Struct rin::math::Isometry

#[repr(C)]
pub struct Isometry<N, D, R> where
    N: Scalar,
    D: DimName,
    DefaultAllocator: Allocator<N, D, U1>,  {
    pub rotation: R,
    pub translation: Translation<N, 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<N, D>

The pure translational part of this isometry.

Implementations

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

From the translation and rotation parts

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

Creates a new isometry from its rotational and translational parts.

Example

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

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

impl<N, D, R> Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

Inversion and in-place composition

#[must_use = "Did you mean to use inverse_mut()?"]

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

Inverts self.

Example

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

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

pub fn inverse_mut(&mut self)

Inverts self in-place.

Example

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

assert_eq!(iso * transformed_pt, pt);

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

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<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));

impl<N, D, R> Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

Transformation of a vector or a point

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

Transform the given point by this isometry.

This is the same as the multiplication self * pt.

Example

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

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

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

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

This is the same as the multiplication self * v.

Example

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

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

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

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

Example

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

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

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

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

Example

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

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

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

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

Conversion to a matrix

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

Converts this isometry into its equivalent homogeneous transformation matrix.

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
) -> Matrix<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer> where
    D: DimNameAdd<U1>,
    R: SubsetOf<Matrix<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

Converts this isometry into its equivalent homogeneous transformation matrix.

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<N, D, R> Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

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

Creates a new identity isometry.

Example

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

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

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

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

Example

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

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

impl<N> Isometry<N, U2, Rotation<N, U2>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

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

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

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

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

Example

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

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

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

Creates a new isometry from the given translation coordinates.

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

Creates a new isometry from the given rotation angle.

impl<N> Isometry<N, U2, Unit<Complex<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

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

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

Its rotational part is represented as an unit complex number.

Example

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

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

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

Creates a new isometry from the given translation coordinates.

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

Creates a new isometry from the given rotation angle.

impl<N> Isometry<N, U3, Unit<Quaternion<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

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

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

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

Example

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

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

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

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

Creates a new isometry from the given translation coordinates.

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

Creates a new isometry from the given rotation angle.

impl<N> Isometry<N, U3, Rotation<N, U3>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

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

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

Example

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

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

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

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

Creates a new isometry from the given translation coordinates.

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

Creates a new isometry from the given rotation angle.

impl<N> Isometry<N, U3, Unit<Quaternion<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

Construction from a 3D eye position and target point

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

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

It maps the z axis to the view direction target - eyeand the origin to the eye.

Arguments

• eye - The observer position.
• target - The target position.
• up - Vertical direction. The only requirement of this parameter is to not be collinear to eye - at. Non-collinearity is not checked.

Example

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

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

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

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

👎 Deprecated:

renamed to face_towards

Deprecated: Use Isometry::face_towards instead.

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

Builds a right-handed look-at view matrix.

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

Arguments

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

Example

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

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

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

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

Builds a left-handed look-at view matrix.

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

Arguments

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

Example

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

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

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

impl<N> Isometry<N, U3, Rotation<N, U3>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField, 

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

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

It maps the z axis to the view direction target - eyeand the origin to the eye.

Arguments

• eye - The observer position.
• target - The target position.
• up - Vertical direction. The only requirement of this parameter is to not be collinear to eye - at. Non-collinearity is not checked.

Example

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

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

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

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

👎 Deprecated:

renamed to face_towards

Deprecated: Use Isometry::face_towards instead.

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

Builds a right-handed look-at view matrix.

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

Arguments

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

Example

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

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

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

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

Builds a left-handed look-at view matrix.

