Struct ggez::graphics::na::Transform

#[repr(C)]
pub struct Transform<N, D, C> where
    C: TCategory,
    D: DimNameAdd<U1>,
    N: Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,  { /* fields omitted */ }

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.

Methods

impl<N, D, C> Transform<N, D, C> where
    C: TCategory,
    D: DimNameAdd<U1>,
    N: Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

fn from_matrix_unchecked(
    matrix: Matrix<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>
) -> Transform<N, D, C>

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

fn unwrap(
    self
) -> Matrix<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>

The underlying matrix.

fn matrix(
    &self
) -> &Matrix<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>

A reference to the underlynig matrix.

fn matrix_mut_unchecked(
    &mut self
) -> &mut Matrix<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>

A mutable reference to the underlying matrix.

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

fn set_category<CNew>(self) -> Transform<N, D, CNew> where
    CNew: SuperTCategoryOf<C>, 

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).

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

Deprecated

: This method is a no-op and will be removed in a future release.

Clones this transform into one that owns its data.

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

Converts this transform into its equivalent homogeneous transformation matrix.

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

Attempts to invert this transformation. You may use .inverse instead of this transformation has a subcategory of TProjective.

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

Inverts this transformation. Use .try_inverse if this transform has the TGeneral category (it may not be invertible).

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.

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).

impl<N, D> Transform<N, D, TGeneral> where
    D: DimNameAdd<U1>,
    N: Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

fn matrix_mut(
    &mut self
) -> &mut Matrix<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>

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

impl<N, D, C> Transform<N, D, C> where
    C: TCategory,
    D: DimNameAdd<U1>,
    N: Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

fn identity() -> Transform<N, D, C>

Creates a new identity transform.

Trait Implementations

impl<N, D, C> Copy for Transform<N, D, C> where
    C: TCategory,
    D: DimNameAdd<U1> + Copy,
    N: Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    <DefaultAllocator as Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer: Copy, 

impl<N, D, C> Clone for Transform<N, D, C> where
    C: TCategory,
    D: DimNameAdd<U1>,
    N: Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

fn clone(&self) -> Transform<N, D, C>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<N, D, C> AbstractMonoid<Multiplicative> for Transform<N, D, C> where
    C: TCategory,
    D: DimNameAdd<U1>,
    N: Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

impl<N1, N2, D, C1, C2> SubsetOf<Transform<N2, D, C2>> for Transform<N1, D, C1> where
    C1: TCategory,
    C2: SuperTCategoryOf<C1>,
    D: DimName + DimNameAdd<U1>,
    N1: Real + SubsetOf<N2>,
    N2: Real,
    DefaultAllocator: Allocator<N1, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    <N1 as ApproxEq>::Epsilon: Copy,
    <N2 as ApproxEq>::Epsilon: Copy, 

fn to_superset(&self) -> Transform<N2, D, C2>

fn is_in_subset(t: &Transform<N2, D, C2>) -> bool

unsafe fn from_superset_unchecked(
    t: &Transform<N2, D, C2>
) -> Transform<N1, D, C1>

impl<N1, N2, D, C> 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 Transform<N1, D, C> where
    C: TCategory,
    D: DimName + DimNameAdd<U1>,
    N1: Real + SubsetOf<N2>,
    N2: Real,
    DefaultAllocator: Allocator<N1, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    <N1 as ApproxEq>::Epsilon: Copy,
    <N2 as ApproxEq>::Epsilon: Copy, 

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

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

unsafe fn from_superset_unchecked(
    m: &Matrix<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output, <DefaultAllocator as Allocator<N2, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>>::Buffer>
) -> Transform<N1, D, C>

impl<N, D, C> Inverse<Multiplicative> for Transform<N, D, C> where
    C: SubTCategoryOf<TProjective>,
    D: DimNameAdd<U1>,
    N: Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

fn inverse(&self) -> Transform<N, D, C>

fn inverse_mut(&mut self)

impl<N, D, C> ProjectiveTransformation<Point<N, D>> for Transform<N, D, C> where
    C: SubTCategoryOf<TProjective>,
    D: DimNameAdd<U1>,
    N: Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, U1>,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

