Struct nalgebra::geometry::Isometry

#[repr(C)]
pub struct Isometry<T, R, const D: usize> {
    pub rotation: R,
    pub translation: Translation<T, D>,
}

A direct isometry, i.e., a rotation followed by a translation (aka. a rigid-body motion).

This is also known as an element of a Special Euclidean (SE) group. The Isometry type can either represent a 2D or 3D isometry. A 2D isometry is composed of:

• A translation part of type Translation2
• A rotation part which can either be a UnitComplex or a Rotation2.

A 3D isometry is composed of:

• A translation part of type Translation3
• A rotation part which can either be a UnitQuaternion or a Rotation3.

Note that instead of using the Isometry type in your code directly, you should use one of its aliases: Isometry2, Isometry3, IsometryMatrix2, IsometryMatrix3. Though keep in mind that all the documentation of all the methods of these aliases will also appears on this page.

Construction

• From a 2D vector and/or an angle new, translation, rotation…
• From a 3D vector and/or an axis-angle new, translation, rotation…
• From a 3D eye position and target point look_at, look_at_lh, face_towards…
• From the translation and rotation parts from_parts…

Transformation and composition

Note that transforming vectors and points can be done by multiplication, e.g., isometry * point. Composing an isometry with another transformation can also be done by multiplication or division.

• Transformation of a vector or a point transform_vector, inverse_transform_point…
• Inversion and in-place composition inverse, append_rotation_wrt_point_mut…
• Interpolation lerp_slerp…

Conversion to a matrix

• Conversion to a matrix to_matrix…

Fields

rotation: R

The pure rotational part of this isometry.

translation: Translation<T, D>

The pure translational part of this isometry.

Implementations

impl<T: Scalar, R: AbstractRotation<T, D>, const D: usize> Isometry<T, R, D>

From the translation and rotation parts

pub fn from_parts(translation: Translation<T, 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);

impl<T: SimdRealField, R: AbstractRotation<T, D>, const D: usize> Isometry<T, R, D>where
    T::Element: SimdRealField,

Inversion and in-place composition

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 inv_mul(&self, rhs: &Isometry<T, R, D>) -> Self

Computes self.inverse() * rhs in a more efficient way.

Example

let mut iso1 = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);
let mut iso2 = Isometry2::new(Vector2::new(10.0, 20.0), f32::consts::FRAC_PI_4);

assert_eq!(iso1.inverse() * iso2, iso1.inv_mul(&iso2));

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

impl<T: SimdRealField, R: AbstractRotation<T, D>, const D: usize> Isometry<T, R, D>where
    T::Element: SimdRealField,

Transformation of a vector or a point

pub fn transform_point(&self, pt: &Point<T, D>) -> Point<T, 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: &SVector<T, D>) -> SVector<T, 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<T, D>) -> Point<T, 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: &SVector<T, D>) -> SVector<T, 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);

pub fn inverse_transform_unit_vector(
    &self,
    v: &Unit<SVector<T, D>>
) -> Unit<SVector<T, D>>

Transform the given unit 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::z() * f32::consts::FRAC_PI_2);
let iso = Isometry3::from_parts(tra, rot);

let transformed_point = iso.inverse_transform_unit_vector(&Vector3::x_axis());
assert_relative_eq!(transformed_point, -Vector3::y_axis(), epsilon = 1.0e-6);

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

Conversion to a matrix

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

Converts this isometry into its equivalent homogeneous transformation matrix.

This is the same as self.to_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);

pub fn to_matrix(
    &self
) -> OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>where
    Const<D>: DimNameAdd<U1>,
    R: SubsetOf<OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

Converts this isometry into its equivalent homogeneous transformation matrix.

This is the same as self.to_homogeneous().

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_matrix(), expected, epsilon = 1.0e-6);

impl<T: SimdRealField, R: AbstractRotation<T, D>, const D: usize> Isometry<T, R, D>where
    T::Element: SimdRealField,

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<T, 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<T: SimdRealField> Isometry<T, Rotation<T, 2>, 2>where
    T::Element: SimdRealField,

Construction from a 2D vector and/or a rotation angle

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

Creates a new isometry from the given translation coordinates.

pub fn rotation(angle: T) -> Self

Creates a new isometry from the given rotation angle.

pub fn cast<To: Scalar>(self) -> IsometryMatrix2<To>where
    IsometryMatrix2<To>: SupersetOf<Self>,

Cast the components of self to another type.

Example

let iso = IsometryMatrix2::<f64>::identity();
let iso2 = iso.cast::<f32>();
assert_eq!(iso2, IsometryMatrix2::<f32>::identity());

impl<T: SimdRealField> Isometry<T, Unit<Complex<T>>, 2>where
    T::Element: SimdRealField,

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

Creates a new isometry from the given translation coordinates.

pub fn rotation(angle: T) -> Self

Creates a new isometry from the given rotation angle.

pub fn cast<To: Scalar>(self) -> Isometry2<To>where
    Isometry2<To>: SupersetOf<Self>,

Cast the components of self to another type.

Example

let iso = Isometry2::<f64>::identity();
let iso2 = iso.cast::<f32>();
assert_eq!(iso2, Isometry2::<f32>::identity());

impl<T: SimdRealField> Isometry<T, Unit<Quaternion<T>>, 3>where
    T::Element: SimdRealField,

Construction from a 3D vector and/or an axis-angle

pub fn new(translation: Vector3<T>, axisangle: Vector3<T>) -> 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: T, y: T, z: T) -> Self

Creates a new isometry from the given translation coordinates.

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

Creates a new isometry from the given rotation angle.

pub fn cast<To: Scalar>(self) -> Isometry3<To>where
    Isometry3<To>: SupersetOf<Self>,

Cast the components of self to another type.

Example

let iso = Isometry3::<f64>::identity();
let iso2 = iso.cast::<f32>();
assert_eq!(iso2, Isometry3::<f32>::identity());

impl<T: SimdRealField> Isometry<T, Rotation<T, 3>, 3>where
    T::Element: SimdRealField,

pub fn new(translation: Vector3<T>, axisangle: Vector3<T>) -> 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: T, y: T, z: T) -> Self

Creates a new isometry from the given translation coordinates.