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

Arguments

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

Example

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

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

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

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

Interpolation

pub fn lerp_slerp(
    &self,
    other: &Isometry<N, U3, Unit<Quaternion<N>>>,
    t: N
) -> Isometry<N, U3, Unit<Quaternion<N>>> where
    N: 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: &Isometry<N, U3, Unit<Quaternion<N>>>,
    t: N,
    epsilon: N
) -> Option<Isometry<N, U3, Unit<Quaternion<N>>>> where
    N: 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<N> Isometry<N, U3, Rotation<N, U3>> where
    N: SimdRealField, 

pub fn lerp_slerp(
    &self,
    other: &Isometry<N, U3, Rotation<N, U3>>,
    t: N
) -> Isometry<N, U3, Rotation<N, U3>> where
    N: 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: &Isometry<N, U3, Rotation<N, U3>>,
    t: N,
    epsilon: N
) -> Option<Isometry<N, U3, Rotation<N, U3>>> where
    N: 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<N> Isometry<N, U2, Unit<Complex<N>>> where
    N: SimdRealField, 

pub fn lerp_slerp(
    &self,
    other: &Isometry<N, U2, Unit<Complex<N>>>,
    t: N
) -> Isometry<N, U2, Unit<Complex<N>>> where
    N: 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<N> Isometry<N, U2, Rotation<N, U2>> where
    N: SimdRealField, 

pub fn lerp_slerp(
    &self,
    other: &Isometry<N, U2, Rotation<N, U2>>,
    t: N
) -> Isometry<N, U2, Rotation<N, U2>> where
    N: 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<N, D, R> AbsDiffEq<Isometry<N, D, R>> for Isometry<N, D, R> where
    N: RealField,
    D: DimName,
    R: AbstractRotation<N, D> + AbsDiffEq<R, Epsilon = <N as AbsDiffEq<N>>::Epsilon>,
    DefaultAllocator: Allocator<N, D, U1>,
    <N as AbsDiffEq<N>>::Epsilon: Copy, 

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

Used for specifying relative comparisons.

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

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

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

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

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

The inverse of AbsDiffEq::abs_diff_eq.

impl<N, D, R> Clone for Isometry<N, D, R> where
    N: Scalar,
    D: DimName,
    R: Clone,
    DefaultAllocator: Allocator<N, D, U1>, 

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

Returns a copy of the value.

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

Performs copy-assignment from source.

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

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

Formats the value using the given formatter.

impl<'de, N, D, R> Deserialize<'de> for Isometry<N, D, R> where
    N: Scalar,
    D: DimName,
    R: Deserialize<'de>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, D, U1>,
    <DefaultAllocator as Allocator<N, D, U1>>::Buffer: Deserialize<'de>, 

pub fn deserialize<__D>(
    __deserializer: __D
) -> Result<Isometry<N, D, R>, <__D as Deserializer<'de>>::Error> where
    __D: Deserializer<'de>, 

Deserialize this value from the given Serde deserializer.

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

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

Formats the value using the given formatter.

impl<'b, N, D, R> Div<&'b Isometry<N, D, R>> for Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Isometry<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'b, N, D, R> Div<&'b Isometry<N, D, R>> for Similarity<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, 'b, N, D, R> Div<&'b Isometry<N, D, R>> for &'a Similarity<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, 'b, N, D, R> Div<&'b Isometry<N, D, R>> for &'a Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Isometry<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'b, N, D> Div<&'b Isometry<N, D, Rotation<N, D>>> for Rotation<N, D> where
    N: SimdRealField,
    D: DimName,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'b, N, D> Div<&'b Rotation<N, D>> for Isometry<N, D, Rotation<N, D>> where
    N: SimdRealField,
    D: DimName,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'b, N, D, R> Div<&'b Similarity<N, D, R>> for Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, 'b, N, D, R> Div<&'b Similarity<N, D, R>> for &'a Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'b, N> Div<&'b Unit<Complex<N>>> for Isometry<N, U2, Unit<Complex<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>,
    DefaultAllocator: Allocator<N, U2, U1>, 

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

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, 'b, N> Div<&'b Unit<Complex<N>>> for &'a Isometry<N, U2, Unit<Complex<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>,
    DefaultAllocator: Allocator<N, U2, U1>, 

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

impl<N, D, R> Div<Isometry<N, D, R>> for Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Isometry<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<N, D, R> Div<Isometry<N, D, R>> for Similarity<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, N, D, R> Div<Isometry<N, D, R>> for &'a Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Isometry<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, N, D, R> Div<Isometry<N, D, R>> for &'a Similarity<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<N, D> Div<Isometry<N, D, Rotation<N, D>>> for Rotation<N, D> where
    N: SimdRealField,
    D: DimName,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, N, D> Div<Isometry<N, D, Rotation<N, D>>> for &'a Rotation<N, D> where
    N: SimdRealField,
    D: DimName,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

The resulting type after applying the / operator.

