Type Alias Isometry2

pub type Isometry2<T> = Isometry<T, UnitComplex<T>, 2>;

A 2-dimensional direct isometry using a unit complex number for its rotational part.

Because this is an alias, not all its methods are listed here. See the Isometry type too.

Also known as a 2D rigid-body motion, or as an element of SE(2).

Aliased Type

struct Isometry2<T> {
    pub rotation: Unit<Complex<T>>,
    pub translation: Translation<T, 2>,
}

Fields

rotation: Unit<Complex<T>>

The pure rotational part of this isometry.

translation: Translation<T, 2>

The pure translational part of this isometry.

Implementations

impl<T: SimdRealField> Isometry2<T>

where T::Element: SimdRealField,

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

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

Its rotational part is represented as an unit complex number.

Example

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

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

pub fn translation(x: T, y: T) -> Self

Creates a new isometry from the given translation coordinates.

pub fn rotation(angle: T) -> Self

Creates a new isometry from the given rotation angle.

pub fn cast<To: Scalar>(self) -> Isometry2<To>

where Isometry2<To>: SupersetOf<Self>,

Cast the components of self to another type.

Example

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

impl<T: SimdRealField> Isometry2<T>

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

where T: RealField,

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

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

Examples:

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

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

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

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

From the translation and rotation parts

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

Creates a new isometry from its rotational and translational parts.

Example

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

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

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

where T::Element: SimdRealField,

Inversion and in-place composition

pub fn inverse(&self) -> Self

Inverts self.

Example

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

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

pub fn inverse_mut(&mut self)

Inverts self in-place.

Example

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

assert_eq!(iso * transformed_pt, pt);

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

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

Example

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

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

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

Appends to self the given translation in-place.

Example

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

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

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

Appends to self the given rotation in-place.

Example

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

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

pub fn append_rotation_wrt_point_mut(&mut self, r: &R, p: &Point<T, D>)

Appends in-place to self a rotation centered at the point p, i.e., the rotation that lets p invariant.

Example

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

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

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

Appends in-place to self a rotation centered at the point with coordinates self.translation.

Example

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

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

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

where T::Element: SimdRealField,

Transformation of a vector or a point

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

Transform the given point by this isometry.

This is the same as the multiplication self * pt.

Example

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

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

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

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

This is the same as the multiplication self * v.

Example

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

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

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

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

Example

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

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

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

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

Example

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

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

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

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

Example

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

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

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

Conversion to a matrix

pub fn to_homogeneous( &self, ) -> OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>

where Const<D>: DimNameAdd<U1>, R: SubsetOf<OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>, DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

Converts this isometry into its equivalent homogeneous transformation matrix.

This is the same as self.to_matrix().

Example

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

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

pub fn to_matrix( &self, ) -> OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>

where Const<D>: DimNameAdd<U1>, R: SubsetOf<OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>, DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

Converts this isometry into its equivalent homogeneous transformation matrix.

This is the same as self.to_homogeneous().

Example

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

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

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

where T::Element: SimdRealField,

pub fn identity() -> Self

Creates a new identity isometry.

Example

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

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

pub fn rotation_wrt_point(r: R, p: Point<T, D>) -> Self

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

Example

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

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

Trait Implementations

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

where R: AbstractRotation<T, D> + AbsDiffEq<Epsilon = T::Epsilon>, T::Epsilon: Clone,

type Epsilon = <T as AbsDiffEq>::Epsilon

Used for specifying relative comparisons.

fn default_epsilon() -> Self::Epsilon

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

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

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

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

The inverse of AbsDiffEq::abs_diff_eq.

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

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

Returns a copy of the value.

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

Performs copy-assignment from source.

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

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

Formats the value using the given formatter.

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

where T::Element: SimdRealField,

fn default() -> Self

Returns the “default value” for a type.

impl<'de, T, R, const D: usize> Deserialize<'de> for Isometry<T, R, D>

where R: Deserialize<'de>, DefaultAllocator: Allocator<T, Const<D>>, Owned<T, Const<D>>: Deserialize<'de>, T: Scalar,

fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

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

where R: Display,

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

Formats the value using the given formatter.

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

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

type Output = Isometry<T, R, D>

The resulting type after applying the / operator.

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

Performs the / operation.

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

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

type Output = Similarity<T, R, D>

The resulting type after applying the / operator.

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

Performs the / operation.

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

where T::Element: SimdRealField,

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

type Output = Similarity<T, R, D>

The resulting type after applying the / operator.

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

Performs the / operation.

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

where T::Element: SimdRealField,

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

type Output = Isometry<T, R, D>

The resulting type after applying the / operator.

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

Performs the / operation.

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

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

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

Performs the /= operation.

impl<'b, T> DivAssign<&'b Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>

where T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField, T::Element: SimdRealField,

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

Performs the /= operation.

impl<T> DivAssign<Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>

where T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField, T::Element: SimdRealField,

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

Performs the /= operation.

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

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

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

Performs the /= operation.

impl<T, R, const D: usize> From<[Isometry<<T as SimdValue>::Element, <R as SimdValue>::Element, D>; 16]> for Isometry<T, R, D>

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

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

Converts to this type from the input type.

impl<T, R, const D: usize> From<[Isometry<<T as SimdValue>::Element, <R as SimdValue>::Element, D>; 2]> for Isometry<T, R, D>

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

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

Converts to this type from the input type.

impl<T, R, const D: usize> From<[Isometry<<T as SimdValue>::Element, <R as SimdValue>::Element, D>; 4]> for Isometry<T, R, D>

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

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

Converts to this type from the input type.

impl<T, R, const D: usize> From<[Isometry<<T as SimdValue>::Element, <R as SimdValue>::Element, D>; 8]> for Isometry<T, R, D>

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

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

Converts to this type from the input type.

