[−][src]Struct euclid::Transform3D
A 3d transform stored as a column-major 4 by 4 matrix.
Transforms can be parametrized over the source and destination units, to describe a
transformation from a space to another.
For example, Transform3D<f32, WorldSpace, ScreenSpace>::transform_point3d
takes a Point3D<f32, WorldSpace>
and returns a Point3D<f32, ScreenSpace>
.
Transforms expose a set of convenience methods for pre- and post-transformations.
Pre-transformations (pre_*
methods) correspond to adding an operation that is
applied before the rest of the transformation, while post-transformations (then_*
methods) add an operation that is applied after.
When translating Transform3D into general matrix representations, consider that the representation follows the column major notation with column vectors.
|x'| | m11 m12 m13 m14 | |x|
|y'| | m21 m22 m23 m24 | |y|
|z'| = | m31 m32 m33 m34 | x |y|
|w | | m41 m42 m43 m44 | |1|
The translation terms are m41, m42 and m43.
Fields
m11: T
m12: T
m13: T
m14: T
m21: T
m22: T
m23: T
m24: T
m31: T
m32: T
m33: T
m34: T
m41: T
m42: T
m43: T
m44: T
Implementations
impl<T, Src, Dst> Transform3D<T, Src, Dst>
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pub const fn new(
m11: T,
m12: T,
m13: T,
m14: T,
m21: T,
m22: T,
m23: T,
m24: T,
m31: T,
m32: T,
m33: T,
m34: T,
m41: T,
m42: T,
m43: T,
m44: T
) -> Self
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m11: T,
m12: T,
m13: T,
m14: T,
m21: T,
m22: T,
m23: T,
m24: T,
m31: T,
m32: T,
m33: T,
m34: T,
m41: T,
m42: T,
m43: T,
m44: T
) -> Self
Create a transform specifying all of it's component as a 4 by 4 matrix.
Components are specified following column-major-column-vector matrix notation. For example, the translation terms m41, m42, m43 are the 13rd, 14th and 15th parameters.
use euclid::default::Transform3D; let tx = 1.0; let ty = 2.0; let tz = 3.0; let translation = Transform3D::new( 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, tx, ty, tz, 1.0, );
pub fn new_2d(m11: T, m12: T, m21: T, m22: T, m41: T, m42: T) -> Self where
T: Zero + One,
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T: Zero + One,
Create a transform representing a 2d transformation from the components of a 2 by 3 matrix transformation.
Components follow the column-major-column-vector notation (m41 and m42 representating the translation terms).
m11 m12 0 0
m21 m22 0 0
0 0 1 0
m41 m42 0 1
pub fn is_2d(&self) -> bool where
T: Zero + One + PartialEq,
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T: Zero + One + PartialEq,
Returns true
if this transform can be represented with a Transform2D
.
impl<T: Copy, Src, Dst> Transform3D<T, Src, Dst>
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pub fn to_array(&self) -> [T; 16]
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Returns an array containing this transform's terms.
The terms are laid out in the same order as they are
specified in Transform3D::new
, that is following the
column-major-column-vector matrix notation.
For example the translation terms are found on the 13th, 14th and 15th slots of the array.
pub fn to_array_transposed(&self) -> [T; 16]
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Returns an array containing this transform's terms transposed.
The terms are laid out in transposed order from the same order of
Transform3D::new
and Transform3D::to_array
, that is following
the row-major-column-vector matrix notation.
For example the translation terms are found at indices 3, 7 and 11 of the array.
pub fn to_arrays(&self) -> [[T; 4]; 4]
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Equivalent to to_array
with elements packed four at a time
in an array of arrays.
pub fn to_arrays_transposed(&self) -> [[T; 4]; 4]
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Equivalent to to_array_transposed
with elements packed
four at a time in an array of arrays.
pub fn from_array(array: [T; 16]) -> Self
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Create a transform providing its components via an array of 16 elements instead of as individual parameters.
The order of the components corresponds to the
column-major-column-vector matrix notation (the same order
as Transform3D::new
).
pub fn from_arrays(array: [[T; 4]; 4]) -> Self
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Equivalent to from_array
with elements packed four at a time
in an array of arrays.
The order of the components corresponds to the
column-major-column-vector matrix notation (the same order
as Transform3D::new
).
pub fn from_untyped(m: &Transform3D<T, UnknownUnit, UnknownUnit>) -> Self
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Tag a unitless value with units.
pub fn to_untyped(&self) -> Transform3D<T, UnknownUnit, UnknownUnit>
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Drop the units, preserving only the numeric value.
pub fn with_source<NewSrc>(&self) -> Transform3D<T, NewSrc, Dst>
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Returns the same transform with a different source unit.
pub fn with_destination<NewDst>(&self) -> Transform3D<T, Src, NewDst>
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Returns the same transform with a different destination unit.
pub fn to_2d(&self) -> Transform2D<T, Src, Dst>
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Create a 2D transform picking the relevant terms from this transform.
