Struct nalgebra::geometry::Transform

#[repr(C)]
pub struct Transform<T: RealField, C: TCategory, const D: usize>where
    Const<D>: DimNameAdd<U1>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,{ /* private fields */ }

A transformation matrix in homogeneous coordinates.

It is stored as a matrix with dimensions (D + 1, D + 1), e.g., it stores a 4x4 matrix for a 3D transformation.

Implementations

impl<T: RealField, C: TCategory, const D: usize> Transform<T, C, D>where
    Const<D>: DimNameAdd<U1>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

pub fn from_matrix_unchecked(
    matrix: OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
) -> Self

Creates a new transformation from the given homogeneous matrix. The transformation category of Self is not checked to be verified by the given matrix.

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

Retrieves the underlying matrix.

Examples

let m = Matrix3::new(1.0, 2.0, 0.0,
                     3.0, 4.0, 0.0,
                     0.0, 0.0, 1.0);
let t = Transform2::from_matrix_unchecked(m);
assert_eq!(t.into_inner(), m);

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

👎Deprecated: use .into_inner() instead

Retrieves the underlying matrix. Deprecated: Use Transform::into_inner instead.

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

A reference to the underlying matrix.

Examples

let m = Matrix3::new(1.0, 2.0, 0.0,
                     3.0, 4.0, 0.0,
                     0.0, 0.0, 1.0);
let t = Transform2::from_matrix_unchecked(m);
assert_eq!(*t.matrix(), m);

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

A mutable reference to the underlying matrix.

It is _unchecked because direct modifications of this matrix may break invariants identified by this transformation category.

Examples

let m = Matrix3::new(1.0, 2.0, 0.0,
                     3.0, 4.0, 0.0,
                     0.0, 0.0, 1.0);
let mut t = Transform2::from_matrix_unchecked(m);
t.matrix_mut_unchecked().m12 = 42.0;
t.matrix_mut_unchecked().m23 = 90.0;


let expected = Matrix3::new(1.0, 42.0, 0.0,
                            3.0, 4.0,  90.0,
                            0.0, 0.0,  1.0);
assert_eq!(*t.matrix(), expected);

pub fn set_category<CNew: SuperTCategoryOf<C>>(self) -> Transform<T, CNew, D>

Sets the category of this transform.

This can be done only if the new category is more general than the current one, e.g., a transform with category TProjective cannot be converted to a transform with category TAffine because not all projective transformations are affine (the other way-round is valid though).

pub fn clone_owned(&self) -> Transform<T, C, D>

👎Deprecated: This method is redundant with automatic Copy and the .clone() method and will be removed in a future release.

Clones this transform into one that owns its data.

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

Converts this transform into its equivalent homogeneous transformation matrix.

Examples

let m = Matrix3::new(1.0, 2.0, 0.0,
                     3.0, 4.0, 0.0,
                     0.0, 0.0, 1.0);
let t = Transform2::from_matrix_unchecked(m);
assert_eq!(t.into_inner(), m);

pub fn try_inverse(self) -> Option<Transform<T, C, D>>

Attempts to invert this transformation. You may use .inverse instead of this transformation has a subcategory of TProjective (i.e. if it is a Projective{2,3} or Affine{2,3}).

Examples

let m = Matrix3::new(2.0, 2.0, -0.3,
                     3.0, 4.0, 0.1,
                     0.0, 0.0, 1.0);
let t = Transform2::from_matrix_unchecked(m);
let inv_t = t.try_inverse().unwrap();
assert_relative_eq!(t * inv_t, Transform2::identity());
assert_relative_eq!(inv_t * t, Transform2::identity());

// Non-invertible case.
let m = Matrix3::new(0.0, 2.0, 1.0,
                     3.0, 0.0, 5.0,
                     0.0, 0.0, 0.0);
let t = Transform2::from_matrix_unchecked(m);
assert!(t.try_inverse().is_none());

pub fn inverse(self) -> Transform<T, C, D>where
    C: SubTCategoryOf<TProjective>,

Inverts this transformation. Use .try_inverse if this transform has the TGeneral category (i.e., a Transform{2,3} may not be invertible).

