Orthographic3 in nalgebra::geometry - Rust
Description: A 3D orthographic projection stored as a homogeneous 4x4 matrix.
Keywords: rust, rustlang, rust-lang, Orthographic3

# Struct nalgebra::geometry::Orthographic3

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    #[repr(C)]pub struct Orthographic3<T> { /* private fields */ }

Expand description

A 3D orthographic projection stored as a homogeneous 4x4 matrix.

## Implementations§

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### impl<T> Orthographic3<T>

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#### pub const fn from_matrix_unchecked(matrix: Matrix4<T>) -> Self

Wraps the given matrix to interpret it as a 3D orthographic matrix.

It is not checked whether or not the given matrix actually represents an orthographic projection.

##### Example

    let mat = Matrix4::new(
        2.0 / 9.0, 0.0,        0.0,         -11.0 / 9.0,
        0.0,       2.0 / 18.0, 0.0,         -22.0 / 18.0,
        0.0,       0.0,       -2.0 / 999.9, -1000.1 / 999.9,
        0.0,       0.0,        0.0,         1.0
    );
    let proj = Orthographic3::from_matrix_unchecked(mat);
    assert_eq!(proj, Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0));

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### impl<T: RealField> Orthographic3<T>

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#### pub fn new(left: T, right: T, bottom: T, top: T, znear: T, zfar: T) -> Self

Creates a new orthographic projection matrix.

This follows the OpenGL convention, so this will flip the `z` axis.

##### Example

    let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
    // Check this projection actually transforms the view cuboid into the double-unit cube.
    // See https://www.nalgebra.org/docs/user_guide/projections#orthographic-projection for more details.
    let p1 = Point3::new(1.0, 2.0, -0.1);
    let p2 = Point3::new(1.0, 2.0, -1000.0);
    let p3 = Point3::new(1.0, 20.0, -0.1);
    let p4 = Point3::new(1.0, 20.0, -1000.0);
    let p5 = Point3::new(10.0, 2.0, -0.1);
    let p6 = Point3::new(10.0, 2.0, -1000.0);
    let p7 = Point3::new(10.0, 20.0, -0.1);
    let p8 = Point3::new(10.0, 20.0, -1000.0);

    assert_relative_eq!(proj.project_point(&p1), Point3::new(-1.0, -1.0, -1.0));
    assert_relative_eq!(proj.project_point(&p2), Point3::new(-1.0, -1.0,  1.0));
    assert_relative_eq!(proj.project_point(&p3), Point3::new(-1.0,  1.0, -1.0));
    assert_relative_eq!(proj.project_point(&p4), Point3::new(-1.0,  1.0,  1.0));
    assert_relative_eq!(proj.project_point(&p5), Point3::new( 1.0, -1.0, -1.0));
    assert_relative_eq!(proj.project_point(&p6), Point3::new( 1.0, -1.0,  1.0));
    assert_relative_eq!(proj.project_point(&p7), Point3::new( 1.0,  1.0, -1.0));
    assert_relative_eq!(proj.project_point(&p8), Point3::new( 1.0,  1.0,  1.0));

    // This also works with flipped axis. In other words, we allow that
    // `left > right`, `bottom > top`, and/or `znear > zfar`.
    let proj = Orthographic3::new(10.0, 1.0, 20.0, 2.0, 1000.0, 0.1);

    assert_relative_eq!(proj.project_point(&p1), Point3::new( 1.0,  1.0,  1.0));
    assert_relative_eq!(proj.project_point(&p2), Point3::new( 1.0,  1.0, -1.0));
    assert_relative_eq!(proj.project_point(&p3), Point3::new( 1.0, -1.0,  1.0));
    assert_relative_eq!(proj.project_point(&p4), Point3::new( 1.0, -1.0, -1.0));
    assert_relative_eq!(proj.project_point(&p5), Point3::new(-1.0,  1.0,  1.0));
    assert_relative_eq!(proj.project_point(&p6), Point3::new(-1.0,  1.0, -1.0));
    assert_relative_eq!(proj.project_point(&p7), Point3::new(-1.0, -1.0,  1.0));
    assert_relative_eq!(proj.project_point(&p8), Point3::new(-1.0, -1.0, -1.0));

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#### pub fn from_fov(aspect: T, vfov: T, znear: T, zfar: T) -> Self

Creates a new orthographic projection matrix from an aspect ratio and the vertical field of view.

