

The resulting type after applying the * operator.
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fn mul(self, right: Similarity<T, Rotation<T, D>, D>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField> Mul<Similarity<T, Unit<Complex<T>>, 2>> for &'a UnitComplex<T>

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

The resulting type after applying the * operator.
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fn mul(self, rhs: Similarity<T, UnitComplex<T>, 2>) -> Self::Output

Performs the * operation. Read more
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impl<T: SimdRealField> Mul<Similarity<T, Unit<Complex<T>>, 2>> for UnitComplex<T>

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

The resulting type after applying the * operator.
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fn mul(self, rhs: Similarity<T, UnitComplex<T>, 2>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField> Mul<Similarity<T, Unit<Quaternion<T>>, 3>> for &'a UnitQuaternion<T>

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

The resulting type after applying the * operator.
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fn mul(self, right: Similarity<T, UnitQuaternion<T>, 3>) -> Self::Output

Performs the * operation. Read more
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impl<T: SimdRealField> Mul<Similarity<T, Unit<Quaternion<T>>, 3>> for UnitQuaternion<T>

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

The resulting type after applying the * operator.
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fn mul(self, right: Similarity<T, UnitQuaternion<T>, 3>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T, C, R, const D: usize> Mul<Transform<T, C, D>> for &'a Similarity<T, R, D>

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

The resulting type after applying the * operator.
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fn mul(self, rhs: Transform<T, C, D>) -> Self::Output

Performs the * operation. Read more
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impl<T, C, R, const D: usize> Mul<Transform<T, C, D>> for Similarity<T, R, D>

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

The resulting type after applying the * operator.
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fn mul(self, rhs: Transform<T, C, D>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField, R, const D: usize> Mul<Translation<T, D>> for &'a Similarity<T, R, D>

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type Output = Similarity<T, R, D>

The resulting type after applying the * operator.
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fn mul(self, right: Translation<T, D>) -> Self::Output

Performs the * operation. Read more
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impl<T: SimdRealField, R, const D: usize> Mul<Translation<T, D>> for Similarity<T, R, D>

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type Output = Similarity<T, R, D>

The resulting type after applying the * operator.
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fn mul(self, right: Translation<T, D>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField> Mul<Unit<Complex<T>>> for &'a Similarity<T, UnitComplex<T>, 2>

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

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the * operation. Read more
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impl<T: SimdRealField> Mul<Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>

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

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the * operation. Read more
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impl<'a, T: SimdRealField> Mul<Unit<Quaternion<T>>> for &'a Similarity<T, UnitQuaternion<T>, 3>

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

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<T: SimdRealField> Mul<Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>

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

The resulting type after applying the * operator.
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fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the * operation. Read more
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impl<T: SimdRealField, R, const D: usize> Mul for Similarity<T, R, D>

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type Output = Similarity<T, R, D>

The resulting type after applying the * operator.
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fn mul(self, rhs: Similarity<T, R, D>) -> Self::Output

Performs the * operation. Read more
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impl<'b, T: SimdRealField, R, const D: usize> MulAssign<&'b Isometry<T, R, D>> for Similarity<T, R, D>

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

Performs the *= operation. Read more
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impl<'b, T, const D: usize> MulAssign<&'b Rotation<T, D>> for Similarity<T, Rotation<T, D>, D>

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

Performs the *= operation. Read more
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impl<'b, T: SimdRealField, R, const D: usize> MulAssign<&'b Similarity<T, R, D>> for Similarity<T, R, D>

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

Performs the *= operation. Read more
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impl<'b, T, C, R, const D: usize> MulAssign<&'b Similarity<T, R, D>> for Transform<T, C, D>

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

Performs the *= operation. Read more
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impl<'b, T: SimdRealField, R, const D: usize> MulAssign<&'b Translation<T, D>> for Similarity<T, R, D>

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

Performs the *= operation. Read more
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impl<'b, T> MulAssign<&'b Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>

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

Performs the *= operation. Read more
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impl<'b, T> MulAssign<&'b Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>

