Struct nalgebra::geometry::Similarity

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

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

Fields

isometry: Isometry<N, D, R>

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

Methods

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

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

Creates a new similarity from its rotational and translational parts.

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

Creates a new similarity from its rotational and translational parts.

pub fn from_scaling(scaling: N) -> Self

Creates a new similarity that applies only a scaling factor.

pub fn inverse(&self) -> Self

Inverts self.

pub fn inverse_mut(&mut self)

Inverts self in-place.

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

The scaling factor of this similarity transformation.

pub fn scaling(&self) -> N

The scaling factor of this similarity transformation.

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

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

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

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

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

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

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

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

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

Appends to self the given translation in-place.

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

Appends to self the given rotation in-place.

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

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

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

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

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

Transform the given point by this similarity.

This is the same as the multiplication self * pt.

Example

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

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

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

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

Example

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

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

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

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

Converts this similarity into its equivalent homogeneous transformation matrix.

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

pub fn identity() -> Self

Creates a new identity similarity.

Example

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

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

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

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

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

Example

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

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

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

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

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

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

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

Example

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

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

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

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

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

Example

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

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

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

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

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

Deprecated:

renamed to face_towards

Deprecated: Use [SimilarityMatrix3::face_towards] instead.

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

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

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

Arguments

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

Example

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

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

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

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

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

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

Arguments

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

Example

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

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

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

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

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

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

Example

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

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

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

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

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

Deprecated:

renamed to face_towards

Deprecated: Use [SimilarityMatrix3::face_towards] instead.

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

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

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

Arguments

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

Example

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

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

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

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

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

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

Arguments

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

Example

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

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

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

Trait Implementations

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

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

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

fn clone(&self) -> Self

Returns a copy of the value.

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

Performs copy-assignment from source.

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

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

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

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

This method tests for !=.

impl<N: RealField, D: DimName, R> From<Similarity<N, D, R>> for MatrixN<N, DimNameSum<D, U1>> where
    D: DimNameAdd<U1>,
    R: SubsetOf<MatrixN<N, DimNameSum<D, U1>>>,
    DefaultAllocator: Allocator<N, D> + Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>, 

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

Performs the conversion.

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

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

Feeds this value into the given [Hasher].

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

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

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

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

Formats the value using the given formatter.

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

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

Formats the value using the given formatter.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Point<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Point<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Point<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Point<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = VectorN<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = VectorN<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = VectorN<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = VectorN<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

fn mul_assign(&mut self, rhs: R)

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

fn div_assign(&mut self, rhs: R)

Performs the /= operation.

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

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

Performs the /= operation.

impl<N: RealField, D: DimName, R> Serialize for Similarity<N, D, R> where
    DefaultAllocator: Allocator<N, D>,
    N: Serialize,
    R: Serialize,
    DefaultAllocator: Allocator<N, D>,
    Owned<N, D>: Serialize, 

fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error> where
    __S: Serializer, 

Serialize this value into the given Serde serializer.

impl<'de, N: RealField, D: DimName, R> Deserialize<'de> for Similarity<N, D, R> where
    DefaultAllocator: Allocator<N, D>,
    N: Deserialize<'de>,
    R: Deserialize<'de>,
    DefaultAllocator: Allocator<N, D>,
    Owned<N, D>: Deserialize<'de>, 

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error> where
    __D: Deserializer<'de>, 

Deserialize this value from the given Serde deserializer.

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

type Epsilon = N::Epsilon

Used for specifying relative comparisons.

fn default_epsilon() -> Self::Epsilon

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

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

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

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

The inverse of ApproxEq::abs_diff_eq.

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

fn default_max_relative() -> Self::Epsilon

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

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

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

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

The inverse of ApproxEq::relative_eq.

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

fn default_max_ulps() -> u32

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

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

A test for equality that uses units in the last place (ULP) if the values are far apart.

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

The inverse of ApproxEq::ulps_eq.

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

fn one() -> Self

Creates a new identity similarity.

fn set_one(&mut self)

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

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

Returns true if self is equal to the multiplicative identity.

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

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

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

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

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

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

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

Performs an operation.

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

Performs specific operation.

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

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

Returns true if latin squareness holds for the given arguments. Approximate equality is used for verifications.

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

Returns true if latin squareness holds for the given arguments.

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

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

Returns true if associativity holds for the given arguments. Approximate equality is used for verifications.

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

Returns true if associativity holds for the given arguments.

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

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

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

Checks whether operating with the identity element is a no-op for the given argument. Approximate equality is used for verifications.

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

Checks whether operating with the identity element is a no-op for the given argument.

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

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

fn two_sided_inverse(&self) -> Self

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

fn two_sided_inverse_mut(&mut self)

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

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

fn identity() -> Self

The identity element.

fn id(O) -> Self

Specific identity.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

type NonUniformScaling = N

Type of the non-uniform scaling to be applied.

type Rotation = R

Type of the first rotation to be applied.

type Translation = Translation<N, D>

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

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

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

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

Appends a translation to this similarity.

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

Prepends a translation to this similarity.

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

Appends a rotation to this similarity.

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

Prepends a rotation to this similarity.

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

Appends a scaling factor to this similarity.

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

Prepends a scaling factor to this similarity.

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

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

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

type Scaling = N

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

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

The pure translational component of this similarity transformation.

fn rotation(&self) -> R

The pure rotational component of this similarity transformation.

fn scaling(&self) -> N

The pure scaling component of this similarity transformation.

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

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

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

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

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

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

fn rotate_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

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

fn scale_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

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

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

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

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

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

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

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

fn inverse_rotate_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

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

fn inverse_scale_vector(
    &self,
    pt: &<E as EuclideanSpace>::Coordinates
) -> <E as EuclideanSpace>::Coordinates

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

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

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

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

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

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