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

impl<N, D, C> Transformation<Point<N, D>> for Transform<N, D, C> where
    C: TCategory,
    D: DimNameAdd<U1>,
    N: Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, U1>,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

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

impl<N, D, CA, CB> Div<Transform<N, D, CB>> for Transform<N, D, CA> where
    CA: TCategoryMul<CB>,
    CB: SubTCategoryOf<TProjective>,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

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

fn div(
    self,
    rhs: Transform<N, D, CB>
) -> <Transform<N, D, CA> as Div<Transform<N, D, CB>>>::Output

impl<N, D, C> Div<Rotation<N, D>> for Transform<N, D, C> where
    C: TCategoryMul<TAffine>,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, D>, 

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

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

impl<'a, 'b, N, D, CA, CB> Div<&'b Transform<N, D, CB>> for &'a Transform<N, D, CA> where
    CA: TCategoryMul<CB>,
    CB: SubTCategoryOf<TProjective>,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

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

fn div(
    self,
    rhs: &'b Transform<N, D, CB>
) -> <&'a Transform<N, D, CA> as Div<&'b Transform<N, D, CB>>>::Output

impl<'a, N, D, CA, CB> Div<Transform<N, D, CB>> for &'a Transform<N, D, CA> where
    CA: TCategoryMul<CB>,
    CB: SubTCategoryOf<TProjective>,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

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

fn div(
    self,
    rhs: Transform<N, D, CB>
) -> <&'a Transform<N, D, CA> as Div<Transform<N, D, CB>>>::Output

impl<'a, 'b, N, C> Div<&'b Unit<Quaternion<N>>> for &'a Transform<N, U3, C> where
    C: TCategoryMul<TAffine>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, U4, U4>,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = Transform<N, U3, <C as TCategoryMul<TAffine>>::Representative>

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

impl<'b, N, C> Div<&'b Unit<Quaternion<N>>> for Transform<N, U3, C> where
    C: TCategoryMul<TAffine>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, U4, U4>,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = Transform<N, U3, <C as TCategoryMul<TAffine>>::Representative>

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

impl<'a, 'b, N, D, C> Div<&'b Rotation<N, D>> for &'a Transform<N, D, C> where
    C: TCategoryMul<TAffine>,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, D>, 

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

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

impl<'b, N, D, CA, CB> Div<&'b Transform<N, D, CB>> for Transform<N, D, CA> where
    CA: TCategoryMul<CB>,
    CB: SubTCategoryOf<TProjective>,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

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

fn div(
    self,
    rhs: &'b Transform<N, D, CB>
) -> <Transform<N, D, CA> as Div<&'b Transform<N, D, CB>>>::Output

impl<'a, N, D, C> Div<Translation<N, D>> for &'a Transform<N, D, C> where
    C: TCategoryMul<TAffine>,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, U1>, 

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

fn div(
    self,
    rhs: Translation<N, D>
) -> <&'a Transform<N, D, C> as Div<Translation<N, D>>>::Output

impl<'b, N, D, C> Div<&'b Rotation<N, D>> for Transform<N, D, C> where
    C: TCategoryMul<TAffine>,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, D>, 

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

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

impl<'b, N, D, C> Div<&'b Translation<N, D>> for Transform<N, D, C> where
    C: TCategoryMul<TAffine>,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, U1>, 

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

fn div(
    self,
    rhs: &'b Translation<N, D>
) -> <Transform<N, D, C> as Div<&'b Translation<N, D>>>::Output

impl<N, C> Div<Unit<Quaternion<N>>> for Transform<N, U3, C> where
    C: TCategoryMul<TAffine>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, U4, U4>,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = Transform<N, U3, <C as TCategoryMul<TAffine>>::Representative>

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

impl<'a, N, D, C> Div<Rotation<N, D>> for &'a Transform<N, D, C> where
    C: TCategoryMul<TAffine>,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, D>, 

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

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

impl<'a, N, C> Div<Unit<Quaternion<N>>> for &'a Transform<N, U3, C> where
    C: TCategoryMul<TAffine>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, U4, U4>,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = Transform<N, U3, <C as TCategoryMul<TAffine>>::Representative>

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

impl<N, D, C> Div<Translation<N, D>> for Transform<N, D, C> where
    C: TCategoryMul<TAffine>,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, U1>, 