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

Performs the / operation.

impl<N> Div<Isometry<N, U3, Unit<Quaternion<N>>>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

impl<N, D> Div<Rotation<N, D>> for Isometry<N, D, Rotation<N, D>> where
    N: SimdRealField,
    D: DimName,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, N, D> Div<Rotation<N, D>> for &'a Isometry<N, D, Rotation<N, D>> where
    N: SimdRealField,
    D: DimName,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

The resulting type after applying the / operator.

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

Performs the / operation.

impl<N, D, R> Div<Similarity<N, D, R>> for Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, N, D, R> Div<Similarity<N, D, R>> for &'a Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, N> Div<Unit<Complex<N>>> for &'a Isometry<N, U2, Unit<Complex<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>,
    DefaultAllocator: Allocator<N, U2, U1>, 

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

The resulting type after applying the / operator.

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

Performs the / operation.

impl<N> Div<Unit<Complex<N>>> for Isometry<N, U2, Unit<Complex<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>,
    DefaultAllocator: Allocator<N, U2, U1>, 

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

The resulting type after applying the / operator.

pub fn div(
    self,
    rhs: Unit<Complex<N>>
) -> <Isometry<N, U2, Unit<Complex<N>>> as Div<Unit<Complex<N>>>>::Output

Performs the / operation.

impl<N> Div<Unit<Quaternion<N>>> for Isometry<N, U3, Unit<Quaternion<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'b, N, D, R> DivAssign<&'b Isometry<N, D, R>> for Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

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

Performs the /= operation.

impl<'b, N, D, R> DivAssign<&'b Isometry<N, D, R>> for Similarity<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

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

Performs the /= operation.

impl<'b, N, D> DivAssign<&'b Rotation<N, D>> for Isometry<N, D, Rotation<N, D>> where
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField,
    D: DimName,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, D, D>, 

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

Performs the /= operation.

impl<'b, N> DivAssign<&'b Unit<Complex<N>>> for Isometry<N, U2, Unit<Complex<N>>> where
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>,
    DefaultAllocator: Allocator<N, U2, U2>, 

pub fn div_assign(&mut self, rhs: &'b Unit<Complex<N>>)

Performs the /= operation.

impl<'b, N> DivAssign<&'b Unit<Quaternion<N>>> for Isometry<N, U3, Unit<Quaternion<N>>> where
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3>,
    DefaultAllocator: Allocator<N, U3, U3>, 

pub fn div_assign(&mut self, rhs: &'b Unit<Quaternion<N>>)

Performs the /= operation.

impl<N, D, R> DivAssign<Isometry<N, D, R>> for Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

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

Performs the /= operation.

impl<N, D, R> DivAssign<Isometry<N, D, R>> for Similarity<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

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

Performs the /= operation.

impl<N, D> DivAssign<Rotation<N, D>> for Isometry<N, D, Rotation<N, D>> where
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField,
    D: DimName,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, D, D>, 

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

Performs the /= operation.

impl<N> DivAssign<Unit<Complex<N>>> for Isometry<N, U2, Unit<Complex<N>>> where
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>,
    DefaultAllocator: Allocator<N, U2, U2>, 

pub fn div_assign(&mut self, rhs: Unit<Complex<N>>)

Performs the /= operation.

impl<N> DivAssign<Unit<Quaternion<N>>> for Isometry<N, U3, Unit<Quaternion<N>>> where
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3>,
    DefaultAllocator: Allocator<N, U3, U3>, 

pub fn div_assign(&mut self, rhs: Unit<Quaternion<N>>)

Performs the /= operation.