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#### pub fn inverse(&self) -> Matrix4<T>

Retrieves the inverse of the underlying homogeneous matrix.

##### Example

    let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
    let inv = proj.inverse();

    assert_relative_eq!(inv * proj.as_matrix(), Matrix4::identity());
    assert_relative_eq!(proj.as_matrix() * inv, Matrix4::identity());

    let proj = Orthographic3::new(10.0, 1.0, 20.0, 2.0, 1000.0, 0.1);
    let inv = proj.inverse();
    assert_relative_eq!(inv * proj.as_matrix(), Matrix4::identity());
    assert_relative_eq!(proj.as_matrix() * inv, Matrix4::identity());

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#### pub fn to_homogeneous(self) -> Matrix4<T>

Computes the corresponding homogeneous matrix.

##### Example

    let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
    let expected = Matrix4::new(
        2.0 / 9.0, 0.0,        0.0,         -11.0 / 9.0,
        0.0,       2.0 / 18.0, 0.0,         -22.0 / 18.0,
        0.0,       0.0,       -2.0 / 999.9, -1000.1 / 999.9,
        0.0,       0.0,        0.0,         1.0
    );
    assert_eq!(proj.to_homogeneous(), expected);

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#### pub fn as_matrix(&self) -> &Matrix4<T>

A reference to the underlying homogeneous transformation matrix.

##### Example

    let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
    let expected = Matrix4::new(
        2.0 / 9.0, 0.0,        0.0,         -11.0 / 9.0,
        0.0,       2.0 / 18.0, 0.0,         -22.0 / 18.0,
        0.0,       0.0,       -2.0 / 999.9, -1000.1 / 999.9,
        0.0,       0.0,        0.0,         1.0
    );
    assert_eq!(*proj.as_matrix(), expected);

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#### pub fn as_projective(&self) -> &Projective3<T>

A reference to this transformation seen as a `Projective3`.

##### Example

    let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
    assert_eq!(proj.as_projective().to_homogeneous(), proj.to_homogeneous());

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#### pub fn to_projective(self) -> Projective3<T>

This transformation seen as a `Projective3`.

##### Example

    let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
    assert_eq!(proj.to_projective().to_homogeneous(), proj.to_homogeneous());

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#### pub fn into_inner(self) -> Matrix4<T>

Retrieves the underlying homogeneous matrix.

##### Example

    let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
    let expected = Matrix4::new(
        2.0 / 9.0, 0.0,        0.0,         -11.0 / 9.0,
        0.0,       2.0 / 18.0, 0.0,         -22.0 / 18.0,
        0.0,       0.0,       -2.0 / 999.9, -1000.1 / 999.9,
        0.0,       0.0,        0.0,         1.0
    );
    assert_eq!(proj.into_inner(), expected);

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#### pub fn unwrap(self) -> Matrix4<T>

👎Deprecated: use `.into_inner()` instead

Retrieves the underlying homogeneous matrix. Deprecated: Use `Orthographic3::into_inner` instead.

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#### pub fn left(&self) -> T

The left offset of the view cuboid.

##### Example

    let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
    assert_relative_eq!(proj.left(), 1.0, epsilon = 1.0e-6);

    let proj = Orthographic3::new(10.0, 1.0, 20.0, 2.0, 1000.0, 0.1);
    assert_relative_eq!(proj.left(), 10.0, epsilon = 1.0e-6);

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#### pub fn right(&self) -> T

The right offset of the view cuboid.

##### Example

    let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
    assert_relative_eq!(proj.right(), 10.0, epsilon = 1.0e-6);

    let proj = Orthographic3::new(10.0, 1.0, 20.0, 2.0, 1000.0, 0.1);
    assert_relative_eq!(proj.right(), 1.0, epsilon = 1.0e-6);

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#### pub fn bottom(&self) -> T

The bottom offset of the view cuboid.

##### Example

    let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
    assert_relative_eq!(proj.bottom(), 2.0, epsilon = 1.0e-6);

    let proj = Orthographic3::new(10.0, 1.0, 20.0, 2.0, 1000.0, 0.1);
    assert_relative_eq!(proj.bottom(), 20.0, epsilon = 1.0e-6);

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#### pub fn top(&self) -> T

The top offset of the view cuboid.

##### Example

    let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
    assert_relative_eq!(proj.top(), 20.0, epsilon = 1.0e-6);

    let proj = Orthographic3::new(10.0, 1.0, 20.0, 2.0, 1000.0, 0.1);
    assert_relative_eq!(proj.top(), 2.0, epsilon = 1.0e-6);

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#### pub fn znear(&self) -> T

The near plane offset of the view cuboid.