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

Creates a new isometry from the given rotation angle.

pub fn cast<To: Scalar>(self) -> IsometryMatrix3<To>where
    IsometryMatrix3<To>: SupersetOf<Self>,

Cast the components of self to another type.

Example

let iso = IsometryMatrix3::<f64>::identity();
let iso2 = iso.cast::<f32>();
assert_eq!(iso2, IsometryMatrix3::<f32>::identity());

impl<T: SimdRealField> Isometry<T, Unit<Quaternion<T>>, 3>where
    T::Element: SimdRealField,

Construction from a 3D eye position and target point

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

👎Deprecated: renamed to face_towards

Deprecated: Use Isometry::face_towards instead.

pub fn look_at_rh(eye: &Point3<T>, target: &Point3<T>, up: &Vector3<T>) -> 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<T>, target: &Point3<T>, up: &Vector3<T>) -> 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<T: SimdRealField> Isometry<T, Rotation<T, 3>, 3>where
    T::Element: SimdRealField,

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

👎Deprecated: renamed to face_towards

Deprecated: Use Isometry::face_towards instead.

pub fn look_at_rh(eye: &Point3<T>, target: &Point3<T>, up: &Vector3<T>) -> 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<T>, target: &Point3<T>, up: &Vector3<T>) -> 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<T: SimdRealField> Isometry<T, Unit<Quaternion<T>>, 3>

Interpolation

pub fn lerp_slerp(&self, other: &Self, t: T) -> Selfwhere
    T: RealField,

Interpolates between two isometries using a linear interpolation for the translation part, and a spherical interpolation for the rotation part.

Panics if the angle between both rotations is 180 degrees (in which case the interpolation is not well-defined). Use .try_lerp_slerp instead to avoid the panic.

Examples:

let t1 = Translation3::new(1.0, 2.0, 3.0);
let t2 = Translation3::new(4.0, 8.0, 12.0);
let q1 = UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0);
let q2 = UnitQuaternion::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0);
let iso1 = Isometry3::from_parts(t1, q1);
let iso2 = Isometry3::from_parts(t2, q2);

let iso3 = iso1.lerp_slerp(&iso2, 1.0 / 3.0);

assert_eq!(iso3.translation.vector, Vector3::new(2.0, 4.0, 6.0));
assert_eq!(iso3.rotation.euler_angles(), (std::f32::consts::FRAC_PI_2, 0.0, 0.0));

pub fn try_lerp_slerp(&self, other: &Self, t: T, epsilon: T) -> Option<Self>where
    T: RealField,

Attempts to interpolate between two isometries using a linear interpolation for the translation part, and a spherical interpolation for the rotation part.

Retuns None if the angle between both rotations is 180 degrees (in which case the interpolation is not well-defined).

Examples:

let t1 = Translation3::new(1.0, 2.0, 3.0);
let t2 = Translation3::new(4.0, 8.0, 12.0);
let q1 = UnitQuaternion::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0);
let q2 = UnitQuaternion::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0);
let iso1 = Isometry3::from_parts(t1, q1);
let iso2 = Isometry3::from_parts(t2, q2);

let iso3 = iso1.lerp_slerp(&iso2, 1.0 / 3.0);

assert_eq!(iso3.translation.vector, Vector3::new(2.0, 4.0, 6.0));
assert_eq!(iso3.rotation.euler_angles(), (std::f32::consts::FRAC_PI_2, 0.0, 0.0));

impl<T: SimdRealField> Isometry<T, Rotation<T, 3>, 3>

pub fn lerp_slerp(&self, other: &Self, t: T) -> Selfwhere
    T: RealField,

Interpolates between two isometries using a linear interpolation for the translation part, and a spherical interpolation for the rotation part.

Panics if the angle between both rotations is 180 degrees (in which case the interpolation is not well-defined). Use .try_lerp_slerp instead to avoid the panic.

Examples:

let t1 = Translation3::new(1.0, 2.0, 3.0);
let t2 = Translation3::new(4.0, 8.0, 12.0);
let q1 = Rotation3::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0);
let q2 = Rotation3::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0);
let iso1 = IsometryMatrix3::from_parts(t1, q1);
let iso2 = IsometryMatrix3::from_parts(t2, q2);

let iso3 = iso1.lerp_slerp(&iso2, 1.0 / 3.0);

assert_eq!(iso3.translation.vector, Vector3::new(2.0, 4.0, 6.0));
assert_eq!(iso3.rotation.euler_angles(), (std::f32::consts::FRAC_PI_2, 0.0, 0.0));

pub fn try_lerp_slerp(&self, other: &Self, t: T, epsilon: T) -> Option<Self>where
    T: RealField,

Attempts to interpolate between two isometries using a linear interpolation for the translation part, and a spherical interpolation for the rotation part.

Retuns None if the angle between both rotations is 180 degrees (in which case the interpolation is not well-defined).

Examples:

let t1 = Translation3::new(1.0, 2.0, 3.0);
let t2 = Translation3::new(4.0, 8.0, 12.0);
let q1 = Rotation3::from_euler_angles(std::f32::consts::FRAC_PI_4, 0.0, 0.0);
let q2 = Rotation3::from_euler_angles(-std::f32::consts::PI, 0.0, 0.0);
let iso1 = IsometryMatrix3::from_parts(t1, q1);
let iso2 = IsometryMatrix3::from_parts(t2, q2);

let iso3 = iso1.lerp_slerp(&iso2, 1.0 / 3.0);

assert_eq!(iso3.translation.vector, Vector3::new(2.0, 4.0, 6.0));
assert_eq!(iso3.rotation.euler_angles(), (std::f32::consts::FRAC_PI_2, 0.0, 0.0));

impl<T: SimdRealField> Isometry<T, Unit<Complex<T>>, 2>

pub fn lerp_slerp(&self, other: &Self, t: T) -> Selfwhere
    T: RealField,

Interpolates between two isometries using a linear interpolation for the translation part, and a spherical interpolation for the rotation part.

Panics if the angle between both rotations is 180 degrees (in which case the interpolation is not well-defined). Use .try_lerp_slerp instead to avoid the panic.