This method assumes that self represents a 2d transformation, callers
should check that self.is_2d()
returns true
beforehand.
impl<T, Src, Dst> Transform3D<T, Src, Dst> where
T: Zero + One,
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T: Zero + One,
pub fn identity() -> Self
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Creates an identity matrix:
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1
pub fn skew(alpha: Angle<T>, beta: Angle<T>) -> Self where
T: Trig,
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T: Trig,
Create a 2d skew transform.
pub fn perspective(d: T) -> Self where
T: Neg<Output = T> + Div<Output = T>,
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T: Neg<Output = T> + Div<Output = T>,
Create a simple perspective projection transform:
1 0 0 0
0 1 0 0
0 0 1 -1/d
0 0 0 1
impl<T, Src, Dst> Transform3D<T, Src, Dst> where
T: Copy + Add<Output = T> + Mul<Output = T>,
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T: Copy + Add<Output = T> + Mul<Output = T>,
Methods for combining generic transformations
#[must_use]pub fn then<NewDst>(
&self,
other: &Transform3D<T, Dst, NewDst>
) -> Transform3D<T, Src, NewDst>
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&self,
other: &Transform3D<T, Dst, NewDst>
) -> Transform3D<T, Src, NewDst>
Returns the multiplication of the two matrices such that mat's transformation applies after self's transformation.
Assuming row vectors, this is equivalent to self * mat
impl<T, Src, Dst> Transform3D<T, Src, Dst> where
T: Zero + One,
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T: Zero + One,
Methods for creating and combining translation transformations
pub fn translation(x: T, y: T, z: T) -> Self
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Create a 3d translation transform:
1 0 0 0
0 1 0 0
0 0 1 0
x y z 1
#[must_use]pub fn pre_translate(&self, v: Vector3D<T, Src>) -> Self where
T: Copy + Add<Output = T> + Mul<Output = T>,
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T: Copy + Add<Output = T> + Mul<Output = T>,
Returns a transform with a translation applied before self's transformation.
#[must_use]pub fn then_translate(&self, v: Vector3D<T, Dst>) -> Self where
T: Copy + Add<Output = T> + Mul<Output = T>,
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T: Copy + Add<Output = T> + Mul<Output = T>,
Returns a transform with a translation applied after self's transformation.
impl<T, Src, Dst> Transform3D<T, Src, Dst> where
T: Copy + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Div<Output = T> + Zero + One + Trig,
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T: Copy + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Div<Output = T> + Zero + One + Trig,
Methods for creating and combining rotation transformations
pub fn rotation(x: T, y: T, z: T, theta: Angle<T>) -> Self
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Create a 3d rotation transform from an angle / axis. The supplied axis must be normalized.
#[must_use]pub fn then_rotate(&self, x: T, y: T, z: T, theta: Angle<T>) -> Self
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Returns a transform with a rotation applied after self's transformation.
#[must_use]pub fn pre_rotate(&self, x: T, y: T, z: T, theta: Angle<T>) -> Self
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Returns a transform with a rotation applied before self's transformation.
impl<T, Src, Dst> Transform3D<T, Src, Dst> where
T: Zero + One,
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T: Zero + One,
Methods for creating and combining scale transformations
pub fn scale(x: T, y: T, z: T) -> Self
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Create a 3d scale transform:
x 0 0 0
0 y 0 0
0 0 z 0
0 0 0 1
#[must_use]pub fn pre_scale(&self, x: T, y: T, z: T) -> Self where
T: Copy + Add<Output = T> + Mul<Output = T>,
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T: Copy + Add<Output = T> + Mul<Output = T>,
Returns a transform with a scale applied before self's transformation.
#[must_use]pub fn then_scale(&self, x: T, y: T, z: T) -> Self where
T: Copy + Add<Output = T> + Mul<Output = T>,
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T: Copy + Add<Output = T> + Mul<Output = T>,
Returns a transform with a scale applied after self's transformation.
impl<T, Src, Dst> Transform3D<T, Src, Dst> where
T: Copy + Add<Output = T> + Mul<Output = T>,
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T: Copy + Add<Output = T> + Mul<Output = T>,
Methods for apply transformations to objects
pub fn transform_point2d_homogeneous(
&self,
p: Point2D<T, Src>
) -> HomogeneousVector<T, Dst>
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&self,
p: Point2D<T, Src>
) -> HomogeneousVector<T, Dst>
Returns the homogeneous vector corresponding to the transformed 2d point.
The input point must be use the unit Src, and the returned point has the unit Dst.
pub fn transform_point2d(&self, p: Point2D<T, Src>) -> Option<Point2D<T, Dst>> where
T: Div<Output = T> + Zero + PartialOrd,
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T: Div<Output = T> + Zero + PartialOrd,
Returns the given 2d point transformed by this transform, if the transform makes sense,
or None
otherwise.
