Struct nalgebra::geometry::Isometry

#[repr(C)]pub struct Isometry<N: RealField, D: DimName, R> where
    DefaultAllocator: Allocator<N, D>,  {
    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.

Implementations

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

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

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) -> Self

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: &VectorN<N, D>) -> VectorN<N, D>

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: &VectorN<N, D>) -> VectorN<N, D>

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

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

Converts this 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: RealField, D: DimName, R: AlgaRotation<Point<N, D>>> Isometry<N, D, R> where
    DefaultAllocator: Allocator<N, D>, 

pub fn identity() -> Self

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>) -> Self

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: RealField> Isometry<N, U2, Rotation2<N>>

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

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) -> Self

Creates a new isometry from the given translation coordinates.

pub fn rotation(angle: N) -> Self

Creates a new isometry from the given rotation angle.

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

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

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) -> Self

Creates a new isometry from the given translation coordinates.

pub fn rotation(angle: N) -> Self

Creates a new isometry from the given rotation angle.

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

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

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) -> Self

Creates a new isometry from the given translation coordinates.

pub fn rotation(axisangle: Vector3<N>) -> Self

Creates a new isometry from the given rotation angle.

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

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: &Point3<N>,
    target: &Point3<N>,
    up: &Vector3<N>
) -> Self

👎 Deprecated:

renamed to face_towards

Deprecated: Use Isometry::face_towards instead.

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

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: &Point3<N>, target: &Point3<N>, up: &Vector3<N>) -> Self

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: RealField> Isometry<N, U3, UnitQuaternion<N>>

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

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) -> Self

Creates a new isometry from the given translation coordinates.

pub fn rotation(axisangle: Vector3<N>) -> Self

Creates a new isometry from the given rotation angle.

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

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: &Point3<N>,
    target: &Point3<N>,
    up: &Vector3<N>
) -> Self

👎 Deprecated:

renamed to face_towards

Deprecated: Use Isometry::face_towards instead.

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

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: &Point3<N>, target: &Point3<N>, up: &Vector3<N>) -> Self

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

type Epsilon = N::Epsilon

Used for specifying relative comparisons.

fn default_epsilon() -> Self::Epsilon

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

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

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

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

The inverse of ApproxEq::abs_diff_eq.

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

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

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

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

Performs an operation.

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

Performs specific operation.

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

pub 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.

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

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

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

pub 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.

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

Returns true if latin squareness holds for the given arguments.

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

pub 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.

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

Returns true if associativity holds for the given arguments.

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

type Rotation = R

Type of the first rotation to be applied.

type NonUniformScaling = Id

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) -> (Self::Translation, R, Id, R)

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

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

Appends a translation to this similarity.

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

Prepends a translation to this similarity.

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

Appends a rotation to this similarity.

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

Prepends a rotation to this similarity.

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

Appends a scaling factor to this similarity.

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

Prepends a scaling factor to this similarity.

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

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

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

fn clone(&self) -> Self

Returns a copy of the value.

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

Performs copy-assignment from source.

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

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

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

Formats the value using the given formatter.

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

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

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

Formats the value using the given formatter.

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

type Output = Isometry<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'b, N: RealField, D: DimName> Div<&'b Isometry<N, D, Rotation<N, D>>> for Rotation<N, D> where
    DefaultAllocator: Allocator<N, D, D> + 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>>) -> Self::Output

Performs the / operation.

impl<'a, 'b, N: RealField, D: DimName> Div<&'b Isometry<N, D, Rotation<N, D>>> for &'a Rotation<N, D> where
    DefaultAllocator: Allocator<N, D, D> + 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>>) -> Self::Output

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<N: RealField, D: DimName> Div<Isometry<N, D, Rotation<N, D>>> for Rotation<N, D> where
    DefaultAllocator: Allocator<N, D, D> + 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>>) -> Self::Output

Performs the / operation.

impl<'a, N: RealField, D: DimName> Div<Isometry<N, D, Rotation<N, D>>> for &'a Rotation<N, D> where
    DefaultAllocator: Allocator<N, D, D> + 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>>) -> Self::Output

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

fn div_assign(&mut self, rhs: R)

Performs the /= operation.

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

impl<N: RealField, D: DimName, R> From<Isometry<N, D, R>> for 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>> + Allocator<N, D>, 

fn from(iso: Isometry<N, D, R>) -> Self

Performs the conversion.

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

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

Feeds this value into the given Hasher.

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

Feeds a slice of this type into the given Hasher.

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

fn identity() -> Self

The identity element.

pub fn id(O) -> Self

Specific identity.

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

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, N: RealField, D: DimName> Mul<&'b Isometry<N, D, Rotation<N, D>>> for Rotation<N, D> where
    DefaultAllocator: Allocator<N, D, D> + 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>>) -> Self::Output

Performs the * operation.

impl<'a, 'b, N: RealField, D: DimName> Mul<&'b Isometry<N, D, Rotation<N, D>>> for &'a Rotation<N, D> where
    DefaultAllocator: Allocator<N, D, D> + 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>>) -> Self::Output

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = VectorN<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = VectorN<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Point<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Point<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Unit<VectorN<N, D>>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Unit<VectorN<N, D>>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N: RealField, D: DimName> Mul<Isometry<N, D, Rotation<N, D>>> for Rotation<N, D> where
    DefaultAllocator: Allocator<N, D, D> + 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>>) -> Self::Output

Performs the * operation.

impl<'a, N: RealField, D: DimName> Mul<Isometry<N, D, Rotation<N, D>>> for &'a Rotation<N, D> where
    DefaultAllocator: Allocator<N, D, D> + 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>>) -> Self::Output

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = VectorN<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = VectorN<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Point<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Point<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Unit<VectorN<N, D>>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Unit<VectorN<N, D>>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

fn mul_assign(&mut self, rhs: R)

Performs the *= operation.

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

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

Performs the *= operation.

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

fn one() -> Self

Creates a new identity isometry.

pub fn set_one(&mut self)

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

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

Returns true if self is equal to the multiplicative identity.

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

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

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

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

This method tests for !=.

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

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

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

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

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

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

fn default_max_relative() -> Self::Epsilon

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

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

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

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

The inverse of ApproxEq::relative_eq.

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

type Scaling = Id

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

The pure scaling component of this similarity transformation.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

pub 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.

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

fn to_superset(&self) -> 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>) -> Self

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

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

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

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

fn to_superset(&self) -> 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>) -> Self

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

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

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

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

fn to_superset(&self) -> 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>) -> Self

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

pub 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 UnitComplex<N1> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    R: AlgaRotation<Point2<N2>> + SupersetOf<Self>, 

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>) -> Self

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

pub 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 UnitQuaternion<N1> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    R: AlgaRotation<Point3<N2>> + SupersetOf<Self>, 

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>) -> Self

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

pub 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
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    R: Rotation<Point<N1, D>> + SubsetOf<MatrixN<N1, DimNameSum<D, U1>>> + SubsetOf<MatrixN<N2, DimNameSum<D, U1>>>,
    D: DimNameAdd<U1> + DimMin<D, Output = D>,
    DefaultAllocator: Allocator<N1, D> + Allocator<N1, D, D> + Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<(usize, usize), D> + Allocator<N2, D, D> + Allocator<N2, D>, 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

fn two_sided_inverse(&self) -> Self

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

fn two_sided_inverse_mut(&mut self)

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

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

fn default_max_ulps() -> u32

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

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

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

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

The inverse of ApproxEq::ulps_eq.