Struct euclid::Transform3D
source · #[repr(C)]pub struct Transform3D<T, Src, Dst> {Show 16 fields
pub m11: T,
pub m12: T,
pub m13: T,
pub m14: T,
pub m21: T,
pub m22: T,
pub m23: T,
pub m24: T,
pub m31: T,
pub m32: T,
pub m33: T,
pub m34: T,
pub m41: T,
pub m42: T,
pub m43: T,
pub m44: T,
/* private fields */
}
Expand description
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§
source§impl<T, Src, Dst> Transform3D<T, Src, Dst>
impl<T, Src, Dst> Transform3D<T, Src, Dst>
sourcepub 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
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
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,
);
sourcepub fn new_2d(m11: T, m12: T, m21: T, m22: T, m41: T, m42: T) -> Selfwhere
T: Zero + One,
pub fn new_2d(m11: T, m12: T, m21: T, m22: T, m41: T, m42: T) -> Selfwhere 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
source§impl<T: Copy, Src, Dst> Transform3D<T, Src, Dst>
impl<T: Copy, Src, Dst> Transform3D<T, Src, Dst>
sourcepub fn to_array(&self) -> [T; 16]
pub fn to_array(&self) -> [T; 16]
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.
sourcepub fn to_array_transposed(&self) -> [T; 16]
pub fn to_array_transposed(&self) -> [T; 16]
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.
sourcepub fn to_arrays(&self) -> [[T; 4]; 4]
pub fn to_arrays(&self) -> [[T; 4]; 4]
Equivalent to to_array
with elements packed four at a time
in an array of arrays.
sourcepub fn to_arrays_transposed(&self) -> [[T; 4]; 4]
pub fn to_arrays_transposed(&self) -> [[T; 4]; 4]
Equivalent to to_array_transposed
with elements packed
four at a time in an array of arrays.
sourcepub fn from_array(array: [T; 16]) -> Self
pub fn from_array(array: [T; 16]) -> Self
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
).
sourcepub fn from_arrays(array: [[T; 4]; 4]) -> Self
pub fn from_arrays(array: [[T; 4]; 4]) -> Self
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
).
sourcepub fn from_untyped(m: &Transform3D<T, UnknownUnit, UnknownUnit>) -> Self
pub fn from_untyped(m: &Transform3D<T, UnknownUnit, UnknownUnit>) -> Self
Tag a unitless value with units.
sourcepub fn to_untyped(&self) -> Transform3D<T, UnknownUnit, UnknownUnit>
pub fn to_untyped(&self) -> Transform3D<T, UnknownUnit, UnknownUnit>
Drop the units, preserving only the numeric value.
sourcepub fn with_source<NewSrc>(&self) -> Transform3D<T, NewSrc, Dst>
pub fn with_source<NewSrc>(&self) -> Transform3D<T, NewSrc, Dst>
Returns the same transform with a different source unit.
sourcepub fn with_destination<NewDst>(&self) -> Transform3D<T, Src, NewDst>
pub fn with_destination<NewDst>(&self) -> Transform3D<T, Src, NewDst>
Returns the same transform with a different destination unit.
sourcepub fn to_2d(&self) -> Transform2D<T, Src, Dst>
pub fn to_2d(&self) -> Transform2D<T, Src, Dst>
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.
source§impl<T, Src, Dst> Transform3D<T, Src, Dst>where
T: Zero + One,
impl<T, Src, Dst> Transform3D<T, Src, Dst>where T: Zero + One,
sourcepub fn perspective(d: T) -> Selfwhere
T: Neg<Output = T> + Div<Output = T>,
pub fn perspective(d: T) -> Selfwhere T: Neg<Output = T> + Div<Output = T>,
Create a simple perspective transform, projecting to the plane z = -d
.
1 0 0 0
0 1 0 0
0 0 1 -1/d
0 0 0 1
See https://drafts.csswg.org/css-transforms-2/#PerspectiveDefined.