The input point must be use the unit Src, and the returned point has the unit Dst.
pub fn transform_vector2d(&self, v: Vector2D<T, Src>) -> Vector2D<T, Dst>
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Returns the given 2d vector transformed by this matrix.
The input point must be use the unit Src, and the returned point has the unit Dst.
pub fn transform_point3d_homogeneous(
&self,
p: Point3D<T, Src>
) -> HomogeneousVector<T, Dst>
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&self,
p: Point3D<T, Src>
) -> HomogeneousVector<T, Dst>
Returns the homogeneous vector corresponding to the transformed 3d point.
The input point must be use the unit Src, and the returned point has the unit Dst.
pub fn transform_point3d(&self, p: Point3D<T, Src>) -> Option<Point3D<T, Dst>> where
T: Div<Output = T> + Zero + PartialOrd,
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T: Div<Output = T> + Zero + PartialOrd,
Returns the given 3d point transformed by this transform, if the transform makes sense,
or None
otherwise.
The input point must be use the unit Src, and the returned point has the unit Dst.
pub fn transform_vector3d(&self, v: Vector3D<T, Src>) -> Vector3D<T, Dst>
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Returns the given 3d vector transformed by this matrix.
The input point must be use the unit Src, and the returned point has the unit Dst.
pub fn outer_transformed_rect(
&self,
rect: &Rect<T, Src>
) -> Option<Rect<T, Dst>> where
T: Sub<Output = T> + Div<Output = T> + Zero + PartialOrd,
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&self,
rect: &Rect<T, Src>
) -> Option<Rect<T, Dst>> where
T: Sub<Output = T> + Div<Output = T> + Zero + PartialOrd,
Returns a rectangle that encompasses the result of transforming the given rectangle by this
transform, if the transform makes sense for it, or None
otherwise.
pub fn outer_transformed_box2d(
&self,
b: &Box2D<T, Src>
) -> Option<Box2D<T, Dst>> where
T: Sub<Output = T> + Div<Output = T> + Zero + PartialOrd,
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&self,
b: &Box2D<T, Src>
) -> Option<Box2D<T, Dst>> where
T: Sub<Output = T> + Div<Output = T> + Zero + PartialOrd,
Returns a 2d box that encompasses the result of transforming the given box by this
transform, if the transform makes sense for it, or None
otherwise.
pub fn outer_transformed_box3d(
&self,
b: &Box3D<T, Src>
) -> Option<Box3D<T, Dst>> where
T: Sub<Output = T> + Div<Output = T> + Zero + PartialOrd,
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&self,
b: &Box3D<T, Src>
) -> Option<Box3D<T, Dst>> where
T: Sub<Output = T> + Div<Output = T> + Zero + PartialOrd,
Returns a 3d box that encompasses the result of transforming the given box by this
transform, if the transform makes sense for it, or None
otherwise.
impl<T, Src, Dst> Transform3D<T, Src, Dst> where
T: Copy + Add<T, Output = T> + Sub<T, Output = T> + Mul<T, Output = T> + Div<T, Output = T> + Neg<Output = T> + PartialOrd + One + Zero,
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T: Copy + Add<T, Output = T> + Sub<T, Output = T> + Mul<T, Output = T> + Div<T, Output = T> + Neg<Output = T> + PartialOrd + One + Zero,
pub fn ortho(left: T, right: T, bottom: T, top: T, near: T, far: T) -> Self
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Create an orthogonal projection transform.
pub fn is_backface_visible(&self) -> bool
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Check whether shapes on the XY plane with Z pointing towards the screen transformed by this matrix would be facing back.
pub fn is_invertible(&self) -> bool
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Returns whether it is possible to compute the inverse transform.
pub fn inverse(&self) -> Option<Transform3D<T, Dst, Src>>
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Returns the inverse transform if possible.
pub fn determinant(&self) -> T
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Compute the determinant of the transform.
#[must_use]pub fn mul_s(&self, x: T) -> Self
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Multiplies all of the transform's component by a scalar and returns the result.
pub fn from_scale(scale: Scale<T, Src, Dst>) -> Self
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Convenience function to create a scale transform from a Scale
.
impl<T, Src, Dst> Transform3D<T, Src, Dst> where
T: Copy + Mul<Output = T> + Div<Output = T> + Zero + One + PartialEq,
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T: Copy + Mul<Output = T> + Div<Output = T> + Zero + One + PartialEq,
pub fn project_to_2d(&self) -> Self
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Returns a projection of this transform in 2d space.
impl<T: NumCast + Copy, Src, Dst> Transform3D<T, Src, Dst>
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pub fn cast<NewT: NumCast>(&self) -> Transform3D<NewT, Src, Dst>
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Cast from one numeric representation to another, preserving the units.
pub fn try_cast<NewT: NumCast>(&self) -> Option<Transform3D<NewT, Src, Dst>>
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Fallible cast from one numeric representation to another, preserving the units.
impl<T: ApproxEq<T>, Src, Dst> Transform3D<T, Src, Dst>
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pub fn approx_eq(&self, other: &Self) -> bool
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Returns true is this transform is approximately equal to the other one, using T's default epsilon value.
