Struct euclid::Transform2D [−][src]
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>
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pub const fn new(m11: T, m12: T, m21: T, m22: T, m31: T, m32: T) -> Self
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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>,
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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>,
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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>
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pub fn to_array(&self) -> [T; 6]
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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 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]
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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 2 and 5 in the array.
pub fn to_arrays(&self) -> [[T; 2]; 3]
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Equivalent to to_array
with elements packed two at a time
in an array of arrays.
pub fn from_array(array: [T; 6]) -> Self
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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
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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>
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Drop the units, preserving only the numeric value.
pub fn from_untyped(p: &Transform2D<T, UnknownUnit, UnknownUnit>) -> Self
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Tag a unitless value with units.
pub fn with_source<NewSrc>(&self) -> Transform2D<T, NewSrc, Dst>
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Returns the same transform with a different source unit.
pub fn with_destination<NewDst>(&self) -> Transform2D<T, Src, NewDst>
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Returns the same transform with a different destination unit.
pub fn to_3d(&self) -> Transform3D<T, Src, Dst> where
T: Zero + One,
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T: Zero + One,
Create a 3D transform from the current transform
impl<T: NumCast + Copy, Src, Dst> Transform2D<T, Src, Dst>
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pub fn cast<NewT: NumCast>(&self) -> Transform2D<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<Transform2D<NewT, Src, Dst>>
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Fallible cast from one numeric representation to another, preserving the units.
impl<T, Src, Dst> Transform2D<T, Src, Dst> where
T: Zero + One,
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T: Zero + One,
impl<T, Src, Dst> Transform2D<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,
mat: &Transform2D<T, Dst, NewDst>
) -> Transform2D<T, Src, NewDst>
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&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,
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T: Zero + One,
Methods for creating and combining translation transformations
pub fn translation(x: T, y: T) -> Self
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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>,
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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>,
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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,
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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
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Returns a rotation transform.
#[must_use]pub fn then_rotate(&self, theta: Angle<T>) -> Self
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Applies a rotation after self’s transformation and returns the resulting transform.
#[must_use]pub fn pre_rotate(&self, theta: Angle<T>) -> Self
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Applies a rotation before self’s transformation and returns the resulting transform.
impl<T, Src, Dst> Transform2D<T, Src, Dst>
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Methods for creating and combining scale transformations
pub fn scale(x: T, y: T) -> Self where
T: Zero,
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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,
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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>,
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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>,
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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>
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Returns the given point transformed by this transform.
#[must_use]pub fn transform_vector(&self, vec: Vector2D<T, Src>) -> Vector2D<T, Dst>
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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,
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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,
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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,
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T: Copy + Sub<Output = T> + Mul<Output = T> + Div<Output = T> + PartialEq + Zero + One,
pub fn determinant(&self) -> T
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Computes and returns the determinant of this transform.
pub fn is_invertible(&self) -> bool
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Returns whether it is possible to compute the inverse transform.
#[must_use]pub fn inverse(&self) -> Option<Transform2D<T, Dst, Src>>
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Returns the inverse transform if possible.
Trait Implementations
impl<T: ApproxEq<T>, Src, Dst> ApproxEq<T> for Transform2D<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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Returns true is this transform is approximately equal to the other one, using a provided epsilon value.
fn approx_eq(&self, other: &Self) -> bool
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impl<T: Clone, Src, Dst> Clone for Transform2D<T, Src, Dst>
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fn clone(&self) -> Self
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pub fn clone_from(&mut self, source: &Self)
1.0.0[src]
impl<T: Copy, Src, Dst> Copy for Transform2D<T, Src, Dst>
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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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T: Copy + Debug + PartialEq + One + Zero,
impl<T, Src, Dst> Default for Transform2D<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 Transform2D<T, Src, Dst> where
T: Eq,
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T: Eq,
impl<T, Src, Dst> Hash for Transform2D<T, Src, Dst> where
T: Hash,
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T: Hash,
fn hash<H: Hasher>(&self, h: &mut H)
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pub fn hash_slice<H>(data: &[Self], state: &mut H) where
H: Hasher,
1.3.0[src]
H: Hasher,
impl<T, Src, Dst> Into<Transform2D<T, Src, Dst>> for Translation2D<T, Src, Dst> where
T: Zero + One,
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T: Zero + One,
fn into(self) -> Transform2D<T, Src, Dst>
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impl<T, Src, Dst> PartialEq<Transform2D<T, Src, Dst>> for Transform2D<T, Src, Dst> where
T: PartialEq,
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T: PartialEq,
Auto Trait Implementations
impl<T, Src, Dst> RefUnwindSafe for Transform2D<T, Src, Dst> where
Dst: RefUnwindSafe,
Src: RefUnwindSafe,
T: RefUnwindSafe,
Dst: RefUnwindSafe,
Src: RefUnwindSafe,
T: RefUnwindSafe,
impl<T, Src, Dst> Send for Transform2D<T, Src, Dst> where
Dst: Send,
Src: Send,
T: Send,
Dst: Send,
Src: Send,
T: Send,
impl<T, Src, Dst> Sync for Transform2D<T, Src, Dst> where
Dst: Sync,
Src: Sync,
T: Sync,
Dst: Sync,
Src: Sync,
T: Sync,
impl<T, Src, Dst> Unpin for Transform2D<T, Src, Dst> where
Dst: Unpin,
Src: Unpin,
T: Unpin,
Dst: Unpin,
Src: Unpin,
T: Unpin,
impl<T, Src, Dst> UnwindSafe for Transform2D<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,
pub 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.
pub fn to_owned(&self) -> T
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pub 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.
pub 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>,