Examples

let m = Matrix3::new(2.0, 2.0, -0.3,
                     3.0, 4.0, 0.1,
                     0.0, 0.0, 1.0);
let proj = Projective2::from_matrix_unchecked(m);
let inv_t = proj.inverse();
assert_relative_eq!(proj * inv_t, Projective2::identity());
assert_relative_eq!(inv_t * proj, Projective2::identity());

pub fn try_inverse_mut(&mut self) -> bool

Attempts to invert this transformation in-place. You may use .inverse_mut instead of this transformation has a subcategory of TProjective.

Examples

let m = Matrix3::new(2.0, 2.0, -0.3,
                     3.0, 4.0, 0.1,
                     0.0, 0.0, 1.0);
let t = Transform2::from_matrix_unchecked(m);
let mut inv_t = t;
assert!(inv_t.try_inverse_mut());
assert_relative_eq!(t * inv_t, Transform2::identity());
assert_relative_eq!(inv_t * t, Transform2::identity());

// Non-invertible case.
let m = Matrix3::new(0.0, 2.0, 1.0,
                     3.0, 0.0, 5.0,
                     0.0, 0.0, 0.0);
let mut t = Transform2::from_matrix_unchecked(m);
assert!(!t.try_inverse_mut());

pub fn inverse_mut(&mut self)where
    C: SubTCategoryOf<TProjective>,

Inverts this transformation in-place. Use .try_inverse_mut if this transform has the TGeneral category (it may not be invertible).

Examples

let m = Matrix3::new(2.0, 2.0, -0.3,
                     3.0, 4.0, 0.1,
                     0.0, 0.0, 1.0);
let proj = Projective2::from_matrix_unchecked(m);
let mut inv_t = proj;
inv_t.inverse_mut();
assert_relative_eq!(proj * inv_t, Projective2::identity());
assert_relative_eq!(inv_t * proj, Projective2::identity());

impl<T, C, const D: usize> Transform<T, C, D>where
    T: RealField,
    C: TCategory,
    Const<D>: DimNameAdd<U1>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> + Allocator<T, DimNameSum<Const<D>, U1>>,

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

Transform the given point by this transformation.

This is the same as the multiplication self * pt.

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

Transform the given vector by this transformation, ignoring the translational component of the transformation.

This is the same as the multiplication self * v.

impl<T: RealField, C, const D: usize> Transform<T, C, D>where
    Const<D>: DimNameAdd<U1>,
    C: SubTCategoryOf<TProjective> + TCategory,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> + Allocator<T, DimNameSum<Const<D>, U1>>,

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

Transform the given point by the inverse of this transformation. This may be cheaper than inverting the transformation and transforming the point.

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

Transform the given vector by the inverse of this transformation. This may be cheaper than inverting the transformation and transforming the vector.

impl<T: RealField, const D: usize> Transform<T, TGeneral, D>where
    Const<D>: DimNameAdd<U1>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

A mutable reference to underlying matrix. Use .matrix_mut_unchecked instead if this transformation category is not TGeneral.

impl<T: RealField, C: TCategory, const D: usize> Transform<T, C, D>where
    Const<D>: DimNameAdd<U1>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

pub fn identity() -> Self

Creates a new identity transform.

Example

let pt = Point2::new(1.0, 2.0);
let t = Projective2::identity();
assert_eq!(t * pt, pt);

let aff = Affine2::identity();
assert_eq!(aff * pt, pt);

let aff = Transform2::identity();
assert_eq!(aff * pt, pt);

// Also works in 3D.
let pt = Point3::new(1.0, 2.0, 3.0);
let t = Projective3::identity();
assert_eq!(t * pt, pt);

let aff = Affine3::identity();
assert_eq!(aff * pt, pt);

let aff = Transform3::identity();
assert_eq!(aff * pt, pt);

Trait Implementations

impl<T: RealField, C: TCategory, const D: usize> AbsDiffEq<Transform<T, C, D>> for Transform<T, C, D>where
    Const<D>: DimNameAdd<U1>,
    T::Epsilon: Clone,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

Used for specifying relative comparisons.

fn default_epsilon() -> Self::Epsilon

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

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

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

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

The inverse of AbsDiffEq::abs_diff_eq.

impl<T: RealField, C: TCategory, const D: usize> Clone for Transform<T, C, D>where
    Const<D>: DimNameAdd<U1>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

fn clone(&self) -> Self

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<T: RealField + Debug, C: TCategory, const D: usize> Debug for Transform<T, C, D>where
    Const<D>: DimNameAdd<U1>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

