Struct Transform3D

#[repr(C)]
pub struct Transform3D<T, Src, Dst> {

    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 */
}

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

impl<T, Src, Dst> Transform3D<T, Src, Dst>

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,
);

pub fn new_2d(m11: T, m12: T, m21: T, m22: T, m41: T, m42: T) -> Self

where 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 representing the translation terms).

m11  m12   0   0
m21  m22   0   0
  0    0   1   0
m41  m42   0   1

pub fn is_2d(&self) -> bool

where T: Zero + One + PartialEq,

Returns true if this transform can be represented with a Transform2D.

See https://drafts.csswg.org/css-transforms/#2d-transform

impl<T: Copy, Src, Dst> Transform3D<T, Src, Dst>

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.

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.

pub fn to_arrays(&self) -> [[T; 4]; 4]

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

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.

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).

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).

pub fn from_untyped(m: &Transform3D<T, UnknownUnit, UnknownUnit>) -> Self

Tag a unitless value with units.

pub fn to_untyped(&self) -> Transform3D<T, UnknownUnit, UnknownUnit>

Drop the units, preserving only the numeric value.

pub fn with_source<NewSrc>(&self) -> Transform3D<T, NewSrc, Dst>

Returns the same transform with a different source unit.

pub fn with_destination<NewDst>(&self) -> Transform3D<T, Src, NewDst>

Returns the same transform with a different destination unit.

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 is_2d returns true beforehand.

impl<T, Src, Dst> Transform3D<T, Src, Dst>

where T: Zero + One,

pub fn identity() -> Self

Creates an identity matrix:

1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1

pub fn skew(alpha: Angle<T>, beta: Angle<T>) -> Self

where T: Trig,

Create a 2d skew transform.

See https://drafts.csswg.org/css-transforms/#funcdef-skew

pub fn perspective(d: T) -> Self

where 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.

impl<T, Src, Dst> Transform3D<T, Src, Dst>

where T: Copy + Add<Output = T> + Mul<Output = T>,

Methods for combining generic transformations

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

impl<T, Src, Dst> Transform3D<T, Src, Dst>

where T: Zero + One,

Methods for creating and combining translation transformations

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

pub fn pre_translate(&self, v: Vector3D<T, Src>) -> Self

where T: Copy + Add<Output = T> + Mul<Output = T>,

Returns a transform with a translation applied before self’s transformation.

pub fn then_translate(&self, v: Vector3D<T, Dst>) -> Self

where T: Copy + Add<Output = T> + Mul<Output = T>,

Returns a transform with a translation applied after self’s transformation.

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

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.

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.

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.

impl<T, Src, Dst> Transform3D<T, Src, Dst>

where T: Zero + One,

Methods for creating and combining scale transformations

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

pub fn pre_scale(&self, x: T, y: T, z: T) -> Self

where T: Copy + Add<Output = T> + Mul<Output = T>,

Returns a transform with a scale applied before self’s transformation.

pub fn then_scale(&self, x: T, y: T, z: T) -> Self

where T: Copy + Add<Output = T> + Mul<Output = T>,

Returns a transform with a scale applied after self’s transformation.

impl<T, Src, Dst> Transform3D<T, Src, Dst>

where T: Copy + Add<Output = T> + Mul<Output = T>,

Methods for apply transformations to objects

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.

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.

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.

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.

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.

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.

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.

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.

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.

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,

pub fn ortho(left: T, right: T, bottom: T, top: T, near: T, far: T) -> Self

Create an orthogonal projection transform.

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.

pub fn is_invertible(&self) -> bool

Returns whether it is possible to compute the inverse transform.

pub fn inverse(&self) -> Option<Transform3D<T, Dst, Src>>

Returns the inverse transform if possible.

pub fn determinant(&self) -> T

Compute the determinant of the transform.

pub fn mul_s(&self, x: T) -> Self

Multiplies all of the transform’s component by a scalar and returns the result.

pub fn from_scale(scale: Scale<T, Src, Dst>) -> Self

Convenience function to create a scale transform from a Scale.

impl<T, Src, Dst> Transform3D<T, Src, Dst>

where T: Copy + Mul<Output = T> + Div<Output = T> + Zero + One + PartialEq,

pub fn project_to_2d(&self) -> Self

Returns a projection of this transform in 2d space.

impl<T: NumCast + Copy, Src, Dst> Transform3D<T, Src, Dst>

pub fn cast<NewT: NumCast>(&self) -> Transform3D<NewT, Src, Dst>

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

pub fn try_cast<NewT: NumCast>(&self) -> Option<Transform3D<NewT, Src, Dst>>

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

impl<T: ApproxEq<T>, Src, Dst> Transform3D<T, Src, Dst>

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

Returns true if 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

Returns true if 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

impl<T: ApproxEq<T>, Src, Dst> ApproxEq<T> for Transform3D<T, Src, Dst>

fn approx_epsilon() -> T

Default epsilon value

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

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

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

Returns true if this object is approximately equal to the other one, using the approx_epsilon epsilon value.

impl<T: Clone, Src, Dst> Clone for Transform3D<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 Transform3D<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 Transform3D<T, Src, Dst>

where T: Zero + One,

fn default() -> Self

Returns the identity transform.

impl<T, Src, Dst> From<Translation3D<T, Src, Dst>> for Transform3D<T, Src, Dst>

where T: Zero + One,

fn from(t: Translation3D<T, Src, Dst>) -> Self

Converts to this type from the input type.

impl<T, Src, Dst> Hash for Transform3D<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, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl<T, Src, Dst> PartialEq for Transform3D<T, Src, Dst>

where T: PartialEq,

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

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<T: Copy, Src, Dst> Copy for Transform3D<T, Src, Dst>

impl<T, Src, Dst> Eq for Transform3D<T, Src, Dst>

where T: Eq,