[][src]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>, 
[src]

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

Creates a new similarity from its rotational and translational parts.

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

Creates a new similarity from its rotational and translational parts.

pub fn from_scaling(scaling: N) -> Self[src]

Creates a new similarity that applies only a scaling factor.

pub fn inverse(&self) -> Self[src]

Inverts self.

pub fn inverse_mut(&mut self)[src]

Inverts self in-place.

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

The scaling factor of this similarity transformation.

pub fn scaling(&self) -> N[src]

The scaling factor of this similarity transformation.

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

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

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

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

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

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

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

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>)[src]

Appends to self the given translation in-place.

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

Appends to self the given rotation in-place.

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

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)[src]

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>[src]

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>[src]

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>[src]

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>[src]

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>, 
[src]

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>>, 
[src]

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>, 
[src]

pub fn identity() -> Self[src]

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>, 
[src]

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

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>>[src]

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

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>>[src]

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

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>>[src]

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

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
[src]

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
[src]

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
[src]

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
[src]

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>>[src]

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

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
[src]

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
[src]

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
[src]

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
[src]

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
[src]

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

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

fn clone_from(&mut self, source: &Self)1.0.0[src]

Performs copy-assignment from source. Read more

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>, 
[src]

#[must_use] fn ne(&self, other: &Rhs) -> bool1.0.0[src]

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>>, 
[src]

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

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

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

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>, 
[src]

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

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

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

The resulting type after applying the * operator.

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

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

The resulting type after applying the * operator.

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

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

The resulting type after applying the * operator.

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

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

The resulting type after applying the * operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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>, 
[src]

type Output = Point<N, D>

The resulting type after applying the * operator.

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>, 
[src]

type Output = Point<N, D>

The resulting type after applying the * operator.

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>, 
[src]

type Output = Point<N, D>

The resulting type after applying the * operator.

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>, 
[src]

type Output = Point<N, D>

The resulting type after applying the * operator.

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>, 
[src]

type Output = VectorN<N, D>

The resulting type after applying the * operator.

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>, 
[src]

type Output = VectorN<N, D>

The resulting type after applying the * operator.

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>, 
[src]

type Output = VectorN<N, D>

The resulting type after applying the * operator.

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>, 
[src]

type Output = VectorN<N, D>

The resulting type after applying the * operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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>, 
[src]

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

The resulting type after applying the * operator.

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>, 
[src]

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

The resulting type after applying the * operator.

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>, 
[src]

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

The resulting type after applying the * operator.

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>, 
[src]

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

The resulting type after applying the * operator.

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

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

The resulting type after applying the * operator.

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>, 
[src]

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

The resulting type after applying the * operator.

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>, 
[src]

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

The resulting type after applying the * operator.

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>, 
[src]

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

The resulting type after applying the * operator.

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>, 
[src]

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

The resulting type after applying the * operator.

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>, 
[src]

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

The resulting type after applying the * operator.

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>, 
[src]

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

The resulting type after applying the * operator.

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>, 
[src]

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

The resulting type after applying the * operator.

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>>, 
[src]

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

The resulting type after applying the * operator.

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>>, 
[src]

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

The resulting type after applying the * operator.

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>>, 
[src]

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

The resulting type after applying the * operator.

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>>, 
[src]

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

The resulting type after applying the * operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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>, 
[src]

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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>, 
[src]

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

The resulting type after applying the / operator.

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>, 
[src]

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

The resulting type after applying the / operator.

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>, 
[src]

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

The resulting type after applying the / operator.

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>, 
[src]

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

The resulting type after applying the / operator.

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

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

The resulting type after applying the / operator.

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>, 
[src]

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

The resulting type after applying the / operator.

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>, 
[src]

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

The resulting type after applying the / operator.

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>, 
[src]

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

The resulting type after applying the / operator.

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>, 
[src]

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>, 
[src]

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>, 
[src]

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>, 
[src]

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>, 
[src]

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>, 
[src]

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

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>, 
[src]

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>, 
[src]

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>, 
[src]

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>, 
[src]

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>, 
[src]

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>, 
[src]

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>, 
[src]

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

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>, 
[src]

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
[src]

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>, 
[src]

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
[src]

type Epsilon = N::Epsilon

Used for specifying relative comparisons.

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

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
[src]

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

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
[src]

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

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>, 
[src]

fn one() -> Self[src]

Creates a new identity similarity.

fn set_one(&mut self)[src]

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

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

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

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>, 
[src]

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

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

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

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

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>, 
[src]

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

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

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

Returns true if latin squareness holds for the given arguments. Read more

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

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

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

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

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>, 
[src]

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

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

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

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

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

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

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

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

fn id(O) -> Self[src]

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>, 
[src]

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

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

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>, 
[src]

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

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

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>, 
[src]

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

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

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>, 
[src]

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

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

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>, 
[src]

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

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

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>, 
[src]

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

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

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>, 
[src]

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

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

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>, 
[src]

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

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

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>, 
[src]

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>, 
[src]

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.

