Struct euclid::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,
    // some fields omitted
}

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

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

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

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,
);

pub fn approx_eq(&self, other: &Self) -> bool where
    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.

pub fn approx_eq_eps(&self, other: &Self, eps: &T) -> bool where
    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.

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

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.

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.

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

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

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).

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).

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

Drop the units, preserving only the numeric value.

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

Tag a unitless value with units.

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

Returns the same transform with a different source unit.

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

Returns the same transform with a different destination unit.

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

Create a 3D transform from the current transform

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

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

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

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

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

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

pub fn identity() -> Self

Create an identity matrix:

1 0
0 1
0 0

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

Methods for combining generic transformations

#[must_use]

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.

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

Methods for creating and combining translation transformations

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

Create a 2d translation transform:

1 0
0 1
x y

#[must_use]

pub fn then_translate(&self, v: Vector2D<T, Dst>) -> Self where
    T: Copy + Add<Output = T> + Mul<Output = T>, 

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

#[must_use]

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

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

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

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

Returns a rotation transform.

#[must_use]

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

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

#[must_use]

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

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

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

Methods for creating and combining scale transformations

pub fn scale(x: T, y: T) -> Self where
    T: Zero, 

Create a 2d scale transform:

x 0
0 y
0 0

#[must_use]

pub fn then_scale(&self, x: T, y: T) -> Self where
    T: Copy + Add<Output = T> + Mul<Output = T> + Zero, 

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

#[must_use]

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

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

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

Methods for apply transformations to objects

#[must_use]

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

Returns the given point transformed by this transform.

#[must_use]

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

Returns the given vector transformed by this matrix.

#[must_use]

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.

#[must_use]

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.

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

pub fn determinant(&self) -> T

Computes and returns the determinant of this transform.

pub fn is_invertible(&self) -> bool

Returns whether it is possible to compute the inverse transform.

#[must_use]

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

Returns the inverse transform if possible.

Trait Implementations

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

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.

fn approx_epsilon() -> T

Default epsilon value

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.

impl<T: Clone, Src, Dst> Clone for Transform2D<T, Src, Dst>

fn clone(&self) -> Self

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<T, Src, Dst> Debug for Transform2D<T, Src, Dst> where
    T: Copy + Debug + PartialEq + One + Zero, 

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

Formats the value using the given formatter.

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

fn default() -> Self

Returns the identity transform.

impl<T, Src, Dst> Hash for Transform2D<T, Src, Dst> where
    T: Hash, 

fn hash<H: Hasher>(&self, h: &mut H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H) where
    H: Hasher, 

Feeds a slice of this type into the given Hasher.

impl<T, Src, Dst> Into<Transform2D<T, Src, Dst>> for Translation2D<T, Src, Dst> where
    T: Zero + One, 

fn into(self) -> Transform2D<T, Src, Dst>

Performs the conversion.

impl<T, Src, Dst> PartialEq<Transform2D<T, Src, Dst>> for Transform2D<T, Src, Dst> where
    T: PartialEq, 

fn eq(&self, other: &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<T: Copy, Src, Dst> Copy for Transform2D<T, Src, Dst>

impl<T, Src, Dst> Eq for Transform2D<T, Src, Dst> where
    T: Eq,