Struct nalgebra::geometry::Transform

#[repr(C)]
pub struct Transform<N: RealField, D: DimNameAdd<U1>, C: TCategory> where
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,  { /* 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: RealField, D: DimNameAdd<U1>, C: TCategory> Transform<N, D, C> where
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>, 

pub fn from_matrix_unchecked(matrix: MatrixN<N, DimNameSum<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) -> MatrixN<N, DimNameSum<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) -> MatrixN<N, DimNameSum<D, U1>>

Deprecated:

use .into_inner() instead

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

pub fn matrix(&self) -> &MatrixN<N, DimNameSum<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 MatrixN<N, DimNameSum<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<N, D, CNew>

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<N, D, C>

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) -> MatrixN<N, DimNameSum<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<N, D, C>>

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<N, D, C> 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<N, D: DimNameAdd<U1>, C> Transform<N, D, C> where
    N: RealField,
    C: TCategory,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, DimNameSum<D, U1>> + Allocator<N, D, D> + Allocator<N, D>, 

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

Transform the given point by this transformation.

This is the same as the multiplication self * pt.

pub fn transform_vector(&self, v: &VectorN<N, D>) -> VectorN<N, 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<N: RealField, D: DimNameAdd<U1>, C: TCategory> Transform<N, D, C> where
    C: SubTCategoryOf<TProjective>,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, DimNameSum<D, U1>> + Allocator<N, D, D> + Allocator<N, D>, 

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

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

impl<N: RealField, D: DimNameAdd<U1>> Transform<N, D, TGeneral> where
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>, 

pub fn matrix_mut(&mut self) -> &mut MatrixN<N, DimNameSum<D, U1>>

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

impl<N: RealField, D: DimNameAdd<U1>, C: TCategory> Transform<N, D, C> where
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<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<N: RealField + Eq, D: DimNameAdd<U1>, C: TCategory> Eq for Transform<N, D, C> where
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>, 

impl<N: RealField, D: DimNameAdd<U1>, C: TCategory> Clone for Transform<N, D, C> where
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<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<N: RealField, D: DimNameAdd<U1>, C: TCategory> PartialEq<Transform<N, D, C>> for Transform<N, D, C> where
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>, 

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

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

#[must_use] fn ne(&self, other: &Rhs) -> bool

This method tests for !=.

impl<N: RealField, D: DimName, C> From<Transform<N, D, C>> for MatrixN<N, DimNameSum<D, U1>> where
    D: DimNameAdd<U1>,
    C: TCategory,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>, 

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

Performs the conversion.

impl<N: RealField, D: DimNameAdd<U1> + Copy, C: TCategory> Copy for Transform<N, D, C> where
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>,
    Owned<N, DimNameSum<D, U1>, DimNameSum<D, U1>>: Copy, 

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

type Output = VectorN<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = VectorN<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = VectorN<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = VectorN<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Point<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Point<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Point<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

type Output = Point<N, D>

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

fn mul(self, rhs: Transform<N, U3, C>) -> Self::Output

Performs the * operation.

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

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

The resulting type after applying the * operator.

fn mul(self, rhs: Transform<N, U3, C>) -> Self::Output

Performs the * operation.

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

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Transform<N, U3, C>) -> Self::Output

Performs the * operation.

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

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

The resulting type after applying the * operator.

fn mul(self, rhs: &'b Transform<N, U3, C>) -> Self::Output

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the * operator.

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

Performs the * operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

fn div(self, rhs: Transform<N, U3, C>) -> Self::Output

Performs the / operation.

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

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

The resulting type after applying the / operator.

fn div(self, rhs: Transform<N, U3, C>) -> Self::Output

Performs the / operation.

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

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

The resulting type after applying the / operator.

fn div(self, rhs: &'b Transform<N, U3, C>) -> Self::Output

Performs the / operation.

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

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

The resulting type after applying the / operator.

fn div(self, rhs: &'b Transform<N, U3, C>) -> Self::Output

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

The resulting type after applying the / operator.

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

Performs the / operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the *= operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

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

Performs the /= operation.

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

type Output = N

The returned type after indexing.

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

Performs the indexing (container[index]) operation.

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

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

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

impl<N: Debug + RealField, D: Debug + DimNameAdd<U1>, C: Debug + TCategory> Debug for Transform<N, D, C> where
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>, 

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

Formats the value using the given formatter.

impl<N: RealField, D: DimNameAdd<U1>, C: TCategory> AbsDiffEq<Transform<N, D, C>> for Transform<N, D, C> where
    N::Epsilon: Copy,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>, 

type Epsilon = N::Epsilon

Used for specifying relative comparisons.

fn default_epsilon() -> Self::Epsilon

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

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

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

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

The inverse of ApproxEq::abs_diff_eq.

impl<N: RealField, D: DimNameAdd<U1>, C: TCategory> RelativeEq<Transform<N, D, C>> for Transform<N, D, C> where
    N::Epsilon: Copy,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<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 ApproxEq::relative_eq.

impl<N: RealField, D: DimNameAdd<U1>, C: TCategory> UlpsEq<Transform<N, D, C>> for Transform<N, D, C> where
    N::Epsilon: Copy,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<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 ApproxEq::ulps_eq.

impl<N: RealField, D: DimNameAdd<U1>, C: TCategory> One for Transform<N, D, C> where
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<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) -> bool where
    Self: PartialEq<Self>, 

Returns true if self is equal to the multiplicative identity.

impl<N: RealField, D: DimNameAdd<U1>, C> AbstractMagma<Multiplicative> for Transform<N, D, C> where
    C: TCategory,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>, 

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

Performs an operation.