Formats the value using the given formatter.

impl<T: RealField, C: TCategory, const D: usize> Default for Transform<T, C, D>where
    Const<D>: DimNameAdd<U1>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

fn default() -> Self

Returns the “default value” for a type.

impl<'a, 'b, T, C, const D: usize> Div<&'b Rotation<T, D>> for &'a Transform<T, C, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    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 div(self, rhs: &'b Rotation<T, D>) -> Self::Output

Performs the / operation.

impl<'b, T, C, const D: usize> Div<&'b Rotation<T, D>> for Transform<T, C, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    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 div(self, rhs: &'b Rotation<T, D>) -> Self::Output

Performs the / operation.

impl<'a, 'b, T, C> Div<&'b Transform<T, C, 3>> for &'a UnitQuaternion<T>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    C: TCategoryMul<TAffine>,

type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 3>

The resulting type after applying the / operator.

fn div(self, rhs: &'b Transform<T, C, 3>) -> Self::Output

Performs the / operation.

impl<'b, T, C> Div<&'b Transform<T, C, 3>> for UnitQuaternion<T>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    C: TCategoryMul<TAffine>,

type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 3>

The resulting type after applying the / operator.

fn div(self, rhs: &'b Transform<T, C, 3>) -> Self::Output

Performs the / operation.

impl<'a, 'b, T, C, const D: usize> Div<&'b Transform<T, C, D>> for &'a Rotation<T, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    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 div(self, rhs: &'b Transform<T, C, D>) -> Self::Output

Performs the / operation.

impl<'a, 'b, T, C, const D: usize> Div<&'b Transform<T, C, D>> for &'a Translation<T, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    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 div(self, rhs: &'b Transform<T, C, D>) -> Self::Output

Performs the / operation.

impl<'b, T, C, const D: usize> Div<&'b Transform<T, C, D>> for Rotation<T, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    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 div(self, rhs: &'b Transform<T, C, D>) -> Self::Output

Performs the / operation.

impl<'b, T, C, const D: usize> Div<&'b Transform<T, C, D>> for Translation<T, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    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 div(self, rhs: &'b Transform<T, C, D>) -> Self::Output

Performs the / operation.

impl<'a, 'b, T, CA, CB, const D: usize> Div<&'b Transform<T, CB, D>> for &'a Transform<T, CA, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    CA: TCategoryMul<CB>,
    CB: SubTCategoryOf<TProjective>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

type Output = Transform<T, <CA as TCategoryMul<CB>>::Representative, D>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'b, T, CA, CB, const D: usize> Div<&'b Transform<T, CB, D>> for Transform<T, CA, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    CA: TCategoryMul<CB>,
    CB: SubTCategoryOf<TProjective>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

type Output = Transform<T, <CA as TCategoryMul<CB>>::Representative, D>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, 'b, T, C, const D: usize> Div<&'b Translation<T, D>> for &'a Transform<T, C, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    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 div(self, rhs: &'b Translation<T, D>) -> Self::Output

Performs the / operation.

impl<'b, T, C, const D: usize> Div<&'b Translation<T, D>> for Transform<T, C, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    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 div(self, rhs: &'b Translation<T, D>) -> Self::Output

Performs the / operation.

impl<'a, 'b, T, C> Div<&'b Unit<Quaternion<T>>> for &'a Transform<T, C, 3>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    C: TCategoryMul<TAffine>,

type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 3>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'b, T, C> Div<&'b Unit<Quaternion<T>>> for Transform<T, C, 3>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    C: TCategoryMul<TAffine>,

type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 3>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, T, C, const D: usize> Div<Rotation<T, D>> for &'a Transform<T, C, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    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 div(self, rhs: Rotation<T, D>) -> Self::Output

Performs the / operation.

impl<T, C, const D: usize> Div<Rotation<T, D>> for Transform<T, C, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    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 div(self, rhs: Rotation<T, D>) -> Self::Output

Performs the / operation.

impl<'a, T, C> Div<Transform<T, C, 3>> for &'a UnitQuaternion<T>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    C: TCategoryMul<TAffine>,

type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 3>

The resulting type after applying the / operator.

fn div(self, rhs: Transform<T, C, 3>) -> Self::Output

Performs the / operation.

