Struct nalgebra::geometry::Isometry

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

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

Fields

rotation: R

The pure rotational part of this isometry.

translation: Translation<N, D>

The pure translational part of this isometry.

Implementations

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

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

Creates a new isometry from its rotational and translational parts.

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

Inverts self.

pub fn inverse_mut(&mut self)

Inverts self.

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

Appends to self the given translation in-place.

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

Appends to self the given rotation in-place.

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.

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.

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

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

Converts this isometry into its equivalent homogeneous transformation matrix.

impl<N: Real, D: DimName, R: AlgaRotation<Point<N, D>>> Isometry<N, D, R>where
    DefaultAllocator: Allocator<N, D>,

pub fn identity() -> Self

Creates a new identity isometry.

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

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

impl<N: Real> Isometry<N, U2, Rotation2<N>>

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

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

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

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

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

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

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

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

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

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

It maps the view direction target - eye to the positive z axis and 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.

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

Builds a right-handed look-at view matrix.

This conforms to the common notion of right handed look-at matrix from the computer graphics community.

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.

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

Builds a left-handed look-at view matrix.

This conforms to the common notion of left handed look-at matrix from the computer graphics community.

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.

impl<N: Real> Isometry<N, U3, UnitQuaternion<N>>

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

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

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

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

It maps the view direction target - eye to the positive z axis and 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.

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

Builds a right-handed look-at view matrix.

This conforms to the common notion of right handed look-at matrix from the computer graphics community.

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.

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

Builds a left-handed look-at view matrix.

This conforms to the common notion of left handed look-at matrix from the computer graphics community.

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.

Trait Implementations

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

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

Used for specifying relative comparisons.

fn default_epsilon() -> Self::Epsilon

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

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

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

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

The inverse of ApproxEq::abs_diff_eq.

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

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

Performs an operation.

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

Performs specific operation.

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

type Rotation = R

Type of the first rotation to be applied.

type NonUniformScaling = Id<Multiplicative>

Type of the non-uniform scaling to be applied.

type Translation = Translation<N, D>

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

fn decompose(&self) -> (Translation<N, D>, R, Id, R)

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

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

Appends a translation to this similarity.

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

Prepends a translation to this similarity.

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

Appends a rotation to this similarity.

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

Prepends a rotation to this similarity.

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

Appends a scaling factor to this similarity.

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

Prepends a scaling factor to this similarity.

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

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

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

fn clone(&self) -> Self

Returns a copy of the value.

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

Performs copy-assignment from source.

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

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

Formats the value using the given formatter.

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

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

Formats the value using the given formatter.

impl<N: Real, D: DimName, R> Distribution<Isometry<N, D, R>> for Standardwhere
    R: AlgaRotation<Point<N, D>>,
    Standard: Distribution<N> + Distribution<R>,
    DefaultAllocator: Allocator<N, D>,

fn sample<'a, G: Rng + ?Sized>(&self, rng: &'a mut G) -> Isometry<N, D, R>

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R, 'a>(&'a self, rng: &'a mut R) -> DistIter<'a, Self, R, T>where
    Self: Sized,
    R: Rng,

Create an iterator that generates random values of T, using rng as the source of randomness.

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

type Output = Isometry<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

fn div_assign(&mut self, rhs: R)

Performs the /= operation.

impl<N: Real, D: DimName, R> From<Isometry<N, D, R>> for MatrixN<N, DimNameSum<D, U1>>where
    D: DimNameAdd<U1>,
    R: SubsetOf<MatrixN<N, DimNameSum<D, U1>>>,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, D>,

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

Converts to this type from the input type.

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

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

Feeds this value into the given Hasher.

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

fn identity() -> Self

The identity element.

fn id(_: O) -> Selfwhere
    Self: Sized,

Specific identity.

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

fn inverse(&self) -> Self

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

fn inverse_mut(&mut self)

In-place inversin of self.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Point<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Point<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Point<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Point<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Similarity<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Isometry<N, D, R>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

fn mul_assign(&mut self, rhs: R)

Performs the *= operation.

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

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

Performs the *= operation.

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

fn one() -> Self

Creates a new identity isometry.

fn set_one(&mut self)

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

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

Returns true if self is equal to the multiplicative identity.

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

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

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

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

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

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

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

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

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

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

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

fn default_max_relative() -> Self::Epsilon

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

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

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

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

The inverse of ApproxEq::relative_eq.

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

type Scaling = Id<Multiplicative>

The type of the pure (uniform) scaling part of this similarity transformation.

fn translation(&self) -> Translation<N, D>

The pure translational component of this similarity transformation.

fn rotation(&self) -> R

The pure rotational component of this similarity transformation.

fn scaling(&self) -> Id

The pure scaling component of this similarity transformation.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

unsafe fn from_superset_unchecked(iso: &Isometry<N2, D, R>) -> Self

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

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

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

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

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

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

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

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

unsafe fn from_superset_unchecked(iso: &Isometry<N2, D, R>) -> Self

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

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

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

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

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

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

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

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

unsafe fn from_superset_unchecked(iso: &Isometry<N2, D, R2>) -> Self

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

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

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

impl<N1, N2, R> SubsetOf<Isometry<N2, U2, R>> for UnitComplex<N1>where
    N1: Real,
    N2: Real + SupersetOf<N1>,
    R: AlgaRotation<Point2<N2>> + SupersetOf<UnitComplex<N1>>,

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

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

fn is_in_subset(iso: &Isometry<N2, U2, R>) -> bool

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

unsafe fn from_superset_unchecked(iso: &Isometry<N2, U2, R>) -> 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<N1, N2, R> SubsetOf<Isometry<N2, U3, R>> for UnitQuaternion<N1>where
    N1: Real,
    N2: Real + SupersetOf<N1>,
    R: AlgaRotation<Point3<N2>> + SupersetOf<UnitQuaternion<N1>>,

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

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

fn is_in_subset(iso: &Isometry<N2, U3, R>) -> bool

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

unsafe fn from_superset_unchecked(iso: &Isometry<N2, U3, R>) -> 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<N1, N2, D, R> SubsetOf<Matrix<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>> for Isometry<N1, D, R>where
    N1: Real,
    N2: Real + SupersetOf<N1>,
    R: Rotation<Point<N1, D>> + SubsetOf<MatrixN<N1, DimNameSum<D, U1>>> + SubsetOf<MatrixN<N2, DimNameSum<D, U1>>>,
    D: DimNameAdd<U1> + DimMin<D, Output = D>,
    DefaultAllocator: Allocator<N1, D> + Allocator<N1, D, D> + Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<(usize, usize), D> + Allocator<N2, D, D> + Allocator<N2, D>,

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

fn default_max_ulps() -> u32

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

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

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

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

The inverse of ApproxEq::ulps_eq.

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

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

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

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

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

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

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

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

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