Struct na::geometry::Isometry

#[repr(C)]
pub struct Isometry<N, D, R> where
    D: DimName,
    N: RealField,
    DefaultAllocator: Allocator<N, D, U1>,  {
    pub rotation: R,
    pub translation: Translation<N, D>,
    // some fields omitted
}

A direct isometry, i.e., a rotation followed by a translation, aka. a rigid-body motion, aka. an element of a Special Euclidean (SE) group.

Fields

rotation: R

The pure rotational part of this isometry.

translation: Translation<N, D>

The pure translational part of this isometry.

Methods

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

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

Creates a new isometry from its rotational and translational parts.

Example

let tra = Translation3::new(0.0, 0.0, 3.0);
let rot = UnitQuaternion::from_scaled_axis(Vector3::y() * f32::consts::PI);
let iso = Isometry3::from_parts(tra, rot);

assert_relative_eq!(iso * Point3::new(1.0, 2.0, 3.0), Point3::new(-1.0, 2.0, 0.0), epsilon = 1.0e-6);

pub fn inverse(&self) -> Isometry<N, D, R>

Inverts self.

Example

let iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);
let inv = iso.inverse();
let pt = Point2::new(1.0, 2.0);

assert_eq!(inv * (iso * pt), pt);

pub fn inverse_mut(&mut self)

Inverts self in-place.

Example

let mut iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);
let pt = Point2::new(1.0, 2.0);
let transformed_pt = iso * pt;
iso.inverse_mut();

assert_eq!(iso * transformed_pt, pt);

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

Appends to self the given translation in-place.

Example

let mut iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);
let tra = Translation2::new(3.0, 4.0);
// Same as `iso = tra * iso`.
iso.append_translation_mut(&tra);

assert_eq!(iso.translation, Translation2::new(4.0, 6.0));

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

Appends to self the given rotation in-place.

Example

let mut iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::PI / 6.0);
let rot = UnitComplex::new(f32::consts::PI / 2.0);
// Same as `iso = rot * iso`.
iso.append_rotation_mut(&rot);

assert_relative_eq!(iso, Isometry2::new(Vector2::new(-2.0, 1.0), f32::consts::PI * 2.0 / 3.0), epsilon = 1.0e-6);

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.

Example

let mut iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);
let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
let pt = Point2::new(1.0, 0.0);
iso.append_rotation_wrt_point_mut(&rot, &pt);

assert_relative_eq!(iso * pt, Point2::new(-2.0, 0.0), epsilon = 1.0e-6);

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.

Example

let mut iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);
let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
iso.append_rotation_wrt_center_mut(&rot);

// The translation part should not have changed.
assert_eq!(iso.translation.vector, Vector2::new(1.0, 2.0));
assert_eq!(iso.rotation, UnitComplex::new(f32::consts::PI));

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

Transform the given point by this isometry.

This is the same as the multiplication self * pt.

Example

let tra = Translation3::new(0.0, 0.0, 3.0);
let rot = UnitQuaternion::from_scaled_axis(Vector3::y() * f32::consts::FRAC_PI_2);
let iso = Isometry3::from_parts(tra, rot);

let transformed_point = iso.transform_point(&Point3::new(1.0, 2.0, 3.0));
assert_relative_eq!(transformed_point, Point3::new(3.0, 2.0, 2.0), epsilon = 1.0e-6);

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

Transform the given vector by this isometry, ignoring the translation component of the isometry.

This is the same as the multiplication self * v.

Example

let tra = Translation3::new(0.0, 0.0, 3.0);
let rot = UnitQuaternion::from_scaled_axis(Vector3::y() * f32::consts::FRAC_PI_2);
let iso = Isometry3::from_parts(tra, rot);

let transformed_point = iso.transform_vector(&Vector3::new(1.0, 2.0, 3.0));
assert_relative_eq!(transformed_point, Vector3::new(3.0, 2.0, -1.0), epsilon = 1.0e-6);

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

Transform the given point by the inverse of this isometry. This may be less expensive than computing the entire isometry inverse and then transforming the point.