##### Example

    let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
    assert_relative_eq!(proj.znear(), 0.1, epsilon = 1.0e-6);

    let proj = Orthographic3::new(10.0, 1.0, 20.0, 2.0, 1000.0, 0.1);
    assert_relative_eq!(proj.znear(), 1000.0, epsilon = 1.0e-6);

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#### pub fn zfar(&self) -> T

The far plane offset of the view cuboid.

##### Example

    let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
    assert_relative_eq!(proj.zfar(), 1000.0, epsilon = 1.0e-6);

    let proj = Orthographic3::new(10.0, 1.0, 20.0, 2.0, 1000.0, 0.1);
    assert_relative_eq!(proj.zfar(), 0.1, epsilon = 1.0e-6);

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#### pub fn project_point(&self, p: &Point3<T>) -> Point3<T>

Projects a point. Faster than matrix multiplication.

##### Example

    let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);

    let p1 = Point3::new(1.0, 2.0, -0.1);
    let p2 = Point3::new(1.0, 2.0, -1000.0);
    let p3 = Point3::new(1.0, 20.0, -0.1);
    let p4 = Point3::new(1.0, 20.0, -1000.0);
    let p5 = Point3::new(10.0, 2.0, -0.1);
    let p6 = Point3::new(10.0, 2.0, -1000.0);
    let p7 = Point3::new(10.0, 20.0, -0.1);
    let p8 = Point3::new(10.0, 20.0, -1000.0);

    assert_relative_eq!(proj.project_point(&p1), Point3::new(-1.0, -1.0, -1.0));
    assert_relative_eq!(proj.project_point(&p2), Point3::new(-1.0, -1.0,  1.0));
    assert_relative_eq!(proj.project_point(&p3), Point3::new(-1.0,  1.0, -1.0));
    assert_relative_eq!(proj.project_point(&p4), Point3::new(-1.0,  1.0,  1.0));
    assert_relative_eq!(proj.project_point(&p5), Point3::new( 1.0, -1.0, -1.0));
    assert_relative_eq!(proj.project_point(&p6), Point3::new( 1.0, -1.0,  1.0));
    assert_relative_eq!(proj.project_point(&p7), Point3::new( 1.0,  1.0, -1.0));
    assert_relative_eq!(proj.project_point(&p8), Point3::new( 1.0,  1.0,  1.0));

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#### pub fn unproject_point(&self, p: &Point3<T>) -> Point3<T>

Un-projects a point. Faster than multiplication by the underlying matrix inverse.

##### Example

    let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);

    let p1 = Point3::new(-1.0, -1.0, -1.0);
    let p2 = Point3::new(-1.0, -1.0,  1.0);
    let p3 = Point3::new(-1.0,  1.0, -1.0);
    let p4 = Point3::new(-1.0,  1.0,  1.0);
    let p5 = Point3::new( 1.0, -1.0, -1.0);
    let p6 = Point3::new( 1.0, -1.0,  1.0);
    let p7 = Point3::new( 1.0,  1.0, -1.0);
    let p8 = Point3::new( 1.0,  1.0,  1.0);

    assert_relative_eq!(proj.unproject_point(&p1), Point3::new(1.0, 2.0, -0.1), epsilon = 1.0e-6);
    assert_relative_eq!(proj.unproject_point(&p2), Point3::new(1.0, 2.0, -1000.0), epsilon = 1.0e-6);
    assert_relative_eq!(proj.unproject_point(&p3), Point3::new(1.0, 20.0, -0.1), epsilon = 1.0e-6);
    assert_relative_eq!(proj.unproject_point(&p4), Point3::new(1.0, 20.0, -1000.0), epsilon = 1.0e-6);
    assert_relative_eq!(proj.unproject_point(&p5), Point3::new(10.0, 2.0, -0.1), epsilon = 1.0e-6);
    assert_relative_eq!(proj.unproject_point(&p6), Point3::new(10.0, 2.0, -1000.0), epsilon = 1.0e-6);
    assert_relative_eq!(proj.unproject_point(&p7), Point3::new(10.0, 20.0, -0.1), epsilon = 1.0e-6);
    assert_relative_eq!(proj.unproject_point(&p8), Point3::new(10.0, 20.0, -1000.0), epsilon = 1.0e-6);

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#### pub fn project_vector<SB>(&self, p: &Vector<T, U3, SB>) -> Vector3<T>where
SB: Storage<T, U3>,

Projects a vector. Faster than matrix multiplication.