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

fn div(
    self,
    rhs: Translation<N, D>
) -> <Transform<N, D, C> as Div<Translation<N, D>>>::Output

impl<'a, 'b, N, D, C> Div<&'b Translation<N, D>> for &'a Transform<N, D, C> where
    C: TCategoryMul<TAffine>,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, U1>, 

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

fn div(
    self,
    rhs: &'b Translation<N, D>
) -> <&'a Transform<N, D, C> as Div<&'b Translation<N, D>>>::Output

impl<N, D, C> AbstractSemigroup<Multiplicative> for Transform<N, D, C> where
    C: TCategory,
    D: DimNameAdd<U1>,
    N: Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

impl<N, D, C> AbstractLoop<Multiplicative> for Transform<N, D, C> where
    C: SubTCategoryOf<TProjective>,
    D: DimNameAdd<U1>,
    N: Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

impl<'b, N, D, CA, CB> DivAssign<&'b Transform<N, D, CB>> for Transform<N, D, CA> where
    CA: SuperTCategoryOf<CB>,
    CB: SubTCategoryOf<TProjective>,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

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

impl<'b, N, D, C> DivAssign<&'b Rotation<N, D>> for Transform<N, D, C> where
    C: TCategory,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, D>, 

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

impl<N, D, CA, CB> DivAssign<Transform<N, D, CB>> for Transform<N, D, CA> where
    CA: SuperTCategoryOf<CB>,
    CB: SubTCategoryOf<TProjective>,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

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

impl<N, C> DivAssign<Unit<Quaternion<N>>> for Transform<N, U3, C> where
    C: TCategory,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, U4, U4>,
    DefaultAllocator: Allocator<N, U4, U1>, 

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

impl<N, D, C> DivAssign<Rotation<N, D>> for Transform<N, D, C> where
    C: TCategory,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, D>, 

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

impl<'b, N, D, C> DivAssign<&'b Translation<N, D>> for Transform<N, D, C> where
    C: TCategory,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

impl<'b, N, C> DivAssign<&'b Unit<Quaternion<N>>> for Transform<N, U3, C> where
    C: TCategory,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, U4, U4>,
    DefaultAllocator: Allocator<N, U4, U1>, 

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

impl<N, D, C> DivAssign<Translation<N, D>> for Transform<N, D, C> where
    C: TCategory,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

impl<N, D, C> PartialEq<Transform<N, D, C>> for Transform<N, D, C> where
    C: TCategory,
    D: DimNameAdd<U1>,
    N: Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

fn eq(&self, right: &Transform<N, D, C>) -> 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 !=.

impl<N, D, C> Debug for Transform<N, D, C> where
    C: TCategory + Debug,
    D: DimNameAdd<U1> + Debug,
    N: Debug + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

fn fmt(&self, __arg_0: &mut Formatter) -> Result<(), Error>

Formats the value using the given formatter.

impl<N, D, C> AbstractQuasigroup<Multiplicative> for Transform<N, D, C> where
    C: SubTCategoryOf<TProjective>,
    D: DimNameAdd<U1>,
    N: Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

impl<N, D, C> AbstractGroup<Multiplicative> for Transform<N, D, C> where
    C: SubTCategoryOf<TProjective>,
    D: DimNameAdd<U1>,
    N: Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

impl<N, D, C> One for Transform<N, D, C> where
    C: TCategory,
    D: DimNameAdd<U1>,
    N: Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

fn one() -> Transform<N, D, C>

Creates a new identity transform.

impl<N, D, C> Index<(usize, usize)> for Transform<N, D, C> where
    C: TCategory,
    D: DimName + DimNameAdd<U1>,
    N: Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

type Output = N

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

impl<N, D, C> Identity<Multiplicative> for Transform<N, D, C> where
    C: TCategory,
    D: DimNameAdd<U1>,
    N: Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

fn identity() -> Transform<N, D, C>

impl<N, D, C> Eq for Transform<N, D, C> where
    C: TCategory,
    D: DimNameAdd<U1>,
    N: Eq + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