source§impl<T, Src, Dst> Transform3D<T, Src, Dst>where
T: Copy + Add<Output = T> + Mul<Output = T>,
impl<T, Src, Dst> Transform3D<T, Src, Dst>where T: Copy + Add<Output = T> + Mul<Output = T>,
Methods for combining generic transformations
sourcepub fn then<NewDst>(
&self,
other: &Transform3D<T, Dst, NewDst>
) -> Transform3D<T, Src, NewDst>
pub fn then<NewDst>( &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
source§impl<T, Src, Dst> Transform3D<T, Src, Dst>where
T: Zero + One,
impl<T, Src, Dst> Transform3D<T, Src, Dst>where T: Zero + One,
Methods for creating and combining translation transformations
sourcepub fn translation(x: T, y: T, z: T) -> Self
pub fn translation(x: T, y: T, z: T) -> Self
Create a 3d translation transform:
1 0 0 0
0 1 0 0
0 0 1 0
x y z 1
source§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,
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,
Methods for creating and combining rotation transformations
sourcepub fn rotation(x: T, y: T, z: T, theta: Angle<T>) -> Self
pub fn rotation(x: T, y: T, z: T, theta: Angle<T>) -> Self
Create a 3d rotation transform from an angle / axis. The supplied axis must be normalized.
sourcepub fn then_rotate(&self, x: T, y: T, z: T, theta: Angle<T>) -> Self
pub fn then_rotate(&self, x: T, y: T, z: T, theta: Angle<T>) -> Self
Returns a transform with a rotation applied after self’s transformation.
sourcepub fn pre_rotate(&self, x: T, y: T, z: T, theta: Angle<T>) -> Self
pub fn pre_rotate(&self, x: T, y: T, z: T, theta: Angle<T>) -> Self
Returns a transform with a rotation applied before self’s transformation.
source§impl<T, Src, Dst> Transform3D<T, Src, Dst>where
T: Zero + One,
impl<T, Src, Dst> Transform3D<T, Src, Dst>where T: Zero + One,
Methods for creating and combining scale transformations
sourcepub fn scale(x: T, y: T, z: T) -> Self
pub fn scale(x: T, y: T, z: T) -> Self
Create a 3d scale transform:
x 0 0 0
0 y 0 0
0 0 z 0
0 0 0 1
sourcepub fn pre_scale(&self, x: T, y: T, z: T) -> Selfwhere
T: Copy + Add<Output = T> + Mul<Output = T>,
pub fn pre_scale(&self, x: T, y: T, z: T) -> Selfwhere T: Copy + Add<Output = T> + Mul<Output = T>,
Returns a transform with a scale applied before self’s transformation.
sourcepub fn then_scale(&self, x: T, y: T, z: T) -> Selfwhere
T: Copy + Add<Output = T> + Mul<Output = T>,
pub fn then_scale(&self, x: T, y: T, z: T) -> Selfwhere T: Copy + Add<Output = T> + Mul<Output = T>,
Returns a transform with a scale applied after self’s transformation.
source§impl<T, Src, Dst> Transform3D<T, Src, Dst>where
T: Copy + Add<Output = T> + Mul<Output = T>,
impl<T, Src, Dst> Transform3D<T, Src, Dst>where T: Copy + Add<Output = T> + Mul<Output = T>,
Methods for apply transformations to objects
sourcepub fn transform_point2d_homogeneous(
&self,
p: Point2D<T, Src>
) -> HomogeneousVector<T, Dst>
pub fn transform_point2d_homogeneous( &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.
sourcepub fn transform_point2d(&self, p: Point2D<T, Src>) -> Option<Point2D<T, Dst>>where
T: Div<Output = T> + Zero + PartialOrd,
pub fn transform_point2d(&self, p: Point2D<T, Src>) -> Option<Point2D<T, Dst>>where 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.
sourcepub fn transform_vector2d(&self, v: Vector2D<T, Src>) -> Vector2D<T, Dst>
pub fn transform_vector2d(&self, v: Vector2D<T, Src>) -> Vector2D<T, Dst>
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.
sourcepub fn transform_point3d_homogeneous(
&self,
p: Point3D<T, Src>
) -> HomogeneousVector<T, Dst>
pub fn transform_point3d_homogeneous( &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.
sourcepub fn transform_point3d(&self, p: Point3D<T, Src>) -> Option<Point3D<T, Dst>>where
T: Div<Output = T> + Zero + PartialOrd,
pub fn transform_point3d(&self, p: Point3D<T, Src>) -> Option<Point3D<T, Dst>>where 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.
sourcepub fn transform_vector3d(&self, v: Vector3D<T, Src>) -> Vector3D<T, Dst>
pub fn transform_vector3d(&self, v: Vector3D<T, Src>) -> Vector3D<T, Dst>
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.
sourcepub fn outer_transformed_rect(
&self,
rect: &Rect<T, Src>
) -> Option<Rect<T, Dst>>where
T: Sub<Output = T> + Div<Output = T> + Zero + PartialOrd,
pub fn outer_transformed_rect( &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.