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>, 
[src]

type Scaling = N

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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
[src]

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
[src]

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>, 
[src]

Auto Trait Implementations

impl<N, D, R> !Unpin for Similarity<N, D, R>

impl<N, D, R> !Sync for Similarity<N, D, R>

impl<N, D, R> !Send for Similarity<N, D, R>

impl<N, D, R> !UnwindSafe for Similarity<N, D, R>

impl<N, D, R> !RefUnwindSafe for Similarity<N, D, R>

Blanket Implementations

impl<T> ToOwned for T where
    T: Clone
[src]

type Owned = T

The resulting type after obtaining ownership.

impl<T> From<T> for T[src]

impl<T, U> Into<U> for T where
    U: From<T>, 
[src]

impl<T> ToString for T where
    T: Display + ?Sized
[src]

impl<T, U> TryFrom<U> for T where
    U: Into<T>, 
[src]

type Error = Infallible

The type returned in the event of a conversion error.

impl<T, U> TryInto<U> for T where
    U: TryFrom<T>, 
[src]

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

The type returned in the event of a conversion error.

impl<T> Borrow<T> for T where
    T: ?Sized
[src]

impl<T> BorrowMut<T> for T where
    T: ?Sized
[src]

impl<T> Any for T where
    T: 'static + ?Sized
[src]

impl<T> Same<T> for T[src]

type Output = T

Should always be Self

impl<SS, SP> SupersetOf<SS> for SP where
    SS: SubsetOf<SP>, 
[src]

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

impl<T, Right> ClosedDiv<Right> for T where
    T: Div<Right, Output = T> + DivAssign<Right>, 
[src]

impl<T> MultiplicativeMagma for T where
    T: AbstractMagma<Multiplicative>, 
[src]

impl<T> MultiplicativeQuasigroup for T where
    T: AbstractQuasigroup<Multiplicative> + ClosedDiv<T> + MultiplicativeMagma
[src]

impl<T> MultiplicativeLoop for T where
    T: AbstractLoop<Multiplicative> + MultiplicativeQuasigroup + One
[src]

impl<T> MultiplicativeSemigroup for T where
    T: AbstractSemigroup<Multiplicative> + ClosedMul<T> + MultiplicativeMagma
[src]

impl<T> MultiplicativeMonoid for T where
    T: AbstractMonoid<Multiplicative> + MultiplicativeSemigroup + One
[src]

impl<T> MultiplicativeGroup for T where
    T: AbstractGroup<Multiplicative> + MultiplicativeLoop + MultiplicativeMonoid
[src]

impl<R, E> Transformation<E> for R where
    E: EuclideanSpace<RealField = R>,
    R: RealField,
    <E as EuclideanSpace>::Coordinates: ClosedMul<R>,
    <E as EuclideanSpace>::Coordinates: ClosedDiv<R>,
    <E as EuclideanSpace>::Coordinates: ClosedNeg
[src]

impl<R, E> AffineTransformation<E> for R where
    E: EuclideanSpace<RealField = R>,
    R: RealField,
    <E as EuclideanSpace>::Coordinates: ClosedMul<R>,
    <E as EuclideanSpace>::Coordinates: ClosedDiv<R>,
    <E as EuclideanSpace>::Coordinates: ClosedNeg
[src]

type Rotation = Id<Multiplicative>

Type of the first rotation to be applied.

type NonUniformScaling = R

Type of the non-uniform scaling to be applied.

type Translation = Id<Multiplicative>

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

fn append_rotation_wrt_point(&self, r: &Self::Rotation, p: &E) -> Option<Self>[src]

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

impl<R, E> Similarity<E> for R where
    E: EuclideanSpace<RealField = R>,
    R: RealField + SubsetOf<R>,
    <E as EuclideanSpace>::Coordinates: ClosedMul<R>,
    <E as EuclideanSpace>::Coordinates: ClosedDiv<R>,
    <E as EuclideanSpace>::Coordinates: ClosedNeg
[src]

type Scaling = R

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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
[src]

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
[src]

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

impl<R, E> ProjectiveTransformation<E> for R where
    E: EuclideanSpace<RealField = R>,
    R: RealField,
    <E as EuclideanSpace>::Coordinates: ClosedMul<R>,
    <E as EuclideanSpace>::Coordinates: ClosedDiv<R>,
    <E as EuclideanSpace>::Coordinates: ClosedNeg
[src]