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

Performs the *= operation. Read more
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impl<T: SimdRealField, R, const D: usize> MulAssign<Isometry<T, R, D>> for Similarity<T, R, D>

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

Performs the *= operation. Read more
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impl<T, const D: usize> MulAssign<Rotation<T, D>> for Similarity<T, Rotation<T, D>, D>

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

Performs the *= operation. Read more
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impl<T, C, R, const D: usize> MulAssign<Similarity<T, R, D>> for Transform<T, C, D>

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

Performs the *= operation. Read more
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impl<T: SimdRealField, R, const D: usize> MulAssign<Translation<T, D>> for Similarity<T, R, D>

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

Performs the *= operation. Read more
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impl<T> MulAssign<Unit<Complex<T>>> for Similarity<T, UnitComplex<T>, 2>

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

Performs the *= operation. Read more
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impl<T> MulAssign<Unit<Quaternion<T>>> for Similarity<T, UnitQuaternion<T>, 3>

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

Performs the *= operation. Read more
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impl<T: SimdRealField, R, const D: usize> MulAssign for Similarity<T, R, D>

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

Performs the *= operation. Read more
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impl<T: SimdRealField, R, const D: usize> One for Similarity<T, R, D>

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fn one() -> Self

Creates a new identity similarity.

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fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.
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fn is_one(&self) -> bool
where Self: PartialEq,

Returns true if self is equal to the multiplicative identity. Read more
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impl<T: SimdRealField, R, const D: usize> PartialEq for Similarity<T, R, D>
where R: AbstractRotation<T, D> + PartialEq,

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

This method tests for self and other values to be equal, and is used by ==.
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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.
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impl<T: RealField, R, const D: usize> RelativeEq for Similarity<T, R, D>
where R: AbstractRotation<T, D> + RelativeEq<Epsilon = T::Epsilon>, T::Epsilon: Clone,

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fn default_max_relative() -> Self::Epsilon

The default relative tolerance for testing values that are far-apart. Read more
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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.
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fn relative_ne( &self, other: &Rhs, epsilon: Self::Epsilon, max_relative: Self::Epsilon ) -> bool

The inverse of RelativeEq::relative_eq.
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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>,

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const LANES: usize = T::LANES

The number of lanes of this SIMD value.
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type Element = Similarity<<T as SimdValue>::Element, <R as SimdValue>::Element, D>

The type of the elements of each lane of this SIMD value.
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type SimdBool = <T as SimdValue>::SimdBool

Type of the result of comparing two SIMD values like self.
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fn splat(val: Self::Element) -> Self

Initializes an SIMD value with each lanes set to val.
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fn extract(&self, i: usize) -> Self::Element

Extracts the i-th lane of self. Read more
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unsafe fn extract_unchecked(&self, i: usize) -> Self::Element

Extracts the i-th lane of self without bound-checking. Read more
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fn replace(&mut self, i: usize, val: Self::Element)

Replaces the i-th lane of self by val. Read more
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unsafe fn replace_unchecked(&mut self, i: usize, val: Self::Element)

Replaces the i-th lane of self by val without bound-checking. Read more
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fn select(self, cond: Self::SimdBool, other: Self) -> Self

Merges self and other depending on the lanes of cond. Read more
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fn map_lanes(self, f: impl Fn(Self::Element) -> Self::Element) -> Self
where Self: Clone,

Applies a function to each lane of self. Read more
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fn zip_map_lanes( self, b: Self, f: impl Fn(Self::Element, Self::Element) -> Self::Element ) -> Self
where Self: Clone,

Applies a function to each lane of self paired with the corresponding lane of b. Read more
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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<<Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>>::Buffer<T2>>> 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<Const<D>, Const<1>, Buffer<T1> = ArrayStorage<T1, D, 1>> + Allocator<DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

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

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

The inclusion map: converts self to the equivalent element of its superset.
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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).
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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.
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fn from_superset(element: &T) -> Option<Self>

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

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

The inclusion map: converts self to the equivalent element of its superset.
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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).
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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.
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fn from_superset(element: &T) -> Option<Self>