Examples:

let t1 = Translation2::new(1.0, 2.0);
let t2 = Translation2::new(4.0, 8.0);
let q1 = UnitComplex::new(std::f32::consts::FRAC_PI_4);
let q2 = UnitComplex::new(-std::f32::consts::PI);
let iso1 = Isometry2::from_parts(t1, q1);
let iso2 = Isometry2::from_parts(t2, q2);

let iso3 = iso1.lerp_slerp(&iso2, 1.0 / 3.0);

assert_eq!(iso3.translation.vector, Vector2::new(2.0, 4.0));
assert_relative_eq!(iso3.rotation.angle(), std::f32::consts::FRAC_PI_2);

impl<T: SimdRealField> Isometry<T, Rotation<T, 2>, 2>

pub fn lerp_slerp(&self, other: &Self, t: T) -> Selfwhere
    T: RealField,

Interpolates between two isometries using a linear interpolation for the translation part, and a spherical interpolation for the rotation part.

Panics if the angle between both rotations is 180 degrees (in which case the interpolation is not well-defined). Use .try_lerp_slerp instead to avoid the panic.

Examples:

let t1 = Translation2::new(1.0, 2.0);
let t2 = Translation2::new(4.0, 8.0);
let q1 = Rotation2::new(std::f32::consts::FRAC_PI_4);
let q2 = Rotation2::new(-std::f32::consts::PI);
let iso1 = IsometryMatrix2::from_parts(t1, q1);
let iso2 = IsometryMatrix2::from_parts(t2, q2);

let iso3 = iso1.lerp_slerp(&iso2, 1.0 / 3.0);

assert_eq!(iso3.translation.vector, Vector2::new(2.0, 4.0));
assert_relative_eq!(iso3.rotation.angle(), std::f32::consts::FRAC_PI_2);

Trait Implementations

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

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

Used for specifying relative comparisons.

fn default_epsilon() -> Self::Epsilon

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

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

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

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

The inverse of AbsDiffEq::abs_diff_eq.

impl<T: Clone, R: Clone, const D: usize> Clone for Isometry<T, R, D>

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

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<T: Debug, R: Debug, const D: usize> Debug for Isometry<T, R, D>

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

Formats the value using the given formatter.

impl<T: SimdRealField, R: AbstractRotation<T, D>, const D: usize> Default for Isometry<T, R, D>where
    T::Element: SimdRealField,

fn default() -> Self

Returns the “default value” for a type.

impl<T: RealField + Display, R, const D: usize> Display for Isometry<T, R, D>where
    R: Display,

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

Formats the value using the given formatter.

impl<'a, 'b, T: SimdRealField, R, const D: usize> Div<&'b Isometry<T, R, D>> for &'a Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

type Output = Isometry<T, R, D>

The resulting type after applying the / operator.

fn div(self, rhs: &'b Isometry<T, R, D>) -> Self::Output

Performs the / operation.

impl<'a, 'b, T: SimdRealField, R, const D: usize> Div<&'b Isometry<T, R, D>> for &'a Similarity<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

type Output = Similarity<T, R, D>

The resulting type after applying the / operator.

fn div(self, rhs: &'b Isometry<T, R, D>) -> Self::Output

Performs the / operation.

impl<'b, T: SimdRealField, R, const D: usize> Div<&'b Isometry<T, R, D>> for Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

type Output = Isometry<T, R, D>

The resulting type after applying the / operator.

fn div(self, rhs: &'b Isometry<T, R, D>) -> Self::Output

Performs the / operation.

impl<'b, T: SimdRealField, R, const D: usize> Div<&'b Isometry<T, R, D>> for Similarity<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

type Output = Similarity<T, R, D>

The resulting type after applying the / operator.

fn div(self, rhs: &'b Isometry<T, R, D>) -> Self::Output

Performs the / operation.

impl<'a, 'b, T: SimdRealField, const D: usize> Div<&'b Isometry<T, Rotation<T, D>, D>> for &'a Rotation<T, D>where
    T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, right: &'b Isometry<T, Rotation<T, D>, D>) -> Self::Output

Performs the / operation.

impl<'b, T: SimdRealField, const D: usize> Div<&'b Isometry<T, Rotation<T, D>, D>> for Rotation<T, D>where
    T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, right: &'b Isometry<T, Rotation<T, D>, D>) -> Self::Output

Performs the / operation.

impl<'a, 'b, T: SimdRealField> Div<&'b Isometry<T, Unit<Quaternion<T>>, 3>> for &'a UnitDualQuaternion<T>where
    T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div(self, rhs: &'b Isometry3<T>) -> Self::Output

Performs the / operation.

impl<'a, 'b, T: SimdRealField> Div<&'b Isometry<T, Unit<Quaternion<T>>, 3>> for &'a UnitQuaternion<T>where
    T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, right: &'b Isometry<T, UnitQuaternion<T>, 3>) -> Self::Output

Performs the / operation.

impl<'b, T: SimdRealField> Div<&'b Isometry<T, Unit<Quaternion<T>>, 3>> for UnitDualQuaternion<T>where
    T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div(self, rhs: &'b Isometry3<T>) -> Self::Output

Performs the / operation.

impl<'b, T: SimdRealField> Div<&'b Isometry<T, Unit<Quaternion<T>>, 3>> for UnitQuaternion<T>where
    T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, right: &'b Isometry<T, UnitQuaternion<T>, 3>) -> Self::Output

Performs the / operation.

impl<'a, 'b, T: SimdRealField, const D: usize> Div<&'b Rotation<T, D>> for &'a Isometry<T, Rotation<T, D>, D>where
    T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, rhs: &'b Rotation<T, D>) -> Self::Output

Performs the / operation.

impl<'b, T: SimdRealField, const D: usize> Div<&'b Rotation<T, D>> for Isometry<T, Rotation<T, D>, D>where
    T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, rhs: &'b Rotation<T, D>) -> Self::Output

Performs the / operation.

impl<'a, 'b, T: SimdRealField, R, const D: usize> Div<&'b Similarity<T, R, D>> for &'a Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

type Output = Similarity<T, R, D>

The resulting type after applying the / operator.

fn div(self, rhs: &'b Similarity<T, R, D>) -> Self::Output

Performs the / operation.

