Struct euclid::Transform2D
source · #[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 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§
source§impl<T, Src, Dst> Transform2D<T, Src, Dst>
impl<T, Src, Dst> Transform2D<T, Src, Dst>
sourcepub const fn new(m11: T, m12: T, m21: T, m22: T, m31: T, m32: T) -> Self
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,
);
sourcepub fn approx_eq(&self, other: &Self) -> boolwhere
T: ApproxEq<T>,
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.
sourcepub fn approx_eq_eps(&self, other: &Self, eps: &T) -> boolwhere
T: ApproxEq<T>,
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.
source§impl<T: Copy, Src, Dst> Transform2D<T, Src, Dst>
impl<T: Copy, Src, Dst> Transform2D<T, Src, Dst>
sourcepub fn to_array(&self) -> [T; 6]
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.
sourcepub fn to_array_transposed(&self) -> [T; 6]
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.
sourcepub fn to_arrays(&self) -> [[T; 2]; 3]
pub fn to_arrays(&self) -> [[T; 2]; 3]
Equivalent to to_array
with elements packed two at a time
in an array of arrays.
sourcepub fn from_array(array: [T; 6]) -> Self
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
).
sourcepub fn from_arrays(array: [[T; 2]; 3]) -> Self
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
).
sourcepub fn to_untyped(&self) -> Transform2D<T, UnknownUnit, UnknownUnit>
pub fn to_untyped(&self) -> Transform2D<T, UnknownUnit, UnknownUnit>
Drop the units, preserving only the numeric value.
sourcepub fn from_untyped(p: &Transform2D<T, UnknownUnit, UnknownUnit>) -> Self
pub fn from_untyped(p: &Transform2D<T, UnknownUnit, UnknownUnit>) -> Self
Tag a unitless value with units.
sourcepub fn with_source<NewSrc>(&self) -> Transform2D<T, NewSrc, Dst>
pub fn with_source<NewSrc>(&self) -> Transform2D<T, NewSrc, Dst>
Returns the same transform with a different source unit.
sourcepub fn with_destination<NewDst>(&self) -> Transform2D<T, Src, NewDst>
pub fn with_destination<NewDst>(&self) -> Transform2D<T, Src, NewDst>
Returns the same transform with a different destination unit.
sourcepub fn to_3d(&self) -> Transform3D<T, Src, Dst>where
T: Zero + One,
pub fn to_3d(&self) -> Transform3D<T, Src, Dst>where T: Zero + One,
Create a 3D transform from the current transform
source§impl<T: NumCast + Copy, Src, Dst> Transform2D<T, Src, Dst>
impl<T: NumCast + Copy, Src, Dst> Transform2D<T, Src, Dst>
sourcepub fn cast<NewT: NumCast>(&self) -> Transform2D<NewT, Src, Dst>
pub fn cast<NewT: NumCast>(&self) -> Transform2D<NewT, Src, Dst>
Cast from one numeric representation to another, preserving the units.
sourcepub fn try_cast<NewT: NumCast>(&self) -> Option<Transform2D<NewT, Src, Dst>>
pub fn try_cast<NewT: NumCast>(&self) -> Option<Transform2D<NewT, Src, Dst>>
Fallible cast from one numeric representation to another, preserving the units.
source§impl<T, Src, Dst> Transform2D<T, Src, Dst>where
T: Zero + One,
impl<T, Src, Dst> Transform2D<T, Src, Dst>where T: Zero + One,
source§impl<T, Src, Dst> Transform2D<T, Src, Dst>where
T: Copy + Add<Output = T> + Mul<Output = T>,
impl<T, Src, Dst> Transform2D<T, Src, Dst>where T: Copy + Add<Output = T> + Mul<Output = T>,
Methods for combining generic transformations
sourcepub fn then<NewDst>(
&self,
mat: &Transform2D<T, Dst, NewDst>
) -> Transform2D<T, Src, NewDst>
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.