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

Performs specific operation.

impl<N: RealField, D: DimNameAdd<U1>, C> AbstractQuasigroup<Multiplicative> for Transform<N, D, C> where
    C: SubTCategoryOf<TProjective>,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>, 

fn prop_inv_is_latin_square_approx(args: (Self, Self)) -> bool where
    Self: RelativeEq<Self>, 

Returns true if latin squareness holds for the given arguments. Approximate equality is used for verifications.

fn prop_inv_is_latin_square(args: (Self, Self)) -> bool where
    Self: Eq, 

Returns true if latin squareness holds for the given arguments.

impl<N: RealField, D: DimNameAdd<U1>, C> AbstractSemigroup<Multiplicative> for Transform<N, D, C> where
    C: TCategory,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>, 

fn prop_is_associative_approx(args: (Self, Self, Self)) -> bool where
    Self: RelativeEq<Self>, 

Returns true if associativity holds for the given arguments. Approximate equality is used for verifications.

fn prop_is_associative(args: (Self, Self, Self)) -> bool where
    Self: Eq, 

Returns true if associativity holds for the given arguments.

impl<N: RealField, D: DimNameAdd<U1>, C> AbstractLoop<Multiplicative> for Transform<N, D, C> where
    C: SubTCategoryOf<TProjective>,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>, 

impl<N: RealField, D: DimNameAdd<U1>, C> AbstractMonoid<Multiplicative> for Transform<N, D, C> where
    C: TCategory,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>, 

fn prop_operating_identity_element_is_noop_approx(args: (Self,)) -> bool where
    Self: RelativeEq<Self>, 

Checks whether operating with the identity element is a no-op for the given argument. Approximate equality is used for verifications.

fn prop_operating_identity_element_is_noop(args: (Self,)) -> bool where
    Self: Eq, 

Checks whether operating with the identity element is a no-op for the given argument.

impl<N: RealField, D: DimNameAdd<U1>, C> AbstractGroup<Multiplicative> for Transform<N, D, C> where
    C: SubTCategoryOf<TProjective>,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>, 

impl<N: RealField, D: DimNameAdd<U1>, C> Identity<Multiplicative> for Transform<N, D, C> where
    C: TCategory,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>, 

fn identity() -> Self

The identity element.

fn id(O) -> Self

Specific identity.

impl<N: RealField, D: DimNameAdd<U1>, C> TwoSidedInverse<Multiplicative> for Transform<N, D, C> where
    C: SubTCategoryOf<TProjective>,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>>, 

fn two_sided_inverse(&self) -> Self

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

fn two_sided_inverse_mut(&mut self)

In-place inversion of self, relative to the operator O.

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

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

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

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

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

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

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

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

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

impl<N1, N2, C> SubsetOf<Transform<N2, U3, C>> for UnitQuaternion<N1> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    C: SuperTCategoryOf<TAffine>, 

fn to_superset(&self) -> Transform<N2, U3, C>

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

fn is_in_subset(t: &Transform<N2, U3, C>) -> bool

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

unsafe fn from_superset_unchecked(t: &Transform<N2, U3, C>) -> Self

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

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

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

impl<N1, N2, C> SubsetOf<Transform<N2, U2, C>> for UnitComplex<N1> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    C: SuperTCategoryOf<TAffine>, 

fn to_superset(&self) -> Transform<N2, U2, C>

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

fn is_in_subset(t: &Transform<N2, U2, C>) -> bool

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

unsafe fn from_superset_unchecked(t: &Transform<N2, U2, C>) -> Self

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

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

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

impl<N1, N2, D, C> SubsetOf<Transform<N2, D, C>> for Translation<N1, D> where
    N1: RealField,
    N2: RealField + SupersetOf<N1>,
    C: SuperTCategoryOf<TAffine>,
    D: DimNameAdd<U1>,
    DefaultAllocator: Allocator<N1, D> + Allocator<N2, D> + Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>, 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

impl<N1, N2, D: DimName, 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
    N1: RealField + SubsetOf<N2>,
    N2: RealField,
    C: TCategory,
    D: DimNameAdd<U1>,
    DefaultAllocator: Allocator<N1, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N2, DimNameSum<D, U1>, DimNameSum<D, U1>>,
    N1::Epsilon: Copy,
    N2::Epsilon: Copy, 

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

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

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

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

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

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

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

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

impl<N, D: DimNameAdd<U1>, C> ProjectiveTransformation<Point<N, D>> for Transform<N, D, C> where
    N: RealField,
    C: SubTCategoryOf<TProjective>,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, DimNameSum<D, U1>> + Allocator<N, D, D> + Allocator<N, D>, 

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

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

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

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

impl<N, D: DimNameAdd<U1>, C> Transformation<Point<N, D>> for Transform<N, D, C> where
    N: RealField,
    C: TCategory,
    DefaultAllocator: Allocator<N, DimNameSum<D, U1>, DimNameSum<D, U1>> + Allocator<N, DimNameSum<D, U1>> + Allocator<N, D, D> + Allocator<N, D>, 

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

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

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

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