impl<T, C> Div<Transform<T, C, 3>> for UnitQuaternion<T>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    C: TCategoryMul<TAffine>,

type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 3>

The resulting type after applying the / operator.

fn div(self, rhs: Transform<T, C, 3>) -> Self::Output

Performs the / operation.

impl<'a, T, C, const D: usize> Div<Transform<T, C, D>> for &'a Rotation<T, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    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 div(self, rhs: Transform<T, C, D>) -> Self::Output

Performs the / operation.

impl<'a, T, C, const D: usize> Div<Transform<T, C, D>> for &'a Translation<T, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    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 div(self, rhs: Transform<T, C, D>) -> Self::Output

Performs the / operation.

impl<T, C, const D: usize> Div<Transform<T, C, D>> for Rotation<T, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    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 div(self, rhs: Transform<T, C, D>) -> Self::Output

Performs the / operation.

impl<T, C, const D: usize> Div<Transform<T, C, D>> for Translation<T, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    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 div(self, rhs: Transform<T, C, D>) -> Self::Output

Performs the / operation.

impl<'a, T, CA, CB, const D: usize> Div<Transform<T, CB, D>> for &'a Transform<T, CA, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    CA: TCategoryMul<CB>,
    CB: SubTCategoryOf<TProjective>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

type Output = Transform<T, <CA as TCategoryMul<CB>>::Representative, D>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<T, CA, CB, const D: usize> Div<Transform<T, CB, D>> for Transform<T, CA, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    CA: TCategoryMul<CB>,
    CB: SubTCategoryOf<TProjective>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

type Output = Transform<T, <CA as TCategoryMul<CB>>::Representative, D>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<'a, T, C, const D: usize> Div<Translation<T, D>> for &'a Transform<T, C, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    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 div(self, rhs: Translation<T, D>) -> Self::Output

Performs the / operation.

impl<T, C, const D: usize> Div<Translation<T, D>> for Transform<T, C, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    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 div(self, rhs: Translation<T, D>) -> Self::Output

Performs the / operation.

impl<'a, T, C> Div<Unit<Quaternion<T>>> for &'a Transform<T, C, 3>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    C: TCategoryMul<TAffine>,

type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 3>

The resulting type after applying the / operator.

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

Performs the / operation.

impl<T, C> Div<Unit<Quaternion<T>>> for Transform<T, C, 3>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    C: TCategoryMul<TAffine>,

type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 3>

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

Performs the /= operation.

impl<'b, T, CA, CB, const D: usize> DivAssign<&'b Transform<T, CB, D>> for Transform<T, CA, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    CA: SuperTCategoryOf<CB>,
    CB: SubTCategoryOf<TProjective>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

Performs the /= operation.

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

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

Performs the /= operation.

impl<'b, T, C> DivAssign<&'b Unit<Complex<T>>> for Transform<T, C, 2>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    C: TCategory,

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

Performs the /= operation.

impl<'b, T, C> DivAssign<&'b Unit<Quaternion<T>>> for Transform<T, C, 3>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    C: TCategory,

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

Performs the /= operation.

impl<T, C, const D: usize> DivAssign<Rotation<T, D>> for Transform<T, C, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategory,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

Performs the /= operation.

impl<T, CA, CB, const D: usize> DivAssign<Transform<T, CB, D>> for Transform<T, CA, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    CA: SuperTCategoryOf<CB>,
    CB: SubTCategoryOf<TProjective>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

Performs the /= operation.

impl<T, C, const D: usize> DivAssign<Translation<T, D>> for Transform<T, C, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategory,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

Performs the /= operation.

impl<T, C> DivAssign<Unit<Complex<T>>> for Transform<T, C, 2>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    C: TCategory,

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

Performs the /= operation.

impl<T, C> DivAssign<Unit<Quaternion<T>>> for Transform<T, C, 3>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    C: TCategory,

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

Performs the /= operation.

impl<T: RealField, C, const D: usize> From<Transform<T, C, D>> for OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>where
    Const<D>: DimNameAdd<U1>,
    C: TCategory,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

fn from(t: Transform<T, C, D>) -> Self

Converts to this type from the input type.