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

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

The inclusion map: converts self to the equivalent element of its superset.
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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).
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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.
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fn from_superset(element: &T) -> Option<Self>

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

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

The inclusion map: converts self to the equivalent element of its superset.
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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).
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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.
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fn from_superset(element: &T) -> Option<Self>

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

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

The inclusion map: converts self to the equivalent element of its superset.
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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).
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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.
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fn from_superset(element: &T) -> Option<Self>

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

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

The inclusion map: converts self to the equivalent element of its superset.
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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).
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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.
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fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more
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impl<T1, T2> SubsetOf<Similarity<T2, Unit<Quaternion<T2>>, 3>> for UnitDualQuaternion<T1>
where T1: RealField, T2: RealField + SupersetOf<T1>,

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

The inclusion map: converts self to the equivalent element of its superset.
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fn is_in_subset(sim: &Similarity3<T2>) -> bool

Checks if element is actually part of the subset Self (and can be converted to it).
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fn from_superset_unchecked(sim: &Similarity3<T2>) -> Self

Use with care! Same as self.to_superset but without any property checks. Always succeeds.
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fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more
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impl<T1, T2, R, C, const D: usize> SubsetOf<Transform<T2, C, D>> for Similarity<T1, R, D>

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

The inclusion map: converts self to the equivalent element of its superset.
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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).
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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.
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fn from_superset(element: &T) -> Option<Self>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more
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impl<T: RealField, R, const D: usize> UlpsEq for Similarity<T, R, D>
where R: AbstractRotation<T, D> + UlpsEq<Epsilon = T::Epsilon>, T::Epsilon: Clone,

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fn default_max_ulps() -> u32

The default ULPs to tolerate when testing values that are far-apart. Read more
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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.
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fn ulps_ne(&self, other: &Rhs, epsilon: Self::Epsilon, max_ulps: u32) -> bool

The inverse of UlpsEq::ulps_eq.
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impl<T: Copy, R: Copy, const D: usize> Copy for Similarity<T, R, D>

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

Auto Trait Implementations§

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

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

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

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

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

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

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

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fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more
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impl<T> Borrow<T> for T
where T: ?Sized,

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fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
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impl<T> BorrowMut<T> for T
where T: ?Sized,

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

Mutably borrows from an owned value. Read more
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impl<T> From<T> for T

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fn from(t: T) -> T

Returns the argument unchanged.

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impl<T, U> Into<U> for T
where U: From<T>,

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fn into(self) -> U

Calls U::from(self).

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

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impl<T> Same for T

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type Output = T

Should always be Self
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impl<SS, SP> SupersetOf<SS> for SP
where SS: SubsetOf<SP>,

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

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more
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fn is_in_subset(&self) -> bool

Checks if self is actually part of its subset T (and can be converted to it).
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fn to_subset_unchecked(&self) -> SS

Use with care! Same as self.to_subset but without any property checks. Always succeeds.
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fn from_subset(element: &SS) -> SP

The inclusion map: converts self to the equivalent element of its superset.
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impl<T> ToOwned for T
where T: Clone,

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type Owned = T

The resulting type after obtaining ownership.
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fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more
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fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more
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impl<T> ToString for T
where T: Display + ?Sized,

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default fn to_string(&self) -> String

Converts the given value to a String. Read more
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impl<T, U> TryFrom<U> for T
where U: Into<T>,

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type Error = Infallible

The type returned in the event of a conversion error.
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fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
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impl<T, U> TryInto<U> for T
where U: TryFrom<T>,

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

The type returned in the event of a conversion error.
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fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.
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impl<T, Right> ClosedDiv<Right> for T
where T: Div<Right, Output = T> + DivAssign<Right>,

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impl<T, Right> ClosedDivAssign<Right> for T
where T: ClosedDiv<Right> + DivAssign<Right>,

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

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impl<T, Right> ClosedMulAssign<Right> for T
where T: ClosedMul<Right> + MulAssign<Right>,

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impl<T> Scalar for T
where T: 'static + Clone + PartialEq + Debug,