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

where R: AbstractRotation<T, D>,

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

Converts to this type from the input type.

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

where R: AbstractRotation<T, D>,

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

Converts to this type from the input type.

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

where R: AbstractRotation<T, D>,

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

Converts to this type from the input type.

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

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

Converts to this type from the input type.

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

where Owned<T, Const<D>>: Hash,

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

Feeds this value into the given Hasher.

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

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

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

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

type Output = Isometry<T, R, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

type Output = Similarity<T, R, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, T, C, R, const D: usize> Mul<&'b Transform<T, C, D>> for Isometry<T, R, D>

where T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField, Const<D>: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>, DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

type Output = Isometry<T, R, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

type Output = Similarity<T, R, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T, C, R, const D: usize> Mul<Transform<T, C, D>> for Isometry<T, R, D>

where T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField, Const<D>: DimNameAdd<U1>, C: TCategoryMul<TAffine>, R: SubsetOf<OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>, DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

type Output = Isometry<T, R, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

where T::Element: SimdRealField,

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

type Output = Isometry<T, R, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

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

Performs the *= operation.

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

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

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

Performs the *= operation.

impl<'b, T> MulAssign<&'b Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>

where T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField, T::Element: SimdRealField,

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

Performs the *= operation.

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

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

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

Performs the *= operation.

impl<T> MulAssign<Unit<Complex<T>>> for Isometry<T, UnitComplex<T>, 2>

where T: Scalar + Zero + One + ClosedAdd + ClosedMul + SimdRealField, T::Element: SimdRealField,

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

Performs the *= operation.

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

where T::Element: SimdRealField, R: AbstractRotation<T, D>,

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

Performs the *= operation.

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

where T::Element: SimdRealField,

fn one() -> Self

Creates a new identity isometry.

fn set_one(&mut self)

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

fn is_one(&self) -> bool

where Self: PartialEq,

Returns true if self is equal to the multiplicative identity.

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

where R: AbstractRotation<T, D> + PartialEq,

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

Tests for self and other values to be equal, and is used by ==.

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

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

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

where R: AbstractRotation<T, D> + RelativeEq<Epsilon = T::Epsilon>, T::Epsilon: Clone,

fn default_max_relative() -> Self::Epsilon

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

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

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

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

The inverse of RelativeEq::relative_eq.

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

where R: Serialize, DefaultAllocator: Allocator<T, Const<D>>, Owned<T, Const<D>>: Serialize, T: Scalar,

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

where __S: Serializer,

Serialize this value into the given Serde serializer.

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

where T::Element: SimdRealField, R: SimdValue<SimdBool = T::SimdBool> + AbstractRotation<T, D>, R::Element: AbstractRotation<T::Element, D>,

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

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

type SimdBool = <T as SimdValue>::SimdBool

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

fn lanes() -> usize

The number of lanes of this SIMD value.

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

Initializes an SIMD value with each lanes set to val.

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

Extracts the i-th lane of self.

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

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

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

Replaces the i-th lane of self by val.

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

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

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

Merges self and other depending on the lanes of cond.

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

where Self: Clone,

Applies a function to each lane of self.

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

where Self: Clone,

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

impl<T1, T2, R1, R2, const D: usize> SubsetOf<Isometry<T2, R2, D>> for Isometry<T1, R1, D>

where T1: RealField, T2: RealField + SupersetOf<T1>, R1: AbstractRotation<T1, D> + SubsetOf<R2>, R2: AbstractRotation<T2, D>,

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

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

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

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

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

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

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

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

impl<T1, T2, R, const D: usize> SubsetOf<Matrix<T2, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output, <DefaultAllocator as Allocator<T2, <Const<D> as DimNameAdd<Const<1>>>::Output, <Const<D> as DimNameAdd<Const<1>>>::Output>>::Buffer>> for Isometry<T1, R, D>

where T1: RealField, T2: RealField + SupersetOf<T1>, R: AbstractRotation<T1, D> + SubsetOf<OMatrix<T1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>> + SubsetOf<OMatrix<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>, Const<D>: DimNameAdd<U1> + DimMin<Const<D>, Output = Const<D>>, DefaultAllocator: Allocator<T1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> + Allocator<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

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

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

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

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

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

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

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

impl<T1, T2, R1, R2, const D: usize> SubsetOf<Similarity<T2, R2, D>> for Isometry<T1, R1, D>

where T1: RealField, T2: RealField + SupersetOf<T1>, R1: AbstractRotation<T1, D> + SubsetOf<R2>, R2: AbstractRotation<T2, D>,

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

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

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

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

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

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

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

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

impl<T1, T2, R, C, const D: usize> SubsetOf<Transform<T2, C, D>> for Isometry<T1, R, D>

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

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

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

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

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

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

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

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

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

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

where R: AbstractRotation<T, D> + UlpsEq<Epsilon = T::Epsilon>, T::Epsilon: Clone,

fn default_max_ulps() -> u32

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

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

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

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

The inverse of UlpsEq::ulps_eq.

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

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

where R: AbstractRotation<T, D> + Eq,