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

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

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

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

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

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

impl<N, C> MulAssign<Unit<Quaternion<N>>> for Transform<N, U3, C> where
    C: TCategory,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, U4, U4>,
    DefaultAllocator: Allocator<N, U4, U1>, 

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

impl<N, D, C> MulAssign<Translation<N, D>> for Transform<N, D, C> where
    C: TCategory,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

impl<'b, N, D, CA, CB> MulAssign<&'b Transform<N, D, CB>> for Transform<N, D, CA> where
    CA: TCategory,
    CB: SubTCategoryOf<CA>,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

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

impl<N, D, CA, CB> MulAssign<Transform<N, D, CB>> for Transform<N, D, CA> where
    CA: TCategory,
    CB: SubTCategoryOf<CA>,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

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

impl<'b, N, D, C> MulAssign<&'b Translation<N, D>> for Transform<N, D, C> where
    C: TCategory,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, U1>, 

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

impl<N, D, C> MulAssign<Rotation<N, D>> for Transform<N, D, C> where
    C: TCategory,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, D>, 

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

impl<'b, N, D, C> MulAssign<&'b Rotation<N, D>> for Transform<N, D, C> where
    C: TCategory,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, D>, 

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

impl<'b, N, C> MulAssign<&'b Unit<Quaternion<N>>> for Transform<N, U3, C> where
    C: TCategory,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, U4, U4>,
    DefaultAllocator: Allocator<N, U4, U1>, 

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

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

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

impl<N, D, C> AbstractMagma<Multiplicative> for Transform<N, D, C> where
    C: TCategory,
    D: DimNameAdd<U1>,
    N: Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

fn operate(&self, rhs: &Transform<N, D, C>) -> Transform<N, D, C>

impl<'a, N, D, C> Mul<Rotation<N, D>> for &'a Transform<N, D, C> where
    C: TCategoryMul<TAffine>,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, D>, 

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

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

impl<'a, 'b, N, D, CA, CB> Mul<&'b Transform<N, D, CB>> for &'a Transform<N, D, CA> where
    CA: TCategoryMul<CB>,
    CB: TCategory,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

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

fn mul(
    self,
    rhs: &'b Transform<N, D, CB>
) -> <&'a Transform<N, D, CA> as Mul<&'b Transform<N, D, CB>>>::Output

impl<'a, 'b, N, D, C> Mul<&'b Rotation<N, D>> for &'a Transform<N, D, C> where
    C: TCategoryMul<TAffine>,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, D>, 

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

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

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

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

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

impl<'a, N, D, C> Mul<Translation<N, D>> for &'a Transform<N, D, C> where
    C: TCategoryMul<TAffine>,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, U1>, 

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

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

impl<'a, 'b, N, D, C> Mul<&'b Translation<N, D>> for &'a Transform<N, D, C> where
    C: TCategoryMul<TAffine>,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, U1>, 

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

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

impl<'a, N, D, CA, CB> Mul<Transform<N, D, CB>> for &'a Transform<N, D, CA> where
    CA: TCategoryMul<CB>,
    CB: TCategory,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

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

fn mul(
    self,
    rhs: Transform<N, D, CB>
) -> <&'a Transform<N, D, CA> as Mul<Transform<N, D, CB>>>::Output

impl<N, C> Mul<Unit<Quaternion<N>>> for Transform<N, U3, C> where
    C: TCategoryMul<TAffine>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, U4, U4>,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = Transform<N, U3, <C as TCategoryMul<TAffine>>::Representative>

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

impl<N, D, C> Mul<Translation<N, D>> for Transform<N, D, C> where
    C: TCategoryMul<TAffine>,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, U1>, 

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

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

impl<'a, N, D, C> Mul<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>> for &'a Transform<N, D, C> where
    C: TCategory,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, U1>, 

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

fn mul(
    self,
    rhs: Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>
) -> <&'a Transform<N, D, C> as Mul<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>>::Output

impl<'b, N, D, CA, CB> Mul<&'b Transform<N, D, CB>> for Transform<N, D, CA> where
    CA: TCategoryMul<CB>,
    CB: TCategory,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

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

fn mul(
    self,
    rhs: &'b Transform<N, D, CB>
) -> <Transform<N, D, CA> as Mul<&'b Transform<N, D, CB>>>::Output