impl<'b, T: SimdRealField, R, const D: usize> Div<&'b Similarity<T, R, D>> for Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

type Output = Similarity<T, R, D>

The resulting type after applying the / operator.

fn div(self, rhs: &'b Similarity<T, R, D>) -> Self::Output

Performs the / operation.

impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for &'a Isometry<T, UnitComplex<T>, 2>where
    T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the / operation.

impl<'b, T: SimdRealField> Div<&'b Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>where
    T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the / operation.

impl<'a, 'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for &'a Isometry<T, UnitQuaternion<T>, 3>where
    T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'b, T: SimdRealField> Div<&'b Unit<Quaternion<T>>> for Isometry<T, UnitQuaternion<T>, 3>where
    T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'a, T: SimdRealField, R, const D: usize> Div<Isometry<T, R, D>> for &'a Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

type Output = Isometry<T, R, D>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, T: SimdRealField, R, const D: usize> Div<Isometry<T, R, D>> for &'a Similarity<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

type Output = Similarity<T, R, D>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<T: SimdRealField, R, const D: usize> Div<Isometry<T, R, D>> for Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

type Output = Isometry<T, R, D>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<T: SimdRealField, R, const D: usize> Div<Isometry<T, R, D>> for Similarity<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

type Output = Similarity<T, R, D>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, T: SimdRealField, const D: usize> Div<Isometry<T, Rotation<T, D>, D>> for &'a Rotation<T, D>where
    T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, right: Isometry<T, Rotation<T, D>, D>) -> Self::Output

Performs the / operation.

impl<T: SimdRealField, const D: usize> Div<Isometry<T, Rotation<T, D>, D>> for Rotation<T, D>where
    T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, right: Isometry<T, Rotation<T, D>, D>) -> Self::Output

Performs the / operation.

impl<'a, T: SimdRealField> Div<Isometry<T, Unit<Quaternion<T>>, 3>> for &'a UnitDualQuaternion<T>where
    T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div(self, rhs: Isometry3<T>) -> Self::Output

Performs the / operation.

impl<'a, T: SimdRealField> Div<Isometry<T, Unit<Quaternion<T>>, 3>> for &'a UnitQuaternion<T>where
    T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, right: Isometry<T, UnitQuaternion<T>, 3>) -> Self::Output

Performs the / operation.

impl<T: SimdRealField> Div<Isometry<T, Unit<Quaternion<T>>, 3>> for UnitDualQuaternion<T>where
    T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the / operator.

fn div(self, rhs: Isometry3<T>) -> Self::Output

Performs the / operation.

impl<T: SimdRealField> Div<Isometry<T, Unit<Quaternion<T>>, 3>> for UnitQuaternion<T>where
    T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, right: Isometry<T, UnitQuaternion<T>, 3>) -> Self::Output

Performs the / operation.

impl<'a, T: SimdRealField, const D: usize> Div<Rotation<T, D>> for &'a Isometry<T, Rotation<T, D>, D>where
    T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, rhs: Rotation<T, D>) -> Self::Output

Performs the / operation.

impl<T: SimdRealField, const D: usize> Div<Rotation<T, D>> for Isometry<T, Rotation<T, D>, D>where
    T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, rhs: Rotation<T, D>) -> Self::Output

Performs the / operation.

impl<'a, T: SimdRealField, R, const D: usize> Div<Similarity<T, R, D>> for &'a Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

type Output = Similarity<T, R, D>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<T: SimdRealField, R, const D: usize> Div<Similarity<T, R, D>> for Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

type Output = Similarity<T, R, D>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, T: SimdRealField> Div<Unit<Complex<T>>> for &'a Isometry<T, UnitComplex<T>, 2>where
    T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, rhs: UnitComplex<T>) -> Self::Output

Performs the / operation.

impl<T: SimdRealField> Div<Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>where
    T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, rhs: UnitComplex<T>) -> Self::Output

Performs the / operation.

impl<'a, T: SimdRealField> Div<Unit<Quaternion<T>>> for &'a Isometry<T, UnitQuaternion<T>, 3>where
    T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the / operation.

impl<T: SimdRealField> Div<Unit<Quaternion<T>>> for Isometry<T, UnitQuaternion<T>, 3>where
    T::Element: SimdRealField,

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

The resulting type after applying the / operator.

fn div(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the / operation.

impl<'b, T: SimdRealField, R, const D: usize> DivAssign<&'b Isometry<T, R, D>> for Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

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

Performs the /= operation.

impl<'b, T: SimdRealField, R, const D: usize> DivAssign<&'b Isometry<T, R, D>> for Similarity<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

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

Performs the /= operation.

impl<'b, T: SimdRealField> DivAssign<&'b Isometry<T, Unit<Quaternion<T>>, 3>> for UnitDualQuaternion<T>where
    T::Element: SimdRealField,

fn div_assign(&mut self, rhs: &'b Isometry3<T>)

Performs the /= operation.

impl<'b, T, const D: usize> DivAssign<&'b Rotation<T, D>> for Isometry<T, Rotation<T, D>, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
    T::Element: SimdRealField,

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

Performs the /= operation.

impl<'b, T> DivAssign<&'b Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
    T::Element: SimdRealField,

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

Performs the /= operation.

impl<'b, T> DivAssign<&'b Unit<Quaternion<T>>> for Isometry<T, UnitQuaternion<T>, 3>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
    T::Element: SimdRealField,

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

Performs the /= operation.

impl<T: SimdRealField, R, const D: usize> DivAssign<Isometry<T, R, D>> for Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

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

Performs the /= operation.

impl<T: SimdRealField, R, const D: usize> DivAssign<Isometry<T, R, D>> for Similarity<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

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

Performs the /= operation.

impl<T: SimdRealField> DivAssign<Isometry<T, Unit<Quaternion<T>>, 3>> for UnitDualQuaternion<T>where
    T::Element: SimdRealField,

fn div_assign(&mut self, rhs: Isometry3<T>)

Performs the /= operation.

impl<T, const D: usize> DivAssign<Rotation<T, D>> for Isometry<T, Rotation<T, D>, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
    T::Element: SimdRealField,

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

Performs the /= operation.