impl<'a> From<&'a Isometry<f32, U2, Unit<Complex<f32>>>> for Model

pub fn from(i: &Isometry<f32, U2, Unit<Complex<f32>>>) -> Model

Performs the conversion.

impl<'a> From<&'a Isometry<f32, U3, Unit<Quaternion<f32>>>> for Model

pub fn from(i: &Isometry<f32, U3, Unit<Quaternion<f32>>>) -> Model

Performs the conversion.

impl<N, D, R> From<[Isometry<<N as SimdValue>::Element, D, <R as SimdValue>::Element>; 16]> for Isometry<N, D, R> where
    N: Scalar + PrimitiveSimdValue + From<[<N as SimdValue>::Element; 16]>,
    D: DimName,
    R: SimdValue + AbstractRotation<N, D> + From<[<R as SimdValue>::Element; 16]>,
    <R as SimdValue>::Element: AbstractRotation<<N as SimdValue>::Element, D>,
    <N as SimdValue>::Element: Scalar,
    <N as SimdValue>::Element: Copy,
    <R as SimdValue>::Element: Scalar,
    <R as SimdValue>::Element: Copy,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<<N as SimdValue>::Element, D, U1>, 

pub fn from(
    arr: [Isometry<<N as SimdValue>::Element, D, <R as SimdValue>::Element>; 16]
) -> Isometry<N, D, R>

Performs the conversion.

impl<N, D, R> From<[Isometry<<N as SimdValue>::Element, D, <R as SimdValue>::Element>; 2]> for Isometry<N, D, R> where
    N: Scalar + PrimitiveSimdValue + From<[<N as SimdValue>::Element; 2]>,
    D: DimName,
    R: SimdValue + AbstractRotation<N, D> + From<[<R as SimdValue>::Element; 2]>,
    <R as SimdValue>::Element: AbstractRotation<<N as SimdValue>::Element, D>,
    <N as SimdValue>::Element: Scalar,
    <N as SimdValue>::Element: Copy,
    <R as SimdValue>::Element: Scalar,
    <R as SimdValue>::Element: Copy,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<<N as SimdValue>::Element, D, U1>, 

pub fn from(
    arr: [Isometry<<N as SimdValue>::Element, D, <R as SimdValue>::Element>; 2]
) -> Isometry<N, D, R>

Performs the conversion.

impl<N, D, R> From<[Isometry<<N as SimdValue>::Element, D, <R as SimdValue>::Element>; 4]> for Isometry<N, D, R> where
    N: Scalar + PrimitiveSimdValue + From<[<N as SimdValue>::Element; 4]>,
    D: DimName,
    R: SimdValue + AbstractRotation<N, D> + From<[<R as SimdValue>::Element; 4]>,
    <R as SimdValue>::Element: AbstractRotation<<N as SimdValue>::Element, D>,
    <N as SimdValue>::Element: Scalar,
    <N as SimdValue>::Element: Copy,
    <R as SimdValue>::Element: Scalar,
    <R as SimdValue>::Element: Copy,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<<N as SimdValue>::Element, D, U1>, 

pub fn from(
    arr: [Isometry<<N as SimdValue>::Element, D, <R as SimdValue>::Element>; 4]
) -> Isometry<N, D, R>

Performs the conversion.

impl<N, D, R> From<[Isometry<<N as SimdValue>::Element, D, <R as SimdValue>::Element>; 8]> for Isometry<N, D, R> where
    N: Scalar + PrimitiveSimdValue + From<[<N as SimdValue>::Element; 8]>,
    D: DimName,
    R: SimdValue + AbstractRotation<N, D> + From<[<R as SimdValue>::Element; 8]>,
    <R as SimdValue>::Element: AbstractRotation<<N as SimdValue>::Element, D>,
    <N as SimdValue>::Element: Scalar,
    <N as SimdValue>::Element: Copy,
    <R as SimdValue>::Element: Scalar,
    <R as SimdValue>::Element: Copy,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<<N as SimdValue>::Element, D, U1>, 

pub fn from(
    arr: [Isometry<<N as SimdValue>::Element, D, <R as SimdValue>::Element>; 8]
) -> Isometry<N, D, R>

Performs the conversion.