Vectors are not affected by the translation part of the projection.

##### Example

    let proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);

    let v1 = Vector3::x();
    let v2 = Vector3::y();
    let v3 = Vector3::z();

    assert_relative_eq!(proj.project_vector(&v1), Vector3::x() * 2.0 / 9.0);
    assert_relative_eq!(proj.project_vector(&v2), Vector3::y() * 2.0 / 18.0);
    assert_relative_eq!(proj.project_vector(&v3), Vector3::z() * -2.0 / 999.9);

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#### pub fn set_left(&mut self, left: T)

Sets the left offset of the view cuboid.

##### Example

    let mut proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
    proj.set_left(2.0);
    assert_relative_eq!(proj.left(), 2.0, epsilon = 1.0e-6);

    // It is OK to set a left offset greater than the current right offset.
    proj.set_left(20.0);
    assert_relative_eq!(proj.left(), 20.0, epsilon = 1.0e-6);

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#### pub fn set_right(&mut self, right: T)

Sets the right offset of the view cuboid.

##### Example

    let mut proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
    proj.set_right(15.0);
    assert_relative_eq!(proj.right(), 15.0, epsilon = 1.0e-6);

    // It is OK to set a right offset smaller than the current left offset.
    proj.set_right(-3.0);
    assert_relative_eq!(proj.right(), -3.0, epsilon = 1.0e-6);

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#### pub fn set_bottom(&mut self, bottom: T)

Sets the bottom offset of the view cuboid.

##### Example

    let mut proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
    proj.set_bottom(8.0);
    assert_relative_eq!(proj.bottom(), 8.0, epsilon = 1.0e-6);

    // It is OK to set a bottom offset greater than the current top offset.
    proj.set_bottom(50.0);
    assert_relative_eq!(proj.bottom(), 50.0, epsilon = 1.0e-6);

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#### pub fn set_top(&mut self, top: T)

Sets the top offset of the view cuboid.

##### Example

    let mut proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
    proj.set_top(15.0);
    assert_relative_eq!(proj.top(), 15.0, epsilon = 1.0e-6);

    // It is OK to set a top offset smaller than the current bottom offset.
    proj.set_top(-3.0);
    assert_relative_eq!(proj.top(), -3.0, epsilon = 1.0e-6);

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#### pub fn set_znear(&mut self, znear: T)

Sets the near plane offset of the view cuboid.

##### Example

    let mut proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
    proj.set_znear(8.0);
    assert_relative_eq!(proj.znear(), 8.0, epsilon = 1.0e-6);

    // It is OK to set a znear greater than the current zfar.
    proj.set_znear(5000.0);
    assert_relative_eq!(proj.znear(), 5000.0, epsilon = 1.0e-6);

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#### pub fn set_zfar(&mut self, zfar: T)

Sets the far plane offset of the view cuboid.

##### Example

    let mut proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
    proj.set_zfar(15.0);
    assert_relative_eq!(proj.zfar(), 15.0, epsilon = 1.0e-6);

    // It is OK to set a zfar smaller than the current znear.
    proj.set_zfar(-3.0);
    assert_relative_eq!(proj.zfar(), -3.0, epsilon = 1.0e-6);

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#### pub fn set_left_and_right(&mut self, left: T, right: T)

Sets the view cuboid offsets along the `x` axis.

##### Example

    let mut proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
    proj.set_left_and_right(7.0, 70.0);
    assert_relative_eq!(proj.left(), 7.0, epsilon = 1.0e-6);
    assert_relative_eq!(proj.right(), 70.0, epsilon = 1.0e-6);

    // It is also OK to have `left > right`.
    proj.set_left_and_right(70.0, 7.0);
    assert_relative_eq!(proj.left(), 70.0, epsilon = 1.0e-6);
    assert_relative_eq!(proj.right(), 7.0, epsilon = 1.0e-6);

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#### pub fn set_bottom_and_top(&mut self, bottom: T, top: T)

Sets the view cuboid offsets along the `y` axis.