impl<T> DivAssign<Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
    T::Element: SimdRealField,

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

Performs the /= operation.

impl<T> DivAssign<Unit<Quaternion<T>>> for Isometry<T, UnitQuaternion<T>, 3>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
    T::Element: SimdRealField,

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

Performs the /= operation.

impl<T, R, const D: usize> From<[Isometry<<T as SimdValue>::Element, <R as SimdValue>::Element, D>; 16]> for Isometry<T, R, D>where
    T: From<[<T as SimdValue>::Element; 16]> + Scalar + PrimitiveSimdValue,
    R: SimdValue + AbstractRotation<T, D> + From<[<R as SimdValue>::Element; 16]>,
    R::Element: AbstractRotation<T::Element, D> + Scalar + Copy,
    T::Element: Scalar + Copy,

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

Converts to this type from the input type.

impl<T, R, const D: usize> From<[Isometry<<T as SimdValue>::Element, <R as SimdValue>::Element, D>; 2]> for Isometry<T, R, D>where
    T: From<[<T as SimdValue>::Element; 2]> + Scalar + PrimitiveSimdValue,
    R: SimdValue + AbstractRotation<T, D> + From<[<R as SimdValue>::Element; 2]>,
    R::Element: AbstractRotation<T::Element, D> + Scalar + Copy,
    T::Element: Scalar + Copy,

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

Converts to this type from the input type.

impl<T, R, const D: usize> From<[Isometry<<T as SimdValue>::Element, <R as SimdValue>::Element, D>; 4]> for Isometry<T, R, D>where
    T: From<[<T as SimdValue>::Element; 4]> + Scalar + PrimitiveSimdValue,
    R: SimdValue + AbstractRotation<T, D> + From<[<R as SimdValue>::Element; 4]>,
    R::Element: AbstractRotation<T::Element, D> + Scalar + Copy,
    T::Element: Scalar + Copy,

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

Converts to this type from the input type.

impl<T, R, const D: usize> From<[Isometry<<T as SimdValue>::Element, <R as SimdValue>::Element, D>; 8]> for Isometry<T, R, D>where
    T: From<[<T as SimdValue>::Element; 8]> + Scalar + PrimitiveSimdValue,
    R: SimdValue + AbstractRotation<T, D> + From<[<R as SimdValue>::Element; 8]>,
    R::Element: AbstractRotation<T::Element, D> + Scalar + Copy,
    T::Element: Scalar + Copy,

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

Converts to this type from the input type.

impl<T: SimdRealField, R, const D: usize> From<[T; D]> for Isometry<T, R, D>where
    R: AbstractRotation<T, D>,

fn from(coords: [T; D]) -> Self

Converts to this type from the input type.

impl<T: SimdRealField, R, const D: usize> From<Isometry<T, R, D>> for OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>where
    Const<D>: DimNameAdd<U1>,
    R: SubsetOf<OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

Converts to this type from the input type.

impl<T: SimdRealField> From<Isometry<T, Unit<Quaternion<T>>, 3>> for UnitDualQuaternion<T>where
    T::Element: SimdRealField,

fn from(iso: Isometry3<T>) -> Self

Converts to this type from the input type.

impl<T: SimdRealField, R, const D: usize> From<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for Isometry<T, R, D>where
    R: AbstractRotation<T, D>,

fn from(coords: SVector<T, D>) -> Self

Converts to this type from the input type.

impl<T: SimdRealField, R, const D: usize> From<OPoint<T, Const<D>>> for Isometry<T, R, D>where
    R: AbstractRotation<T, D>,

fn from(coords: Point<T, D>) -> Self

Converts to this type from the input type.

impl<T: SimdRealField, R: AbstractRotation<T, D>, const D: usize> From<Translation<T, D>> for Isometry<T, R, D>

fn from(tra: Translation<T, D>) -> Self

Converts to this type from the input type.

impl<T: Scalar + Hash, R: Hash, const D: usize> Hash for Isometry<T, R, D>where
    Owned<T, Const<D>>: Hash,

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

Feeds this value into the given Hasher.

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

Feeds a slice of this type into the given Hasher.

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

type Output = Isometry<T, R, D>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Isometry<T, R, D>) -> Self::Output

Performs the * operation.

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

type Output = Similarity<T, R, D>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Isometry<T, R, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T, C, R, const D: usize> Mul<&'b Isometry<T, R, D>> for &'a Transform<T, C, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    R: SubsetOf<OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Isometry<T, R, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField, R, const D: usize> Mul<&'b Isometry<T, R, D>> for &'a Translation<T, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

type Output = Isometry<T, R, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Isometry<T, R, D>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField, R, const D: usize> Mul<&'b Isometry<T, R, D>> for Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

type Output = Isometry<T, R, D>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Isometry<T, R, D>) -> Self::Output

Performs the * operation.

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

type Output = Similarity<T, R, D>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Isometry<T, R, D>) -> Self::Output

Performs the * operation.

impl<'b, T, C, R, const D: usize> Mul<&'b Isometry<T, R, D>> for Transform<T, C, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    R: SubsetOf<OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Isometry<T, R, D>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField, R, const D: usize> Mul<&'b Isometry<T, R, D>> for Translation<T, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

type Output = Isometry<T, R, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Isometry<T, R, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField, const D: usize> Mul<&'b Isometry<T, Rotation<T, D>, D>> for &'a Rotation<T, D>where
    T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, right: &'b Isometry<T, Rotation<T, D>, D>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField, const D: usize> Mul<&'b Isometry<T, Rotation<T, D>, D>> for Rotation<T, D>where
    T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, right: &'b Isometry<T, Rotation<T, D>, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField> Mul<&'b Isometry<T, Unit<Complex<T>>, 2>> for &'a UnitComplex<T>where
    T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Isometry<T, UnitComplex<T>, 2>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField> Mul<&'b Isometry<T, Unit<Complex<T>>, 2>> for UnitComplex<T>where
    T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Isometry<T, UnitComplex<T>, 2>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField> Mul<&'b Isometry<T, Unit<Quaternion<T>>, 3>> for &'a UnitDualQuaternion<T>where
    T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Isometry3<T>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField> Mul<&'b Isometry<T, Unit<Quaternion<T>>, 3>> for &'a UnitQuaternion<T>where
    T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, right: &'b Isometry<T, UnitQuaternion<T>, 3>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField> Mul<&'b Isometry<T, Unit<Quaternion<T>>, 3>> for UnitDualQuaternion<T>where
    T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Isometry3<T>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField> Mul<&'b Isometry<T, Unit<Quaternion<T>>, 3>> for UnitQuaternion<T>where
    T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, right: &'b Isometry<T, UnitQuaternion<T>, 3>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField, R, const D: usize> Mul<&'b Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for &'a Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