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

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

Performs the conversion.

impl From<Isometry<f32, U3, Unit<Quaternion<f32>>>> for Node

pub fn from(i: Isometry<f32, U3, Unit<Quaternion<f32>>>) -> Node

Performs the conversion.

impl<N, D, R> From<Translation<N, D>> for Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    DefaultAllocator: Allocator<N, D, U1>, 

pub fn from(tra: Translation<N, D>) -> Isometry<N, D, R>

Performs the conversion.

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

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

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> IsometryOps<N> for Isometry<N, U3, Unit<Quaternion<N>>> where
    N: RealField, 

pub fn absolute_transform_vector(
    &self,
    v: &Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>
) -> Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>

Transform a vector by the absolute value of the homogeneous matrix equivalent to self.

pub fn inverse_transform_unit_vector(
    &self,
    v: &Unit<Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>>
) -> Unit<Matrix<N, U3, U1, <DefaultAllocator as Allocator<N, U3, U1>>::Buffer>>

Transform a unit vector by the inverse of self.

pub fn lerp_slerp(
    &self,
    other: &Isometry<N, U3, Unit<Quaternion<N>>>,
    t: N
) -> Isometry<N, U3, Unit<Quaternion<N>>>

Interpolates between two isometries, using LERP for the translation part and SLERP for the rotation part.

impl<'b, N, D, R> Mul<&'b Isometry<N, D, R>> for Similarity<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b, N, D, R> Mul<&'b Isometry<N, D, R>> for &'a Similarity<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b, N, D, R> Mul<&'b Isometry<N, D, R>> for &'a Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, N, D, R> Mul<&'b Isometry<N, D, R>> for Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, N, D, R> Mul<&'b Isometry<N, D, R>> for Translation<N, D> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b, N, D, R> Mul<&'b Isometry<N, D, R>> for &'a Translation<N, D> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, N, D> Mul<&'b Isometry<N, D, Rotation<N, D>>> for Rotation<N, D> where
    N: SimdRealField,
    D: DimName,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, N> Mul<&'b Isometry<N, U2, Unit<Complex<N>>>> for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b, N, D, R> Mul<&'b Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>> for &'a Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, N, D, R> Mul<&'b Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>> for Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b, N, D, R> Mul<&'b Point<N, D>> for &'a Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Point<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, N, D, R> Mul<&'b Point<N, D>> for Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Point<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, N, D> Mul<&'b Rotation<N, D>> for Isometry<N, D, Rotation<N, D>> where
    N: SimdRealField,
    D: DimName,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b, N, D, R> Mul<&'b Similarity<N, D, R>> for &'a Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, N, D, R> Mul<&'b Similarity<N, D, R>> for Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b, N, D, R> Mul<&'b Translation<N, D>> for &'a Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, N, D, R> Mul<&'b Translation<N, D>> for Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, N> Mul<&'b Unit<Complex<N>>> for Isometry<N, U2, Unit<Complex<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>,
    DefaultAllocator: Allocator<N, U2, U1>, 

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b, N, D, R> Mul<&'b Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>> for &'a Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, N, D, R> Mul<&'b Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>> for Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N, D, R> Mul<Isometry<N, D, R>> for Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N, D, R> Mul<Isometry<N, D, R>> for &'a Similarity<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N, D, R> Mul<Isometry<N, D, R>> for &'a Translation<N, D> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N, D, R> Mul<Isometry<N, D, R>> for Translation<N, D> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N, D, R> Mul<Isometry<N, D, R>> for Similarity<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N, D, R> Mul<Isometry<N, D, R>> for &'a Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N, D> Mul<Isometry<N, D, Rotation<N, D>>> for Rotation<N, D> where
    N: SimdRealField,
    D: DimName,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N, D> Mul<Isometry<N, D, Rotation<N, D>>> for &'a Rotation<N, D> where
    N: SimdRealField,
    D: DimName,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N> Mul<Isometry<N, U2, Unit<Complex<N>>>> for &'a Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N> Mul<Isometry<N, U2, Unit<Complex<N>>>> for Unit<Complex<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>, 