impl<T: RealField + Hash, C: TCategory, const D: usize> Hash for Transform<T, C, D>where
    Const<D>: DimNameAdd<U1>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
    Owned<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>: 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<T: RealField, C: TCategory, const D: usize> Index<(usize, usize)> for Transform<T, C, D>where
    Const<D>: DimNameAdd<U1>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

type Output = T

The returned type after indexing.

fn index(&self, ij: (usize, usize)) -> &T

Performs the indexing (container[index]) operation.

impl<T: RealField, const D: usize> IndexMut<(usize, usize)> for Transform<T, TGeneral, D>where
    Const<D>: DimNameAdd<U1>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

fn index_mut(&mut self, ij: (usize, usize)) -> &mut T

Performs the mutable indexing (container[index]) operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b, T, C, const D: usize> Mul<&'b Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for &'a Transform<T, C, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategory,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, T, C, const D: usize> Mul<&'b Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for Transform<T, C, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategory,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b, T, C, const D: usize> Mul<&'b OPoint<T, Const<D>>> for &'a Transform<T, C, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategory,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b, T, C, const D: usize> Mul<&'b Rotation<T, D>> for &'a Transform<T, C, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    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 Rotation<T, D>) -> Self::Output

Performs the * operation.

impl<'b, T, C, const D: usize> Mul<&'b Rotation<T, D>> for Transform<T, C, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    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 Rotation<T, D>) -> Self::Output

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b, T, C> Mul<&'b Transform<T, C, 2>> for &'a UnitComplex<T>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    C: TCategoryMul<TAffine>,

type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 2>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, T, C> Mul<&'b Transform<T, C, 2>> for UnitComplex<T>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    C: TCategoryMul<TAffine>,

type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 2>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b, T, C> Mul<&'b Transform<T, C, 3>> for &'a UnitQuaternion<T>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    C: TCategoryMul<TAffine>,

type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 3>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Transform<T, C, 3>) -> Self::Output

Performs the * operation.

impl<'b, T, C> Mul<&'b Transform<T, C, 3>> for UnitQuaternion<T>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    C: TCategoryMul<TAffine>,

type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 3>

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Transform<T, C, 3>) -> Self::Output

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b, T, CA, CB, const D: usize> Mul<&'b Transform<T, CB, D>> for &'a Transform<T, CA, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    CA: TCategoryMul<CB>,
    CB: TCategory,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

type Output = Transform<T, <CA as TCategoryMul<CB>>::Representative, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, T, CA, CB, const D: usize> Mul<&'b Transform<T, CB, D>> for Transform<T, CA, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    CA: TCategoryMul<CB>,
    CB: TCategory,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

type Output = Transform<T, <CA as TCategoryMul<CB>>::Representative, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b, T, C, const D: usize> Mul<&'b Translation<T, D>> for &'a Transform<T, C, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    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 Translation<T, D>) -> Self::Output

Performs the * operation.

impl<'b, T, C, const D: usize> Mul<&'b Translation<T, D>> for Transform<T, C, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    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 Translation<T, D>) -> Self::Output

Performs the * operation.

impl<'a, 'b, T, C> Mul<&'b Unit<Complex<T>>> for &'a Transform<T, C, 2>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    C: TCategoryMul<TAffine>,

type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 2>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, T, C> Mul<&'b Unit<Complex<T>>> for Transform<T, C, 2>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    C: TCategoryMul<TAffine>,

type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 2>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, 'b, T, C> Mul<&'b Unit<Quaternion<T>>> for &'a Transform<T, C, 3>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    C: TCategoryMul<TAffine>,

type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 3>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'b, T, C> Mul<&'b Unit<Quaternion<T>>> for Transform<T, C, 3>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    C: TCategoryMul<TAffine>,

type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 3>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, T, C, const D: usize> Mul<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for &'a Transform<T, C, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategory,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T, C, const D: usize> Mul<Matrix<T, Const<D>, Const<1>, ArrayStorage<T, D, 1>>> for Transform<T, C, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategory,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, T, C, const D: usize> Mul<OPoint<T, Const<D>>> for &'a Transform<T, C, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategory,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T, C, const D: usize> Mul<OPoint<T, Const<D>>> for Transform<T, C, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategory,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, T, C, const D: usize> Mul<Rotation<T, D>> for &'a Transform<T, C, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    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: Rotation<T, D>) -> Self::Output

Performs the * operation.

impl<T, C, const D: usize> Mul<Rotation<T, D>> for Transform<T, C, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    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: Rotation<T, D>) -> Self::Output