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

The resulting type after applying the * operator.

fn mul(self, right: &'b SVector<T, D>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField, R, const D: usize> Mul<&'b Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

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

The resulting type after applying the * operator.

fn mul(self, right: &'b SVector<T, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField, R, const D: usize> Mul<&'b OPoint<T, Const<D>>> for &'a Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

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

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<T, D>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField, R, const D: usize> Mul<&'b OPoint<T, Const<D>>> for Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

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

The resulting type after applying the * operator.

fn mul(self, right: &'b Point<T, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField, const D: usize> Mul<&'b Rotation<T, D>> for &'a Isometry<T, Rotation<T, D>, D>where
    T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Rotation<T, D>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField, const D: usize> Mul<&'b Rotation<T, D>> for Isometry<T, Rotation<T, D>, D>where
    T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Rotation<T, D>) -> Self::Output

Performs the * operation.

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

type Output = Similarity<T, R, D>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Similarity<T, R, D>) -> Self::Output

Performs the * operation.

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

type Output = Similarity<T, R, D>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Similarity<T, R, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T, C, R, const D: usize> Mul<&'b Transform<T, C, D>> for &'a Isometry<T, R, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    R: SubsetOf<OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Transform<T, C, D>) -> Self::Output

Performs the * operation.

impl<'b, T, C, R, const D: usize> Mul<&'b Transform<T, C, D>> for Isometry<T, R, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    R: SubsetOf<OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Transform<T, C, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField, R, const D: usize> Mul<&'b Translation<T, D>> for &'a Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

type Output = Isometry<T, R, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Translation<T, D>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField, R, const D: usize> Mul<&'b Translation<T, D>> for Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

type Output = Isometry<T, R, D>

The resulting type after applying the * operator.

fn mul(self, right: &'b Translation<T, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for &'a Isometry<T, UnitComplex<T>, 2>where
    T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField> Mul<&'b Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>where
    T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitComplex<T>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField, R, const D: usize> Mul<&'b Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>> for &'a Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

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

The resulting type after applying the * operator.

fn mul(self, right: &'b Unit<SVector<T, D>>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField, R, const D: usize> Mul<&'b Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>> for Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

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

The resulting type after applying the * operator.

fn mul(self, right: &'b Unit<SVector<T, D>>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for &'a Isometry<T, UnitQuaternion<T>, 3>where
    T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField> Mul<&'b Unit<Quaternion<T>>> for Isometry<T, UnitQuaternion<T>, 3>where
    T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField, R, const D: usize> Mul<Isometry<T, R, D>> for &'a Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

type Output = Isometry<T, R, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<T, R, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, T, C, R, const D: usize> Mul<Isometry<T, R, D>> for &'a Transform<T, C, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    R: SubsetOf<OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, T: SimdRealField, R, const D: usize> Mul<Isometry<T, R, D>> for &'a Translation<T, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

type Output = Isometry<T, R, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T: SimdRealField, R, const D: usize> Mul<Isometry<T, R, D>> for Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

type Output = Isometry<T, R, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T: SimdRealField, R, const D: usize> Mul<Isometry<T, R, D>> for Similarity<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

type Output = Similarity<T, R, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T: SimdRealField, R, const D: usize> Mul<Isometry<T, R, D>> for Translation<T, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

type Output = Isometry<T, R, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, T: SimdRealField, const D: usize> Mul<Isometry<T, Rotation<T, D>, D>> for &'a Rotation<T, D>where
    T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, right: Isometry<T, Rotation<T, D>, D>) -> Self::Output

Performs the * operation.

impl<T: SimdRealField, const D: usize> Mul<Isometry<T, Rotation<T, D>, D>> for Rotation<T, D>where
    T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, right: Isometry<T, Rotation<T, D>, D>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField> Mul<Isometry<T, Unit<Complex<T>>, 2>> for &'a UnitComplex<T>where
    T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: Isometry<T, UnitComplex<T>, 2>) -> Self::Output

Performs the * operation.

impl<T: SimdRealField> Mul<Isometry<T, Unit<Complex<T>>, 2>> for UnitComplex<T>where
    T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: Isometry<T, UnitComplex<T>, 2>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField> Mul<Isometry<T, Unit<Quaternion<T>>, 3>> for &'a UnitDualQuaternion<T>where
    T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: Isometry3<T>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField> Mul<Isometry<T, Unit<Quaternion<T>>, 3>> for &'a UnitQuaternion<T>where
    T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, right: Isometry<T, UnitQuaternion<T>, 3>) -> Self::Output

Performs the * operation.

impl<T: SimdRealField> Mul<Isometry<T, Unit<Quaternion<T>>, 3>> for UnitDualQuaternion<T>where
    T::Element: SimdRealField,

type Output = Unit<DualQuaternion<T>>

The resulting type after applying the * operator.

fn mul(self, rhs: Isometry3<T>) -> Self::Output

Performs the * operation.

impl<T: SimdRealField> Mul<Isometry<T, Unit<Quaternion<T>>, 3>> for UnitQuaternion<T>where
    T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, right: Isometry<T, UnitQuaternion<T>, 3>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField, R, const D: usize> Mul<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for &'a Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

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

The resulting type after applying the * operator.

fn mul(self, right: SVector<T, D>) -> Self::Output

Performs the * operation.

impl<T: SimdRealField, R, const D: usize> Mul<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

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

The resulting type after applying the * operator.

fn mul(self, right: SVector<T, D>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField, R, const D: usize> Mul<OPoint<T, Const<D>>> for &'a Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T: SimdRealField, R, const D: usize> Mul<OPoint<T, Const<D>>> for Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, T: SimdRealField, const D: usize> Mul<Rotation<T, D>> for &'a Isometry<T, Rotation<T, D>, D>where
    T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: Rotation<T, D>) -> Self::Output

Performs the * operation.

impl<T: SimdRealField, const D: usize> Mul<Rotation<T, D>> for Isometry<T, Rotation<T, D>, D>where
    T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: Rotation<T, D>) -> Self::Output

Performs the * operation.