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N> Mul<Isometry<N, U3, Unit<Quaternion<N>>>> for Unit<Quaternion<N>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N, D, R> Mul<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>> for &'a Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N, D, R> Mul<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>> for Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N, D, R> Mul<Point<N, D>> for Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Point<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N, D, R> Mul<Point<N, D>> for &'a Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Point<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N, D> Mul<Rotation<N, D>> for Isometry<N, D, Rotation<N, D>> where
    N: SimdRealField,
    D: DimName,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N, D> Mul<Rotation<N, D>> for &'a Isometry<N, D, Rotation<N, D>> where
    N: SimdRealField,
    D: DimName,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N, D, R> Mul<Similarity<N, D, R>> for &'a Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N, D, R> Mul<Similarity<N, D, R>> for Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N, D, R> Mul<Translation<N, D>> for Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N, D, R> Mul<Translation<N, D>> for &'a Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N> Mul<Unit<Complex<N>>> for &'a Isometry<N, U2, Unit<Complex<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>,
    DefaultAllocator: Allocator<N, U2, U1>, 

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N> Mul<Unit<Complex<N>>> for Isometry<N, U2, Unit<Complex<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U1>,
    DefaultAllocator: Allocator<N, U2, U1>, 

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, N, D, R> Mul<Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>> for &'a Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N, D, R> Mul<Unit<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>> for Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<N> Mul<Unit<Quaternion<N>>> for Isometry<N, U3, Unit<Quaternion<N>>> where
    N: SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U3, U1>, 

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, N, D, R> MulAssign<&'b Isometry<N, D, R>> for Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

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

Performs the *= operation.

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

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

Performs the *= operation.

impl<'b, N, D, R> MulAssign<&'b Isometry<N, D, R>> for Similarity<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

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

Performs the *= operation.

impl<'b, N, D> MulAssign<&'b Rotation<N, D>> for Isometry<N, D, Rotation<N, D>> where
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField,
    D: DimName,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, D, D>, 

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

Performs the *= operation.

impl<'b, N, D, R> MulAssign<&'b Translation<N, D>> for Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

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

Performs the *= operation.

impl<'b, N> MulAssign<&'b Unit<Complex<N>>> for Isometry<N, U2, Unit<Complex<N>>> where
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>,
    DefaultAllocator: Allocator<N, U2, U2>, 

pub fn mul_assign(&mut self, rhs: &'b Unit<Complex<N>>)

Performs the *= operation.

impl<'b, N> MulAssign<&'b Unit<Quaternion<N>>> for Isometry<N, U3, Unit<Quaternion<N>>> where
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3>,
    DefaultAllocator: Allocator<N, U3, U3>, 

pub fn mul_assign(&mut self, rhs: &'b Unit<Quaternion<N>>)

Performs the *= operation.

impl<N, D, R> MulAssign<Isometry<N, D, R>> for Similarity<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

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

Performs the *= operation.

impl<N, D, R> MulAssign<Isometry<N, D, R>> for Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

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

Performs the *= operation.

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

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

Performs the *= operation.

impl<N, D> MulAssign<Rotation<N, D>> for Isometry<N, D, Rotation<N, D>> where
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField,
    D: DimName,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, D, D>, 

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

Performs the *= operation.

impl<N, D, R> MulAssign<Translation<N, D>> for Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

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

Performs the *= operation.

impl<N> MulAssign<Unit<Complex<N>>> for Isometry<N, U2, Unit<Complex<N>>> where
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U2, U2>,
    DefaultAllocator: Allocator<N, U2, U2>, 

pub fn mul_assign(&mut self, rhs: Unit<Complex<N>>)

Performs the *= operation.

impl<N> MulAssign<Unit<Quaternion<N>>> for Isometry<N, U3, Unit<Quaternion<N>>> where
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + SimdRealField,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, U3, U3>,
    DefaultAllocator: Allocator<N, U3, U3>, 

pub fn mul_assign(&mut self, rhs: Unit<Quaternion<N>>)

Performs the *= operation.

impl<N, D, R> One for Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    DefaultAllocator: Allocator<N, D, U1>, 

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

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, D, R> PartialEq<Isometry<N, D, R>> for Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D> + PartialEq<R>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

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

#[must_use]

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

This method tests for !=.