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, T, C> Mul<Transform<T, C, 2>> for &'a UnitComplex<T>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    C: TCategoryMul<TAffine>,

type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 2>

The resulting type after applying the * operator.

fn mul(self, rhs: Transform<T, C, 2>) -> Self::Output

Performs the * operation.

impl<T, C> Mul<Transform<T, C, 2>> for UnitComplex<T>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    C: TCategoryMul<TAffine>,

type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 2>

The resulting type after applying the * operator.

fn mul(self, rhs: Transform<T, C, 2>) -> Self::Output

Performs the * operation.

impl<'a, T, C> Mul<Transform<T, C, 3>> for &'a UnitQuaternion<T>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    C: TCategoryMul<TAffine>,

type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 3>

The resulting type after applying the * operator.

fn mul(self, rhs: Transform<T, C, 3>) -> Self::Output

Performs the * operation.

impl<T, C> Mul<Transform<T, C, 3>> for UnitQuaternion<T>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    C: TCategoryMul<TAffine>,

type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 3>

The resulting type after applying the * operator.

fn mul(self, rhs: Transform<T, C, 3>) -> Self::Output

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, T, CA, CB, const D: usize> Mul<Transform<T, CB, D>> for &'a Transform<T, CA, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    CA: TCategoryMul<CB>,
    CB: TCategory,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

type Output = Transform<T, <CA as TCategoryMul<CB>>::Representative, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T, CA, CB, const D: usize> Mul<Transform<T, CB, D>> for Transform<T, CA, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    CA: TCategoryMul<CB>,
    CB: TCategory,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

type Output = Transform<T, <CA as TCategoryMul<CB>>::Representative, D>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, T, C, const D: usize> Mul<Translation<T, D>> for &'a Transform<T, C, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    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: Translation<T, D>) -> Self::Output

Performs the * operation.

impl<T, C, const D: usize> Mul<Translation<T, D>> for Transform<T, C, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    C: TCategoryMul<TAffine>,
    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: Translation<T, D>) -> Self::Output

Performs the * operation.

impl<'a, T, C> Mul<Unit<Complex<T>>> for &'a Transform<T, C, 2>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    C: TCategoryMul<TAffine>,

type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 2>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T, C> Mul<Unit<Complex<T>>> for Transform<T, C, 2>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    C: TCategoryMul<TAffine>,

type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 2>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<'a, T, C> Mul<Unit<Quaternion<T>>> for &'a Transform<T, C, 3>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    C: TCategoryMul<TAffine>,

type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 3>

The resulting type after applying the * operator.

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

Performs the * operation.

impl<T, C> Mul<Unit<Quaternion<T>>> for Transform<T, C, 3>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    C: TCategoryMul<TAffine>,

type Output = Transform<T, <C as TCategoryMul<TAffine>>::Representative, 3>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

impl<'b, T, CA, CB, const D: usize> MulAssign<&'b Transform<T, CB, D>> for Transform<T, CA, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    CA: TCategory,
    CB: SubTCategoryOf<CA>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

Performs the *= operation.

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

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

Performs the *= operation.

impl<'b, T, C> MulAssign<&'b Unit<Complex<T>>> for Transform<T, C, 2>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    C: TCategory,

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

Performs the *= operation.

impl<'b, T, C> MulAssign<&'b Unit<Quaternion<T>>> for Transform<T, C, 3>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    C: TCategory,

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

impl<T, CA, CB, const D: usize> MulAssign<Transform<T, CB, D>> for Transform<T, CA, D>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    Const<D>: DimNameAdd<U1>,
    CA: TCategory,
    CB: SubTCategoryOf<CA>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

Performs the *= operation.