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

type Output = Similarity<T, R, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T: SimdRealField, R, const D: usize> Mul<Similarity<T, R, D>> for Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

type Output = Similarity<T, R, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, T, C, R, const D: usize> Mul<Transform<T, C, D>> for &'a Isometry<T, R, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    R: SubsetOf<OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, T: SimdRealField, R, const D: usize> Mul<Translation<T, D>> for &'a Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

type Output = Isometry<T, R, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T: SimdRealField, R, const D: usize> Mul<Translation<T, D>> for Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

type Output = Isometry<T, R, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, T: SimdRealField> Mul<Unit<Complex<T>>> for &'a Isometry<T, UnitComplex<T>, 2>where
    T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the * operation.

impl<T: SimdRealField> Mul<Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>where
    T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: UnitComplex<T>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField, R, const D: usize> Mul<Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>> for &'a Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

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

The resulting type after applying the * operator.

fn mul(self, right: Unit<SVector<T, D>>) -> Self::Output

Performs the * operation.

impl<T: SimdRealField, R, const D: usize> Mul<Unit<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>>> for Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

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

The resulting type after applying the * operator.

fn mul(self, right: Unit<SVector<T, D>>) -> Self::Output

Performs the * operation.

impl<'a, T: SimdRealField> Mul<Unit<Quaternion<T>>> for &'a Isometry<T, UnitQuaternion<T>, 3>where
    T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<T: SimdRealField> Mul<Unit<Quaternion<T>>> for Isometry<T, UnitQuaternion<T>, 3>where
    T::Element: SimdRealField,

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

The resulting type after applying the * operator.

fn mul(self, rhs: UnitQuaternion<T>) -> Self::Output

Performs the * operation.

impl<'b, T: SimdRealField, R, const D: usize> MulAssign<&'b Isometry<T, R, D>> for Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

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

Performs the *= operation.

impl<'b, T: SimdRealField, R, const D: usize> MulAssign<&'b Isometry<T, R, D>> for Similarity<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

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

Performs the *= operation.

impl<'b, T, C, R, const D: usize> MulAssign<&'b Isometry<T, R, D>> for Transform<T, C, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategory,
    R: SubsetOf<OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

Performs the *= operation.

impl<'b, T: SimdRealField> MulAssign<&'b Isometry<T, Unit<Quaternion<T>>, 3>> for UnitDualQuaternion<T>where
    T::Element: SimdRealField,

fn mul_assign(&mut self, rhs: &'b Isometry3<T>)

Performs the *= operation.

impl<'b, T, const D: usize> MulAssign<&'b Rotation<T, D>> for Isometry<T, Rotation<T, D>, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
    T::Element: SimdRealField,

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

Performs the *= operation.

impl<'b, T: SimdRealField, R, const D: usize> MulAssign<&'b Translation<T, D>> for Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

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

Performs the *= operation.

impl<'b, T> MulAssign<&'b Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
    T::Element: SimdRealField,

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

Performs the *= operation.

impl<'b, T> MulAssign<&'b Unit<Quaternion<T>>> for Isometry<T, UnitQuaternion<T>, 3>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
    T::Element: SimdRealField,

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

Performs the *= operation.

impl<T: SimdRealField, R, const D: usize> MulAssign<Isometry<T, R, D>> for Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

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

Performs the *= operation.

impl<T: SimdRealField, R, const D: usize> MulAssign<Isometry<T, R, D>> for Similarity<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

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

Performs the *= operation.

impl<T, C, R, const D: usize> MulAssign<Isometry<T, R, D>> for Transform<T, C, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategory,
    R: SubsetOf<OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

Performs the *= operation.

impl<T: SimdRealField> MulAssign<Isometry<T, Unit<Quaternion<T>>, 3>> for UnitDualQuaternion<T>where
    T::Element: SimdRealField,

fn mul_assign(&mut self, rhs: Isometry3<T>)

Performs the *= operation.

impl<T, const D: usize> MulAssign<Rotation<T, D>> for Isometry<T, Rotation<T, D>, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
    T::Element: SimdRealField,

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

Performs the *= operation.

impl<T: SimdRealField, R, const D: usize> MulAssign<Translation<T, D>> for Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: AbstractRotation<T, D>,

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

Performs the *= operation.

impl<T> MulAssign<Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
    T::Element: SimdRealField,

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

Performs the *= operation.

impl<T> MulAssign<Unit<Quaternion<T>>> for Isometry<T, UnitQuaternion<T>, 3>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField,
    T::Element: SimdRealField,

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

Performs the *= operation.

impl<T: SimdRealField, R: AbstractRotation<T, D>, const D: usize> One for Isometry<T, R, D>where
    T::Element: SimdRealField,

fn one() -> Self

Creates a new identity isometry.

fn set_one(&mut self)

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

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

Returns true if self is equal to the multiplicative identity.

impl<T: SimdRealField, R, const D: usize> PartialEq<Isometry<T, R, D>> for Isometry<T, R, D>where
    R: AbstractRotation<T, D> + PartialEq,

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

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

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

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

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

fn default_max_relative() -> Self::Epsilon

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

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

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

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

The inverse of RelativeEq::relative_eq.

impl<T: SimdRealField, R, const D: usize> SimdValue for Isometry<T, R, D>where
    T::Element: SimdRealField,
    R: SimdValue<SimdBool = T::SimdBool> + AbstractRotation<T, D>,
    R::Element: AbstractRotation<T::Element, D>,

type Element = Isometry<<T as SimdValue>::Element, <R as SimdValue>::Element, D>

The type of the elements of each lane of this SIMD value.

type SimdBool = <T as SimdValue>::SimdBool

Type of the result of comparing two SIMD values like self.