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

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

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

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

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

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

The inverse of RelativeEq::relative_eq.

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

pub fn position_at_time(&self, N) -> Isometry<N, U3, Unit<Quaternion<N>>>

Get a position at the time t.

impl<N, D, R> Serialize for Isometry<N, D, R> where
    N: Scalar,
    D: DimName,
    R: Serialize,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, D, U1>,
    <DefaultAllocator as Allocator<N, D, U1>>::Buffer: Serialize, 

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

Serialize this value into the given Serde serializer.

impl<N, D, R> SimdValue for Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: SimdValue<SimdBool = <N as SimdValue>::SimdBool> + AbstractRotation<N, D>,
    <N as SimdValue>::Element: SimdRealField,
    <R as SimdValue>::Element: AbstractRotation<<N as SimdValue>::Element, D>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<<N as SimdValue>::Element, D, U1>, 

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

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

type SimdBool = <N as SimdValue>::SimdBool

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

pub fn lanes() -> usize

The number of lanes of this SIMD value.

pub fn splat(
    val: <Isometry<N, D, R> as SimdValue>::Element
) -> Isometry<N, D, R>

Initializes an SIMD value with each lanes set to val.

pub fn extract(&self, i: usize) -> <Isometry<N, D, R> as SimdValue>::Element

Extracts the i-th lane of self.

pub unsafe fn extract_unchecked(
    &self,
    i: usize
) -> <Isometry<N, D, R> as SimdValue>::Element

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

pub fn replace(
    &mut self,
    i: usize,
    val: <Isometry<N, D, R> as SimdValue>::Element
)

Replaces the i-th lane of self by val.

pub unsafe fn replace_unchecked(
    &mut self,
    i: usize,
    val: <Isometry<N, D, R> as SimdValue>::Element
)

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

pub fn select(
    self,
    cond: <Isometry<N, D, R> as SimdValue>::SimdBool,
    other: Isometry<N, D, R>
) -> Isometry<N, D, R>

Merges self and other depending on the lanes of cond.

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

Applies a function to each lane of self.

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

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

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

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

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

pub 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).

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

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

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

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

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

pub 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).

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

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

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

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

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

pub 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).

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

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

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 Unit<Complex<N1>> where
    R: AbstractRotation<N2, U2> + SupersetOf<Unit<Complex<N1>>>,
    N1: RealField,
    N2: RealField + SupersetOf<N1>, 

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

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

pub 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).

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

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

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 Unit<Quaternion<N1>> where
    R: AbstractRotation<N2, U3> + SupersetOf<Unit<Quaternion<N1>>>,
    N1: RealField,
    N2: RealField + SupersetOf<N1>, 

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

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

pub 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).

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

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

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

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

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

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

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

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

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

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

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

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

pub 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).

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

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

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
    C: SuperTCategoryOf<TAffine>,
    D: DimNameAdd<U1> + DimMin<D, Output = D>,
    R: AbstractRotation<N1, D> + SubsetOf<Matrix<N1, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N1, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>> + SubsetOf<Matrix<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>>,
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    DefaultAllocator: Allocator<N1, D, U1>,
    DefaultAllocator: Allocator<N1, D, D>,
    DefaultAllocator: Allocator<N1, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<(usize, usize), D, U1>,
    DefaultAllocator: Allocator<N2, D, D>,
    DefaultAllocator: Allocator<N2, D, U1>, 

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

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

pub 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).

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

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

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

pub fn default_max_ulps() -> u32

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

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

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

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

The inverse of UlpsEq::ulps_eq.

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

impl<N, D, R> Eq for Isometry<N, D, R> where
    N: SimdRealField,
    D: DimName,
    R: AbstractRotation<N, D> + Eq,
    DefaultAllocator: Allocator<N, D, U1>,