# Struct euclid::transform2d::Transform2D

``````#[repr(C)]pub struct Transform2D<T, Src, Dst> {
pub m11: T,
pub m12: T,
pub m21: T,
pub m22: T,
pub m31: T,
pub m32: T,
/* private fields */
}``````
Expand description

A 2d transform represented by a column-major 3 by 3 matrix, compressed down to 3 by 2.

Transforms can be parametrized over the source and destination units, to describe a transformation from a space to another. For example, `Transform2D<f32, WorldSpace, ScreenSpace>::transform_point4d` takes a `Point2D<f32, WorldSpace>` and returns a `Point2D<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.

The matrix representation is conceptually equivalent to a 3 by 3 matrix transformation compressed to 3 by 2 with the components that aren’t needed to describe the set of 2d transformations we are interested in implicitly defined:

`````` | m11 m21 m31 |   |x|   |x'|
| m12 m22 m32 | x |y| = |y'|
|   0   0   1 |   |1|   |1 |
``````

When translating Transform2D into general matrix representations, consider that the representation follows the column-major notation with column vectors.

The translation terms are m31 and m32.

## Fields§

§`m11: T`§`m12: T`§`m21: T`§`m22: T`§`m31: T`§`m32: T`

## Implementations§

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### impl<T, Src, Dst> Transform2D<T, Src, Dst>

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#### pub const fn new(m11: T, m12: T, m21: T, m22: T, m31: T, m32: T) -> Self

Create a transform specifying its components in using the column-major-column-vector matrix notation.

For example, the translation terms m31 and m32 are the last two parameters parameters.

``````use euclid::default::Transform2D;
let tx = 1.0;
let ty = 2.0;
let translation = Transform2D::new(
1.0, 0.0,
0.0, 1.0,
tx,  ty,
);``````
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#### pub fn approx_eq(&self, other: &Self) -> boolwhere T: ApproxEq<T>,

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.

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#### pub fn approx_eq_eps(&self, other: &Self, eps: &T) -> boolwhere T: ApproxEq<T>,

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.

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### impl<T: Copy, Src, Dst> Transform2D<T, Src, Dst>

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#### pub fn to_array(&self) -> [T; 6]

Returns an array containing this transform’s terms.

The terms are laid out in the same order as they are specified in `Transform2D::new`, that is following the column-major-column-vector matrix notation.

For example the translation terms are found in the last two slots of the array.

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#### pub fn to_array_transposed(&self) -> [T; 6]

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 2 and 5 in the array.

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#### pub fn to_arrays(&self) -> [[T; 2]; 3]

Equivalent to `to_array` with elements packed two at a time in an array of arrays.

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#### pub fn from_array(array: [T; 6]) -> Self

Create a transform providing its components via an array of 6 elements instead of as individual parameters.

The order of the components corresponds to the column-major-column-vector matrix notation (the same order as `Transform2D::new`).

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#### pub fn from_arrays(array: [[T; 2]; 3]) -> Self

Equivalent to `from_array` with elements packed two 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`).

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#### pub fn to_untyped(&self) -> Transform2D<T, UnknownUnit, UnknownUnit>

Drop the units, preserving only the numeric value.

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#### pub fn from_untyped(p: &Transform2D<T, UnknownUnit, UnknownUnit>) -> Self

Tag a unitless value with units.

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#### pub fn with_source<NewSrc>(&self) -> Transform2D<T, NewSrc, Dst>

Returns the same transform with a different source unit.

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#### pub fn with_destination<NewDst>(&self) -> Transform2D<T, Src, NewDst>

Returns the same transform with a different destination unit.

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#### pub fn to_3d(&self) -> Transform3D<T, Src, Dst>where T: Zero + One,

Create a 3D transform from the current transform

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### impl<T: NumCast + Copy, Src, Dst> Transform2D<T, Src, Dst>

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#### pub fn cast<NewT: NumCast>(&self) -> Transform2D<NewT, Src, Dst>

Cast from one numeric representation to another, preserving the units.