fn lanes() -> usize

The number of lanes of this SIMD value.

fn splat(val: Self::Element) -> Self

Initializes an SIMD value with each lanes set to val.

fn extract(&self, i: usize) -> Self::Element

Extracts the i-th lane of self.

unsafe fn extract_unchecked(&self, i: usize) -> Self::Element

Extracts the i-th lane of self without bound-checking.

fn replace(&mut self, i: usize, val: Self::Element)

Replaces the i-th lane of self by val.

unsafe fn replace_unchecked(&mut self, i: usize, val: Self::Element)

Replaces the i-th lane of self by val without bound-checking.

fn select(self, cond: Self::SimdBool, other: Self) -> Self

Merges self and other depending on the lanes of cond.

fn map_lanes(self, f: impl Fn(Self::Element) -> Self::Element) -> Selfwhere
    Self: Clone,

Applies a function to each lane of self.

fn zip_map_lanes(
    self,
    b: Self,
    f: impl Fn(Self::Element, Self::Element) -> Self::Element
) -> Selfwhere
    Self: Clone,

Applies a function to each lane of self paired with the corresponding lane of b.

impl<T1, T2, R> SubsetOf<Isometry<T2, R, 2>> for UnitComplex<T1>where
    T1: RealField,
    T2: RealField + SupersetOf<T1>,
    R: AbstractRotation<T2, 2> + SupersetOf<Self>,

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

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

fn is_in_subset(iso: &Isometry<T2, R, 2>) -> bool

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

fn from_superset_unchecked(iso: &Isometry<T2, R, 2>) -> Self

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

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

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

impl<T1, T2, R> SubsetOf<Isometry<T2, R, 3>> for UnitQuaternion<T1>where
    T1: RealField,
    T2: RealField + SupersetOf<T1>,
    R: AbstractRotation<T2, 3> + SupersetOf<Self>,

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

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

fn is_in_subset(iso: &Isometry<T2, R, 3>) -> bool

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

fn from_superset_unchecked(iso: &Isometry<T2, R, 3>) -> Self

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

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

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

impl<T1, T2, R, const D: usize> SubsetOf<Isometry<T2, R, D>> for Rotation<T1, D>where
    T1: RealField,
    T2: RealField + SupersetOf<T1>,
    R: AbstractRotation<T2, D> + SupersetOf<Self>,

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

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

fn is_in_subset(iso: &Isometry<T2, R, D>) -> bool

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

fn from_superset_unchecked(iso: &Isometry<T2, R, D>) -> Self

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

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

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

impl<T1, T2, R, const D: usize> SubsetOf<Isometry<T2, R, D>> for Translation<T1, D>where
    T1: RealField,
    T2: RealField + SupersetOf<T1>,
    R: AbstractRotation<T2, D>,

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

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

fn is_in_subset(iso: &Isometry<T2, R, D>) -> bool

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

fn from_superset_unchecked(iso: &Isometry<T2, R, D>) -> Self

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

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

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

impl<T1, T2, R1, R2, const D: usize> SubsetOf<Isometry<T2, R2, D>> for Isometry<T1, R1, D>where
    T1: RealField,
    T2: RealField + SupersetOf<T1>,
    R1: AbstractRotation<T1, D> + SubsetOf<R2>,
    R2: AbstractRotation<T2, D>,

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

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

fn is_in_subset(iso: &Isometry<T2, R2, D>) -> bool

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

fn from_superset_unchecked(iso: &Isometry<T2, R2, D>) -> Self

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

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

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

impl<T1, T2> SubsetOf<Isometry<T2, Unit<Quaternion<T2>>, 3>> for UnitDualQuaternion<T1>where
    T1: RealField,
    T2: RealField + SupersetOf<T1>,

fn to_superset(&self) -> Isometry3<T2>

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

fn is_in_subset(iso: &Isometry3<T2>) -> bool

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

fn from_superset_unchecked(iso: &Isometry3<T2>) -> Self

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

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

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

impl<T1, T2, R, const D: usize> SubsetOf<Matrix<T2, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output, <DefaultAllocator as Allocator<T2, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>>::Buffer>> for Isometry<T1, R, D>where
    T1: RealField,
    T2: RealField + SupersetOf<T1>,
    R: AbstractRotation<T1, D> + SubsetOf<OMatrix<T1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>> + SubsetOf<OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>,
    Const<D>: DimNameAdd<U1> + DimMin<Const<D>, Output = Const<D>>,
    DefaultAllocator: Allocator<T1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> + Allocator<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> + Allocator<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

fn to_superset(
    &self
) -> OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>

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

fn is_in_subset(
    m: &OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
) -> bool

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

fn from_superset_unchecked(
    m: &OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
) -> Self

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

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

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

impl<T1, T2, R1, R2, const D: usize> SubsetOf<Similarity<T2, R2, D>> for Isometry<T1, R1, D>where
    T1: RealField,
    T2: RealField + SupersetOf<T1>,
    R1: AbstractRotation<T1, D> + SubsetOf<R2>,
    R2: AbstractRotation<T2, D>,

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

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

fn is_in_subset(sim: &Similarity<T2, R2, D>) -> bool

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

fn from_superset_unchecked(sim: &Similarity<T2, R2, D>) -> Self

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

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

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

impl<T1, T2, R, C, const D: usize> SubsetOf<Transform<T2, C, D>> for Isometry<T1, R, D>where
    T1: RealField,
    T2: RealField + SupersetOf<T1>,
    C: SuperTCategoryOf<TAffine>,
    R: AbstractRotation<T1, D> + SubsetOf<OMatrix<T1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>> + SubsetOf<OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>,
    Const<D>: DimNameAdd<U1> + DimMin<Const<D>, Output = Const<D>>,
    DefaultAllocator: Allocator<T1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> + Allocator<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> + Allocator<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

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

fn is_in_subset(t: &Transform<T2, C, D>) -> bool

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

fn from_superset_unchecked(t: &Transform<T2, C, D>) -> Self

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

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

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

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

fn default_max_ulps() -> u32

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

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

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

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

The inverse of UlpsEq::ulps_eq.

impl<T: Copy, R: Copy, const D: usize> Copy for Isometry<T, R, D>

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