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

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

Performs the *= operation.

impl<T, C> MulAssign<Unit<Complex<T>>> for Transform<T, C, 2>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    C: TCategory,

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

Performs the *= operation.

impl<T, C> MulAssign<Unit<Quaternion<T>>> for Transform<T, C, 3>where
    T: Scalar + Zero + One + ClosedAdd + ClosedMul + RealField,
    C: TCategory,

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

Performs the *= operation.

impl<T: RealField, C: TCategory, const D: usize> One for Transform<T, C, D>where
    Const<D>: DimNameAdd<U1>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

fn one() -> Self

Creates a new identity transform.

fn set_one(&mut self)

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

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

Returns true if self is equal to the multiplicative identity.

impl<T: RealField, C: TCategory, const D: usize> PartialEq<Transform<T, C, D>> for Transform<T, C, D>where
    Const<D>: DimNameAdd<U1>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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

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

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

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

impl<T: RealField, C: TCategory, const D: usize> RelativeEq<Transform<T, C, D>> for Transform<T, C, D>where
    Const<D>: DimNameAdd<U1>,
    T::Epsilon: Clone,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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: RealField, C, const D: usize> SimdValue for Transform<T, C, D>where
    T::Element: Scalar,
    C: TCategory,
    Const<D>: DimNameAdd<U1>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> + Allocator<T::Element, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

type Element = Transform<<T as SimdValue>::Element, C, D>

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

type SimdBool = <T as SimdValue>::SimdBool

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

fn lanes() -> usize

The number of lanes of this SIMD value.

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

Initializes an SIMD value with each lanes set to val.

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

Extracts the i-th lane of self.

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

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

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

Replaces the i-th lane of self by val.

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

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

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

Merges self and other depending on the lanes of cond.

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

Applies a function to each lane of self.

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

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

impl<T1, T2, C, 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 Transform<T1, C, D>where
    T1: RealField + SubsetOf<T2>,
    T2: RealField,
    C: TCategory,
    Const<D>: DimNameAdd<U1>,
    DefaultAllocator: Allocator<T1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> + Allocator<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
    T1::Epsilon: Copy,
    T2::Epsilon: Copy,

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, C> SubsetOf<Transform<T2, C, 2>> for UnitComplex<T1>where
    T1: RealField,
    T2: RealField + SupersetOf<T1>,
    C: SuperTCategoryOf<TAffine>,

fn to_superset(&self) -> Transform<T2, C, 2>

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

fn is_in_subset(t: &Transform<T2, C, 2>) -> 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, 2>) -> Self

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

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

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

impl<T1, T2, C> SubsetOf<Transform<T2, C, 3>> for UnitDualQuaternion<T1>where
    T1: RealField,
    T2: RealField + SupersetOf<T1>,
    C: SuperTCategoryOf<TAffine>,

fn to_superset(&self) -> Transform<T2, C, 3>

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

fn is_in_subset(t: &Transform<T2, C, 3>) -> 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, 3>) -> Self

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

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

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

impl<T1, T2, C> SubsetOf<Transform<T2, C, 3>> for UnitQuaternion<T1>where
    T1: RealField,
    T2: RealField + SupersetOf<T1>,
    C: SuperTCategoryOf<TAffine>,

fn to_superset(&self) -> Transform<T2, C, 3>

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

fn is_in_subset(t: &Transform<T2, C, 3>) -> 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, 3>) -> Self

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

impl<T1, T2, C, const D: usize> SubsetOf<Transform<T2, C, D>> for Translation<T1, D>where
    T1: RealField,
    T2: RealField + SupersetOf<T1>,
    C: SuperTCategoryOf<TAffine>,
    Const<D>: DimNameAdd<U1>,
    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<T1, T2, C1, C2, const D: usize> SubsetOf<Transform<T2, C2, D>> for Transform<T1, C1, D>where
    T1: RealField + SubsetOf<T2>,
    T2: RealField,
    C1: TCategory,
    C2: SuperTCategoryOf<C1>,
    Const<D>: DimNameAdd<U1>,
    DefaultAllocator: Allocator<T1, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>> + Allocator<T2, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
    T1::Epsilon: Copy,
    T2::Epsilon: Copy,

fn to_superset(&self) -> Transform<T2, C2, D>

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

fn is_in_subset(t: &Transform<T2, C2, 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, C2, 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, C: TCategory, const D: usize> UlpsEq<Transform<T, C, D>> for Transform<T, C, D>where
    Const<D>: DimNameAdd<U1>,
    T::Epsilon: Clone,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,

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: RealField + Copy, C: TCategory, const D: usize> Copy for Transform<T, C, D>where
    Const<D>: DimNameAdd<U1>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
    Owned<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>: Copy,

impl<T: RealField + Eq, C: TCategory, const D: usize> Eq for Transform<T, C, D>where
    Const<D>: DimNameAdd<U1>,
    DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,