The same as ApproxEq::approx_eq()
but available without importing trait.
pub fn approx_eq_eps(&self, other: &Self, eps: &T) -> bool
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Returns true is this transform is approximately equal to the other one, using a provided epsilon value.
The same as ApproxEq::approx_eq_eps()
but available without importing trait.
Trait Implementations
impl<T: ApproxEq<T>, Src, Dst> ApproxEq<T> for Transform3D<T, Src, Dst>
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fn approx_epsilon() -> T
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fn approx_eq_eps(&self, other: &Self, eps: &T) -> bool
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fn approx_eq(&self, other: &Self) -> bool
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impl<T: Clone, Src, Dst> Clone for Transform3D<T, Src, Dst>
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fn clone(&self) -> Self
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fn clone_from(&mut self, source: &Self)
1.0.0[src]
impl<T: Copy, Src, Dst> Copy for Transform3D<T, Src, Dst>
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impl<T, Src, Dst> Debug for Transform3D<T, Src, Dst> where
T: Copy + Debug + PartialEq + One + Zero,
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T: Copy + Debug + PartialEq + One + Zero,
impl<T, Src, Dst> Default for Transform3D<T, Src, Dst> where
T: Zero + One,
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T: Zero + One,
fn default() -> Self
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Returns the identity transform.
impl<T, Src, Dst> Eq for Transform3D<T, Src, Dst> where
T: Eq,
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T: Eq,
impl<T, Src, Dst> Hash for Transform3D<T, Src, Dst> where
T: Hash,
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T: Hash,
fn hash<H: Hasher>(&self, h: &mut H)
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fn hash_slice<H>(data: &[Self], state: &mut H) where
H: Hasher,
1.3.0[src]
H: Hasher,
impl<T, Src, Dst> Into<Transform3D<T, Src, Dst>> for Translation3D<T, Src, Dst> where
T: Zero + One,
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T: Zero + One,
fn into(self) -> Transform3D<T, Src, Dst>
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impl<T, Src, Dst> PartialEq<Transform3D<T, Src, Dst>> for Transform3D<T, Src, Dst> where
T: PartialEq,
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T: PartialEq,
Auto Trait Implementations
impl<T, Src, Dst> RefUnwindSafe for Transform3D<T, Src, Dst> where
Dst: RefUnwindSafe,
Src: RefUnwindSafe,
T: RefUnwindSafe,
Dst: RefUnwindSafe,
Src: RefUnwindSafe,
T: RefUnwindSafe,
impl<T, Src, Dst> Send for Transform3D<T, Src, Dst> where
Dst: Send,
Src: Send,
T: Send,
Dst: Send,
Src: Send,
T: Send,
impl<T, Src, Dst> Sync for Transform3D<T, Src, Dst> where
Dst: Sync,
Src: Sync,
T: Sync,
Dst: Sync,
Src: Sync,
T: Sync,
impl<T, Src, Dst> Unpin for Transform3D<T, Src, Dst> where
Dst: Unpin,
Src: Unpin,
T: Unpin,
Dst: Unpin,
Src: Unpin,
T: Unpin,
impl<T, Src, Dst> UnwindSafe for Transform3D<T, Src, Dst> where
Dst: UnwindSafe,
Src: UnwindSafe,
T: UnwindSafe,
Dst: UnwindSafe,
Src: UnwindSafe,
T: UnwindSafe,
Blanket Implementations
impl<T> Any for T where
T: 'static + ?Sized,
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T: 'static + ?Sized,
impl<T> Borrow<T> for T where
T: ?Sized,
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T: ?Sized,
impl<T> BorrowMut<T> for T where
T: ?Sized,
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T: ?Sized,
fn borrow_mut(&mut self) -> &mut T
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impl<T> From<T> for T
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impl<T, U> Into<U> for T where
U: From<T>,
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U: From<T>,
impl<T> ToOwned for T where
T: Clone,
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T: Clone,
type Owned = T
The resulting type after obtaining ownership.
fn to_owned(&self) -> T
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fn clone_into(&self, target: &mut T)
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impl<T, U> TryFrom<U> for T where
U: Into<T>,
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U: Into<T>,
type Error = Infallible
The type returned in the event of a conversion error.
fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>
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impl<T, U> TryInto<U> for T where
U: TryFrom<T>,
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U: TryFrom<T>,