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#### pub fn try_cast<NewT: NumCast>(&self) -> Option<Transform2D<NewT, Src, Dst>>

Fallible cast from one numeric representation to another, preserving the units.

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### impl<T, Src, Dst> Transform2D<T, Src, Dst>where T: Zero + One,

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#### pub fn identity() -> Self

Create an identity matrix:

``````1 0
0 1
0 0
``````
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#### fn is_identity(&self) -> boolwhere T: PartialEq,

Intentional not public, because it checks for exact equivalence while most consumers will probably want some sort of approximate equivalence to deal with floating-point errors.

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### impl<T, Src, Dst> Transform2D<T, Src, Dst>where T: Copy + Add<Output = T> + Mul<Output = T>,

Methods for combining generic transformations

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#### pub fn then<NewDst>( &self, mat: &Transform2D<T, Dst, NewDst> ) -> Transform2D<T, Src, NewDst>

Returns the multiplication of the two matrices such that mat’s transformation applies after self’s transformation.

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### impl<T, Src, Dst> Transform2D<T, Src, Dst>where T: Zero + One,

Methods for creating and combining translation transformations

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#### pub fn translation(x: T, y: T) -> Self

Create a 2d translation transform:

``````1 0
0 1
x y
``````
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#### pub fn then_translate(&self, v: Vector2D<T, Dst>) -> Selfwhere T: Copy + Add<Output = T> + Mul<Output = T>,

Applies a translation after self’s transformation and returns the resulting transform.

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#### pub fn pre_translate(&self, v: Vector2D<T, Src>) -> Selfwhere T: Copy + Add<Output = T> + Mul<Output = T>,

Applies a translation before self’s transformation and returns the resulting transform.

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### impl<T, Src, Dst> Transform2D<T, Src, Dst>where T: Copy + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Zero + Trig,

Methods for creating and combining rotation transformations

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#### pub fn rotation(theta: Angle<T>) -> Self

Returns a rotation transform.

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#### pub fn then_rotate(&self, theta: Angle<T>) -> Self

Applies a rotation after self’s transformation and returns the resulting transform.

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#### pub fn pre_rotate(&self, theta: Angle<T>) -> Self

Applies a rotation before self’s transformation and returns the resulting transform.

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### impl<T, Src, Dst> Transform2D<T, Src, Dst>

Methods for creating and combining scale transformations

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#### pub fn scale(x: T, y: T) -> Selfwhere T: Zero,

Create a 2d scale transform:

``````x 0
0 y
0 0
``````
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#### pub fn then_scale(&self, x: T, y: T) -> Selfwhere T: Copy + Add<Output = T> + Mul<Output = T> + Zero,

Applies a scale after self’s transformation and returns the resulting transform.

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#### pub fn pre_scale(&self, x: T, y: T) -> Selfwhere T: Copy + Mul<Output = T>,

Applies a scale before self’s transformation and returns the resulting transform.

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### impl<T, Src, Dst> Transform2D<T, Src, Dst>where T: Copy + Add<Output = T> + Mul<Output = T>,

Methods for apply transformations to objects

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#### pub fn transform_point(&self, point: Point2D<T, Src>) -> Point2D<T, Dst>

Returns the given point transformed by this transform.

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#### pub fn transform_vector(&self, vec: Vector2D<T, Src>) -> Vector2D<T, Dst>

Returns the given vector transformed by this matrix.

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#### pub fn outer_transformed_rect(&self, rect: &Rect<T, Src>) -> Rect<T, Dst>where T: Sub<Output = T> + Zero + PartialOrd,

Returns a rectangle that encompasses the result of transforming the given rectangle by this transform.

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#### pub fn outer_transformed_box(&self, b: &Box2D<T, Src>) -> Box2D<T, Dst>where T: Sub<Output = T> + Zero + PartialOrd,

Returns a box that encompasses the result of transforming the given box by this transform.

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### impl<T, Src, Dst> Transform2D<T, Src, Dst>where T: Copy + Sub<Output = T> + Mul<Output = T> + Div<Output = T> + PartialEq + Zero + One,

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#### pub fn determinant(&self) -> T

Computes and returns the determinant of this transform.