Example

let tra = Translation3::new(0.0, 0.0, 3.0);
let rot = UnitQuaternion::from_scaled_axis(Vector3::y() * f32::consts::FRAC_PI_2);
let iso = Isometry3::from_parts(tra, rot);

let transformed_point = iso.inverse_transform_point(&Point3::new(1.0, 2.0, 3.0));
assert_relative_eq!(transformed_point, Point3::new(0.0, 2.0, 1.0), epsilon = 1.0e-6);

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

Transform the given vector by the inverse of this isometry, ignoring the translation component of the isometry. This may be less expensive than computing the entire isometry inverse and then transforming the point.

Example

let tra = Translation3::new(0.0, 0.0, 3.0);
let rot = UnitQuaternion::from_scaled_axis(Vector3::y() * f32::consts::FRAC_PI_2);
let iso = Isometry3::from_parts(tra, rot);

let transformed_point = iso.inverse_transform_vector(&Vector3::new(1.0, 2.0, 3.0));
assert_relative_eq!(transformed_point, Vector3::new(-3.0, 2.0, 1.0), epsilon = 1.0e-6);

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

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

Converts this isometry into its equivalent homogeneous transformation matrix.

Example

let iso = Isometry2::new(Vector2::new(10.0, 20.0), f32::consts::FRAC_PI_6);
let expected = Matrix3::new(0.8660254, -0.5,      10.0,
                            0.5,       0.8660254, 20.0,
                            0.0,       0.0,       1.0);

assert_relative_eq!(iso.to_homogeneous(), expected, epsilon = 1.0e-6);

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

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

Creates a new identity isometry.

Example

let iso = Isometry2::identity();
let pt = Point2::new(1.0, 2.0);
assert_eq!(iso * pt, pt);

let iso = Isometry3::identity();
let pt = Point3::new(1.0, 2.0, 3.0);
assert_eq!(iso * pt, pt);

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

The isometry that applies the rotation r with its axis passing through the point p. This effectively lets p invariant.

Example

let rot = UnitComplex::new(f32::consts::PI);
let pt = Point2::new(1.0, 0.0);
let iso = Isometry2::rotation_wrt_point(rot, pt);

assert_eq!(iso * pt, pt); // The rotation center is not affected.
assert_relative_eq!(iso * Point2::new(1.0, 2.0), Point2::new(1.0, -2.0), epsilon = 1.0e-6);

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

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

Creates a new 2D isometry from a translation and a rotation angle.

Its rotational part is represented as a 2x2 rotation matrix.

Example

let iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);

assert_eq!(iso * Point2::new(3.0, 4.0), Point2::new(-3.0, 5.0));

pub fn translation(x: N, y: N) -> Isometry<N, U2, Rotation<N, U2>>

Creates a new isometry from the given translation coordinates.

pub fn rotation(angle: N) -> Isometry<N, U2, Rotation<N, U2>>

Creates a new isometry from the given rotation angle.

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

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

Creates a new 2D isometry from a translation and a rotation angle.

Its rotational part is represented as an unit complex number.

Example

let iso = IsometryMatrix2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);

assert_eq!(iso * Point2::new(3.0, 4.0), Point2::new(-3.0, 5.0));

pub fn translation(x: N, y: N) -> Isometry<N, U2, Unit<Complex<N>>>

Creates a new isometry from the given translation coordinates.

pub fn rotation(angle: N) -> Isometry<N, U2, Unit<Complex<N>>>

Creates a new isometry from the given rotation angle.

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

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

Creates a new isometry from a translation and a rotation axis-angle.