##### Example

    let mut proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
    proj.set_bottom_and_top(7.0, 70.0);
    assert_relative_eq!(proj.bottom(), 7.0, epsilon = 1.0e-6);
    assert_relative_eq!(proj.top(), 70.0, epsilon = 1.0e-6);

    // It is also OK to have `bottom > top`.
    proj.set_bottom_and_top(70.0, 7.0);
    assert_relative_eq!(proj.bottom(), 70.0, epsilon = 1.0e-6);
    assert_relative_eq!(proj.top(), 7.0, epsilon = 1.0e-6);

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#### pub fn set_znear_and_zfar(&mut self, znear: T, zfar: T)

Sets the near and far plane offsets of the view cuboid.

##### Example

    let mut proj = Orthographic3::new(1.0, 10.0, 2.0, 20.0, 0.1, 1000.0);
    proj.set_znear_and_zfar(50.0, 5000.0);
    assert_relative_eq!(proj.znear(), 50.0, epsilon = 1.0e-6);
    assert_relative_eq!(proj.zfar(), 5000.0, epsilon = 1.0e-6);

    // It is also OK to have `znear > zfar`.
    proj.set_znear_and_zfar(5000.0, 0.5);
    assert_relative_eq!(proj.znear(), 5000.0, epsilon = 1.0e-6);
    assert_relative_eq!(proj.zfar(), 0.5, epsilon = 1.0e-6);

## Trait Implementations§

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### impl<T: Clone> Clone for Orthographic3<T>

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#### fn clone(&self) -> Orthographic3<T>

Returns a copy of the value. Read more
1.0.0 · source§

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

Performs copy-assignment from `source`. Read more
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### impl<T: RealField> Debug for Orthographic3<T>

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

Formats the value using the given formatter. Read more
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### impl<T: RealField> From<Orthographic3<T>> for Matrix4<T>

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#### fn from(orth: Orthographic3<T>) -> Self

Converts to this type from the input type.
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### impl<T: RealField> PartialEq<Orthographic3<T>> for Orthographic3<T>

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

This method tests for `self` and `other` values to be equal, and is used by `==`. Read more
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#### fn ne(&self, other: &Rhs) -> bool

This method tests for `!=`. The default implementation is almost always sufficient, and should not be overridden without very good reason. Read more
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### impl<T: Copy> Copy for Orthographic3<T>

## Auto Trait Implementations§

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### impl<T> RefUnwindSafe for Orthographic3<T>where
T: RefUnwindSafe,

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### impl<T> Send for Orthographic3<T>where
T: Send,

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### impl<T> Sync for Orthographic3<T>where
T: Sync,

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### impl<T> Unpin for Orthographic3<T>where
T: Unpin,

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### impl<T> UnwindSafe for Orthographic3<T>where
T: UnwindSafe,

## Blanket Implementations§

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### impl<T> Any for Twhere
T: 'static + ?Sized,

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#### fn type_id(&self) -> TypeId

Gets the `TypeId` of `self`. Read more
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### impl<T> Borrow<T> for Twhere
T: ?Sized,

const: unstable · source§

#### fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
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### impl<T> BorrowMut<T> for Twhere
T: ?Sized,

const: unstable · source§

#### fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more
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### impl<T> From<T> for T

const: unstable · source§

#### fn from(t: T) -> T

Returns the argument unchanged.

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### impl<T, U> Into<U> for Twhere
U: From<T>,

const: unstable · source§

#### fn into(self) -> U

Calls `U::from(self)`.

That is, this conversion is whatever the implementation of `From<T> for U` chooses to do.

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### impl<T> Same<T> for T

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#### type Output = T

Should always be `Self`
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### impl<SS, SP> SupersetOf<SS> for SPwhere
SS: SubsetOf<SP>,

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#### fn to_subset(&self) -> Option<SS>

The inverse inclusion map: attempts to construct `self` from the equivalent element of its superset. Read more
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#### fn is_in_subset(&self) -> bool

Checks if `self` is actually part of its subset `T` (and can be converted to it).
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#### fn to_subset_unchecked(&self) -> SS

Use with care! Same as `self.to_subset` but without any property checks. Always succeeds.
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#### fn from_subset(element: &SS) -> SP

The inclusion map: converts `self` to the equivalent element of its superset.
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### impl<T> ToOwned for Twhere
T: Clone,

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#### type Owned = T

The resulting type after obtaining ownership.
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#### fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more
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#### fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more
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### impl<T, U> TryFrom<U> for Twhere
U: Into<T>,

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#### type Error = Infallible

The type returned in the event of a conversion error.
const: unstable · source§

#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
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### impl<T, U> TryInto<U> for Twhere
U: TryFrom<T>,

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#### type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.
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#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.