sourcepub fn outer_transformed_box2d(
&self,
b: &Box2D<T, Src>
) -> Option<Box2D<T, Dst>>where
T: Sub<Output = T> + Div<Output = T> + Zero + PartialOrd,
pub fn outer_transformed_box2d( &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.
sourcepub fn outer_transformed_box3d(
&self,
b: &Box3D<T, Src>
) -> Option<Box3D<T, Dst>>where
T: Sub<Output = T> + Div<Output = T> + Zero + PartialOrd,
pub fn outer_transformed_box3d( &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.
source§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,
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,
sourcepub fn ortho(left: T, right: T, bottom: T, top: T, near: T, far: T) -> Self
pub fn ortho(left: T, right: T, bottom: T, top: T, near: T, far: T) -> Self
Create an orthogonal projection transform.
sourcepub fn is_backface_visible(&self) -> bool
pub fn is_backface_visible(&self) -> bool
Check whether shapes on the XY plane with Z pointing towards the screen transformed by this matrix would be facing back.
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<Transform3D<T, Dst, Src>>
pub fn inverse(&self) -> Option<Transform3D<T, Dst, Src>>
Returns the inverse transform if possible.
sourcepub fn determinant(&self) -> T
pub fn determinant(&self) -> T
Compute the determinant of the transform.
sourcepub fn mul_s(&self, x: T) -> Self
pub fn mul_s(&self, x: T) -> Self
Multiplies all of the transform’s component by a scalar and returns the result.
sourcepub fn from_scale(scale: Scale<T, Src, Dst>) -> Self
pub fn from_scale(scale: Scale<T, Src, Dst>) -> Self
Convenience function to create a scale transform from a Scale
.
source§impl<T, Src, Dst> Transform3D<T, Src, Dst>where
T: Copy + Mul<Output = T> + Div<Output = T> + Zero + One + PartialEq,
impl<T, Src, Dst> Transform3D<T, Src, Dst>where T: Copy + Mul<Output = T> + Div<Output = T> + Zero + One + PartialEq,
sourcepub fn project_to_2d(&self) -> Self
pub fn project_to_2d(&self) -> Self
Returns a projection of this transform in 2d space.
source§impl<T: NumCast + Copy, Src, Dst> Transform3D<T, Src, Dst>
impl<T: NumCast + Copy, Src, Dst> Transform3D<T, Src, Dst>
sourcepub fn cast<NewT: NumCast>(&self) -> Transform3D<NewT, Src, Dst>
pub fn cast<NewT: NumCast>(&self) -> Transform3D<NewT, Src, Dst>
Cast from one numeric representation to another, preserving the units.
sourcepub fn try_cast<NewT: NumCast>(&self) -> Option<Transform3D<NewT, Src, Dst>>
pub fn try_cast<NewT: NumCast>(&self) -> Option<Transform3D<NewT, Src, Dst>>
Fallible cast from one numeric representation to another, preserving the units.
source§impl<T: ApproxEq<T>, Src, Dst> Transform3D<T, Src, Dst>
impl<T: ApproxEq<T>, Src, Dst> Transform3D<T, Src, Dst>
sourcepub fn approx_eq(&self, other: &Self) -> bool
pub fn approx_eq(&self, other: &Self) -> bool
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) -> bool
pub 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.
The same as ApproxEq::approx_eq_eps()
but available without importing trait.
Trait Implementations§
source§impl<T: ApproxEq<T>, Src, Dst> ApproxEq<T> for Transform3D<T, Src, Dst>
impl<T: ApproxEq<T>, Src, Dst> ApproxEq<T> for Transform3D<T, Src, Dst>
source§fn approx_epsilon() -> T
fn approx_epsilon() -> T
source§impl<T: Clone, Src, Dst> Clone for Transform3D<T, Src, Dst>
impl<T: Clone, Src, Dst> Clone for Transform3D<T, Src, Dst>
source§impl<T, Src, Dst> Debug for Transform3D<T, Src, Dst>where
T: Copy + Debug + PartialEq + One + Zero,
impl<T, Src, Dst> Debug for Transform3D<T, Src, Dst>where T: Copy + Debug + PartialEq + One + Zero,
source§impl<T, Src, Dst> Default for Transform3D<T, Src, Dst>where
T: Zero + One,
impl<T, Src, Dst> Default for Transform3D<T, Src, Dst>where T: Zero + One,
source§fn default() -> Self
fn default() -> Self
Returns the identity transform.