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);

// Isometry with its rotation part represented as a UnitQuaternion
let iso = Isometry3::new(translation, axisangle);
assert_relative_eq!(iso * pt, Point3::new(7.0, 7.0, -1.0), epsilon = 1.0e-6);
assert_relative_eq!(iso * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);

// Isometry with its rotation part represented as a Rotation3 (a 3x3 rotation matrix).
let iso = IsometryMatrix3::new(translation, axisangle);
assert_relative_eq!(iso * pt, Point3::new(7.0, 7.0, -1.0), epsilon = 1.0e-6);
assert_relative_eq!(iso * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);

pub fn translation(x: N, y: N, z: N) -> Isometry<N, U3, Rotation<N, U3>>

Creates a new isometry from the given translation coordinates.

pub fn rotation(
    axisangle: Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>
) -> Isometry<N, U3, Rotation<N, U3>>

Creates a new isometry from the given rotation angle.

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

Creates an isometry that corresponds to the local frame of an observer standing at the point eye and looking toward target.

It maps the z axis to the view direction target - eyeand 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();

// Isometry with its rotation part represented as a UnitQuaternion
let iso = Isometry3::face_towards(&eye, &target, &up);
assert_eq!(iso * Point3::origin(), eye);
assert_relative_eq!(iso * Vector3::z(), Vector3::x());

// Isometry with its rotation part represented as Rotation3 (a 3x3 rotation matrix).
let iso = IsometryMatrix3::face_towards(&eye, &target, &up);
assert_eq!(iso * Point3::origin(), eye);
assert_relative_eq!(iso * Vector3::z(), Vector3::x());

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

Deprecated:

renamed to face_towards

Deprecated: Use Isometry::face_towards instead.

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

Builds a right-handed look-at view matrix.

It maps the view direction target - eye to the negative z axis to and the eye to the origin. This conforms to the common notion of right handed camera look-at view matrix from the computer graphics community, i.e. the camera is assumed to look toward its local -z axis.

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();

// Isometry with its rotation part represented as a UnitQuaternion
let iso = Isometry3::look_at_rh(&eye, &target, &up);
assert_eq!(iso * eye, Point3::origin());
assert_relative_eq!(iso * Vector3::x(), -Vector3::z());

// Isometry with its rotation part represented as Rotation3 (a 3x3 rotation matrix).
let iso = IsometryMatrix3::look_at_rh(&eye, &target, &up);
assert_eq!(iso * eye, Point3::origin());
assert_relative_eq!(iso * Vector3::x(), -Vector3::z());

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

Builds a left-handed look-at view matrix.

It maps the view direction target - eye to the positive z axis and the eye to the origin. This conforms to the common notion of right handed camera look-at view matrix from the computer graphics community, i.e. the camera is assumed to look toward its local z axis.

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();

// Isometry with its rotation part represented as a UnitQuaternion
let iso = Isometry3::look_at_lh(&eye, &target, &up);
assert_eq!(iso * eye, Point3::origin());
assert_relative_eq!(iso * Vector3::x(), Vector3::z());

// Isometry with its rotation part represented as Rotation3 (a 3x3 rotation matrix).
let iso = IsometryMatrix3::look_at_lh(&eye, &target, &up);
assert_eq!(iso * eye, Point3::origin());
assert_relative_eq!(iso * Vector3::x(), Vector3::z());

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

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

Creates a new isometry from a translation and a rotation axis-angle.

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);

// Isometry with its rotation part represented as a UnitQuaternion
let iso = Isometry3::new(translation, axisangle);
assert_relative_eq!(iso * pt, Point3::new(7.0, 7.0, -1.0), epsilon = 1.0e-6);
assert_relative_eq!(iso * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);

// Isometry with its rotation part represented as a Rotation3 (a 3x3 rotation matrix).
let iso = IsometryMatrix3::new(translation, axisangle);
assert_relative_eq!(iso * pt, Point3::new(7.0, 7.0, -1.0), epsilon = 1.0e-6);
assert_relative_eq!(iso * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);

pub fn translation(x: N, y: N, z: N) -> Isometry<N, U3, Unit<Quaternion<N>>>

Creates a new isometry from the given translation coordinates.

pub fn rotation(
    axisangle: Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>
) -> Isometry<N, U3, Unit<Quaternion<N>>>

Creates a new isometry from the given rotation angle.