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#### pub fn is_invertible(&self) -> bool

Returns whether it is possible to compute the inverse transform.

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#### pub fn inverse(&self) -> Option<Transform2D<T, Dst, Src>>

Returns the inverse transform if possible.

## Trait Implementations§

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### impl<T: ApproxEq<T>, Src, Dst> ApproxEq<T> for Transform2D<T, Src, Dst>

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#### fn approx_eq_eps(&self, other: &Self, eps: &T) -> bool

Returns true is this transform is approximately equal to the other one, using a provided epsilon value.

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#### fn approx_epsilon() -> T

Default epsilon value
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#### fn approx_eq(&self, other: &Self) -> bool

Returns `true` is this object is approximately equal to the other one, using the `approx_epsilon()` epsilon value.
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### impl<T: Clone, Src, Dst> Clone for Transform2D<T, Src, Dst>

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#### fn clone(&self) -> Self

Returns a copy of the value. Read more
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#### fn clone_from(&mut self, source: &Self)

Performs copy-assignment from `source`. Read more
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### impl<T, Src, Dst> Debug for Transform2D<T, Src, Dst>where T: Copy + Debug + PartialEq + One + Zero,

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

Formats the value using the given formatter. Read more
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### impl<T, Src, Dst> Default for Transform2D<T, Src, Dst>where T: Zero + One,

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#### fn default() -> Self

Returns the identity transform.

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### impl<'de, T, Src, Dst> Deserialize<'de> for Transform2D<T, Src, Dst>where T: Deserialize<'de>,

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#### fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer. Read more
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### impl<T, Src, Dst> From<Translation2D<T, Src, Dst>> for Transform2D<T, Src, Dst>where T: Zero + One,

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#### fn from(t: Translation2D<T, Src, Dst>) -> Self

Converts to this type from the input type.
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### impl<T, Src, Dst> Hash for Transform2D<T, Src, Dst>where T: Hash,

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

Feeds this value into the given `Hasher`. Read more
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#### fn hash_slice<H>(data: &[Self], state: &mut H)where H: Hasher, Self: Sized,

Feeds a slice of this type into the given `Hasher`. Read more
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### impl<T, Src, Dst> PartialEq for Transform2D<T, Src, Dst>where T: PartialEq,

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

This method tests for `self` and `other` values to be equal, and is used by `==`.
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#### fn ne(&self, other: &Rhs) -> bool

This method tests for `!=`. The default implementation is almost always sufficient, and should not be overridden without very good reason.
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### impl<T, Src, Dst> Serialize for Transform2D<T, Src, Dst>where T: Serialize,

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#### fn serialize<__S>(&self, __serializer: __S) -> Result<__S::Ok, __S::Error>where __S: Serializer,

Serialize this value into the given Serde serializer. Read more
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## Blanket Implementations§

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### impl<T> Any for Twhere T: 'static + ?Sized,

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#### fn type_id(&self) -> TypeId

Gets the `TypeId` of `self`. Read more
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### impl<T> Borrow<T> for Twhere T: ?Sized,

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#### fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
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### impl<T> BorrowMut<T> for Twhere T: ?Sized,

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#### fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more
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### impl<T> From<T> for T

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#### fn from(t: T) -> T

Returns the argument unchanged.

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### impl<T, U> Into<U> for Twhere U: From<T>,

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#### fn into(self) -> U

Calls `U::from(self)`.

That is, this conversion is whatever the implementation of `From<T> for U` chooses to do.

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### impl<T> ToOwned for Twhere T: Clone,

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#### type Owned = T

The resulting type after obtaining ownership.
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#### fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more
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#### fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more
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### impl<T, U> TryFrom<U> for Twhere U: Into<T>,

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#### type Error = Infallible

The type returned in the event of a conversion error.
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#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
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### impl<T, U> TryInto<U> for Twhere U: TryFrom<T>,

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#### type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.
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#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.
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