source§impl<T, Src, Dst> Transform2D<T, Src, Dst>where
T: Zero + One,
impl<T, Src, Dst> Transform2D<T, Src, Dst>where T: Zero + One,
Methods for creating and combining translation transformations
sourcepub fn translation(x: T, y: T) -> Self
pub fn translation(x: T, y: T) -> Self
Create a 2d translation transform:
1 0
0 1
x y
source§impl<T, Src, Dst> Transform2D<T, Src, Dst>where
T: Copy + Add<Output = T> + Sub<Output = T> + Mul<Output = T> + Zero + Trig,
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
sourcepub fn then_rotate(&self, theta: Angle<T>) -> Self
pub fn then_rotate(&self, theta: Angle<T>) -> Self
Applies a rotation after self’s transformation and returns the resulting transform.
sourcepub fn pre_rotate(&self, theta: Angle<T>) -> Self
pub fn pre_rotate(&self, theta: Angle<T>) -> Self
Applies a rotation before self’s transformation and returns the resulting transform.
source§impl<T, Src, Dst> Transform2D<T, Src, Dst>
impl<T, Src, Dst> Transform2D<T, Src, Dst>
Methods for creating and combining scale transformations
source§impl<T, Src, Dst> Transform2D<T, Src, Dst>where
T: Copy + Add<Output = T> + Mul<Output = T>,
impl<T, Src, Dst> Transform2D<T, Src, Dst>where T: Copy + Add<Output = T> + Mul<Output = T>,
Methods for apply transformations to objects
sourcepub fn transform_point(&self, point: Point2D<T, Src>) -> Point2D<T, Dst>
pub fn transform_point(&self, point: Point2D<T, Src>) -> Point2D<T, Dst>
Returns the given point transformed by this transform.
sourcepub fn transform_vector(&self, vec: Vector2D<T, Src>) -> Vector2D<T, Dst>
pub fn transform_vector(&self, vec: Vector2D<T, Src>) -> Vector2D<T, Dst>
Returns the given vector transformed by this matrix.
sourcepub fn outer_transformed_rect(&self, rect: &Rect<T, Src>) -> Rect<T, Dst>where
T: Sub<Output = T> + Zero + PartialOrd,
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.
sourcepub fn outer_transformed_box(&self, b: &Box2D<T, Src>) -> Box2D<T, Dst>where
T: Sub<Output = T> + Zero + PartialOrd,
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.
source§impl<T, Src, Dst> Transform2D<T, Src, Dst>where
T: Copy + Sub<Output = T> + Mul<Output = T> + Div<Output = T> + PartialEq + Zero + One,
impl<T, Src, Dst> Transform2D<T, Src, Dst>where T: Copy + Sub<Output = T> + Mul<Output = T> + Div<Output = T> + PartialEq + Zero + One,
sourcepub fn determinant(&self) -> T
pub fn determinant(&self) -> T
Computes and returns the determinant of this transform.
sourcepub fn is_invertible(&self) -> bool
pub fn is_invertible(&self) -> bool
Returns whether it is possible to compute the inverse transform.
sourcepub fn inverse(&self) -> Option<Transform2D<T, Dst, Src>>
pub fn inverse(&self) -> Option<Transform2D<T, Dst, Src>>
Returns the inverse transform if possible.
Trait Implementations§
source§impl<T: ApproxEq<T>, Src, Dst> ApproxEq<T> for Transform2D<T, Src, Dst>
impl<T: ApproxEq<T>, Src, Dst> ApproxEq<T> for Transform2D<T, Src, Dst>
source§fn approx_eq_eps(&self, other: &Self, eps: &T) -> bool
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.
source§fn approx_epsilon() -> T
fn approx_epsilon() -> T
source§impl<T: Clone, Src, Dst> Clone for Transform2D<T, Src, Dst>
impl<T: Clone, Src, Dst> Clone for Transform2D<T, Src, Dst>
source§impl<T, Src, Dst> Debug for Transform2D<T, Src, Dst>where
T: Copy + Debug + PartialEq + One + Zero,
impl<T, Src, Dst> Debug for Transform2D<T, Src, Dst>where T: Copy + Debug + PartialEq + One + Zero,
source§impl<T, Src, Dst> Default for Transform2D<T, Src, Dst>where
T: Zero + One,
impl<T, Src, Dst> Default for Transform2D<T, Src, Dst>where T: Zero + One,
source§fn default() -> Self
fn default() -> Self
Returns the identity transform.