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

Creates an isometry that corresponds to the local frame of an observer standing at the point eye and looking toward target.

It maps the z axis to the view direction target - eyeand 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();

// Isometry with its rotation part represented as a UnitQuaternion
let iso = Isometry3::face_towards(&eye, &target, &up);
assert_eq!(iso * Point3::origin(), eye);
assert_relative_eq!(iso * Vector3::z(), Vector3::x());

// Isometry with its rotation part represented as Rotation3 (a 3x3 rotation matrix).
let iso = IsometryMatrix3::face_towards(&eye, &target, &up);
assert_eq!(iso * Point3::origin(), eye);
assert_relative_eq!(iso * Vector3::z(), Vector3::x());

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

Deprecated:

renamed to face_towards

Deprecated: Use Isometry::face_towards instead.

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

Builds a right-handed look-at view matrix.

It maps the view direction target - eye to the negative z axis to and the eye to the origin. This conforms to the common notion of right handed camera look-at view matrix from the computer graphics community, i.e. the camera is assumed to look toward its local -z axis.

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();

// Isometry with its rotation part represented as a UnitQuaternion
let iso = Isometry3::look_at_rh(&eye, &target, &up);
assert_eq!(iso * eye, Point3::origin());
assert_relative_eq!(iso * Vector3::x(), -Vector3::z());

// Isometry with its rotation part represented as Rotation3 (a 3x3 rotation matrix).
let iso = IsometryMatrix3::look_at_rh(&eye, &target, &up);
assert_eq!(iso * eye, Point3::origin());
assert_relative_eq!(iso * Vector3::x(), -Vector3::z());

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

Builds a left-handed look-at view matrix.

It maps the view direction target - eye to the positive z axis and the eye to the origin. This conforms to the common notion of right handed camera look-at view matrix from the computer graphics community, i.e. the camera is assumed to look toward its local z axis.

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();

// Isometry with its rotation part represented as a UnitQuaternion
let iso = Isometry3::look_at_lh(&eye, &target, &up);
assert_eq!(iso * eye, Point3::origin());
assert_relative_eq!(iso * Vector3::x(), Vector3::z());

// Isometry with its rotation part represented as Rotation3 (a 3x3 rotation matrix).
let iso = IsometryMatrix3::look_at_lh(&eye, &target, &up);
assert_eq!(iso * eye, Point3::origin());
assert_relative_eq!(iso * Vector3::x(), Vector3::z());

Trait Implementations

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

default 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.

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

Returns true if associativity holds for the given arguments.

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

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

Performs the *= operation.

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

fn mul_assign(&mut self, rhs: R)

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

default 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.

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

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

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

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

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

Returns a copy of the value.

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

Performs copy-assignment from source.

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

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

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

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

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

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

The inverse of ApproxEq::relative_eq.

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

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

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

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

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

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

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

Formats the value using the given formatter.

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

type Rotation = R

Type of the first rotation to be applied.

type NonUniformScaling = Id<Multiplicative>

Type of the non-uniform scaling to be applied.

type Translation = Translation<N, D>

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

fn decompose(
    &self
) -> (<Isometry<N, D, R> as AffineTransformation<Point<N, D>>>::Translation, R, Id<Multiplicative>, 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: &<Isometry<N, D, R> as AffineTransformation<Point<N, D>>>::Translation
) -> Isometry<N, D, R>

Appends a translation to this similarity.

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

Prepends a translation to this similarity.

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

Appends a rotation to this similarity.

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

Prepends a rotation to this similarity.

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

Appends a scaling factor to this similarity.

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

Prepends a scaling factor to this similarity.