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

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

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

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

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

fn mul(
    self,
    rhs: &'b Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>
) -> <Transform<N, D, C> as Mul<&'b Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>>::Output

impl<'a, 'b, N, D, C> Mul<&'b Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>> for &'a Transform<N, D, C> where
    C: TCategory,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, U1>, 

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

fn mul(
    self,
    rhs: &'b Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>
) -> <&'a Transform<N, D, C> as Mul<&'b Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>>::Output

impl<N, D, C> Mul<Rotation<N, D>> for Transform<N, D, C> where
    C: TCategoryMul<TAffine>,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, D>, 

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

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

impl<'a, N, D, C> Mul<Point<N, D>> for &'a Transform<N, D, C> where
    C: TCategory,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, U1>,
    DefaultAllocator: Allocator<N, D, D>, 

type Output = Point<N, D>

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

impl<N, D, CA, CB> Mul<Transform<N, D, CB>> for Transform<N, D, CA> where
    CA: TCategoryMul<CB>,
    CB: TCategory,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

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

fn mul(
    self,
    rhs: Transform<N, D, CB>
) -> <Transform<N, D, CA> as Mul<Transform<N, D, CB>>>::Output

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

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

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

impl<N, D, C> Mul<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>> for Transform<N, D, C> where
    C: TCategory,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, U1>, 

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

fn mul(
    self,
    rhs: Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>
) -> <Transform<N, D, C> as Mul<Matrix<N, D, U1, <DefaultAllocator as Allocator<N, D, U1>>::Buffer>>>::Output

impl<N, D, C> Mul<Point<N, D>> for Transform<N, D, C> where
    C: TCategory,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, U1>,
    DefaultAllocator: Allocator<N, D, D>, 

type Output = Point<N, D>

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

impl<'b, N, D, C> Mul<&'b Translation<N, D>> for Transform<N, D, C> where
    C: TCategoryMul<TAffine>,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, U1>, 

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

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

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

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

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

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

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

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

impl<'a, 'b, N, D, C> Mul<&'b Point<N, D>> for &'a Transform<N, D, C> where
    C: TCategory,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, U1>,
    DefaultAllocator: Allocator<N, D, D>, 

type Output = Point<N, D>

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

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

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

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

impl<'b, N, D, C> Mul<&'b Point<N, D>> for Transform<N, D, C> where
    C: TCategory,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, U1>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, U1>,
    DefaultAllocator: Allocator<N, D, D>, 

type Output = Point<N, D>

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

impl<'a, N, C> Mul<Unit<Quaternion<N>>> for &'a Transform<N, U3, C> where
    C: TCategoryMul<TAffine>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, U4, U4>,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = Transform<N, U3, <C as TCategoryMul<TAffine>>::Representative>

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

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

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

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

impl<'b, N, C> Mul<&'b Unit<Quaternion<N>>> for Transform<N, U3, C> where
    C: TCategoryMul<TAffine>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, U4, U4>,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = Transform<N, U3, <C as TCategoryMul<TAffine>>::Representative>

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

impl<'b, N, D, C> Mul<&'b Rotation<N, D>> for Transform<N, D, C> where
    C: TCategoryMul<TAffine>,
    D: DimNameAdd<U1>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>,
    DefaultAllocator: Allocator<N, D, D>,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, D>, 

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

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

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

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

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

impl<'a, 'b, N, C> Mul<&'b Unit<Quaternion<N>>> for &'a Transform<N, U3, C> where
    C: TCategoryMul<TAffine>,
    N: Scalar + Zero + One + ClosedAdd<N> + ClosedMul<N> + Real,
    DefaultAllocator: Allocator<N, U4, U4>,
    DefaultAllocator: Allocator<N, U4, U1>,
    DefaultAllocator: Allocator<N, U4, U1>, 

type Output = Transform<N, U3, <C as TCategoryMul<TAffine>>::Representative>

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

impl<N, D> IndexMut<(usize, usize)> for Transform<N, D, TGeneral> where
    D: DimName + DimNameAdd<U1>,
    N: Real,
    DefaultAllocator: Allocator<N, <D as DimNameAdd<U1>>::Output, <D as DimNameAdd<U1>>::Output>, 

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