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

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

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

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

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

fn two_sided_inverse_mut(&mut self)

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

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

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

Performs an operation.

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

Performs specific operation.

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

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

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

#[must_use]

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

This method tests for !=.

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

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

Feeds this value into the given [Hasher].

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

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

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

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

Used for specifying relative comparisons.

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

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

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

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

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

The inverse of ApproxEq::abs_diff_eq.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

fn div_assign(&mut self, rhs: R)

Performs the /= operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

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

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

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

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

unsafe fn from_superset_unchecked(t: &Transform<N2, D, C>) -> Isometry<N1, D, R>

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

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

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

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

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

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

fn is_in_subset(iso: &Isometry<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(
    iso: &Isometry<N2, D, R2>
) -> Isometry<N1, D, R1>

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

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

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

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

fn is_in_subset(iso: &Isometry<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(
    iso: &Isometry<N2, D, R>
) -> Translation<N1, D>

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

default 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<Isometry<N2, U3, R>> for Unit<Quaternion<N1>> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    R: Rotation<Point<N2, U3>> + SupersetOf<Unit<Quaternion<N1>>>, 

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

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

fn is_in_subset(iso: &Isometry<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(
    iso: &Isometry<N2, U3, R>
) -> Unit<Quaternion<N1>>

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

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

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

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

fn is_in_subset(iso: &Isometry<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(
    iso: &Isometry<N2, U2, R>
) -> Unit<Complex<N1>>

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

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

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

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

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

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

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

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

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

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

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

fn is_in_subset(iso: &Isometry<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(iso: &Isometry<N2, D, R>) -> Rotation<N1, D>

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

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

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

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

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

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

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

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

unsafe fn from_superset_unchecked(
    sim: &Similarity<N2, D, R2>
) -> Isometry<N1, D, R1>

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

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

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

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

default 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.

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

Returns true if latin squareness holds for the given arguments.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Point<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

fn mul(
    self,
    right: Isometry<N, D, Rotation<N, D>>
) -> <Rotation<N, D> as Mul<Isometry<N, D, Rotation<N, D>>>>::Output

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Point<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Point<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

fn mul(
    self,
    right: Isometry<N, D, Rotation<N, D>>
) -> <&'a Rotation<N, D> as Mul<Isometry<N, D, Rotation<N, D>>>>::Output

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

fn mul(
    self,
    right: &'b Isometry<N, D, Rotation<N, D>>
) -> <Rotation<N, D> as Mul<&'b Isometry<N, D, Rotation<N, D>>>>::Output

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Point<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

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

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

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

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

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

The identity element.

default fn id(O) -> Self

Specific identity.

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

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

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

type Scaling = Id<Multiplicative>

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) -> Id<Multiplicative>

The pure scaling component of this similarity transformation.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

default 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.

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

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

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

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

fn div(
    self,
    right: Isometry<N, D, Rotation<N, D>>
) -> <Rotation<N, D> as Div<Isometry<N, D, Rotation<N, D>>>>::Output

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

fn div(
    self,
    right: &'b Isometry<N, D, Rotation<N, D>>
) -> <Rotation<N, D> as Div<&'b Isometry<N, D, Rotation<N, D>>>>::Output

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

fn div(
    self,
    right: Isometry<N, D, Rotation<N, D>>
) -> <&'a Rotation<N, D> as Div<Isometry<N, D, Rotation<N, D>>>>::Output

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

Formats the value using the given formatter.

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

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

Creates a new identity isometry.

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

Returns true if self is equal to the multiplicative identity.

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

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

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

Performs the conversion.

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

fn default_max_ulps() -> u32

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

fn ulps_eq(
    &self,
    other: &Isometry<N, D, R>,
    epsilon: <Isometry<N, D, R> as AbsDiffEq<Isometry<N, D, R>>>::Epsilon,
    max_ulps: u32
) -> bool

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

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

The inverse of ApproxEq::ulps_eq.

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