Struct nalgebra::geometry::Orthographic3

pub struct Orthographic3<N: RealField> { /* fields omitted */ }

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

Implementations

impl<N: RealField> Orthographic3<N>

pub fn new(left: N, right: N, bottom: N, top: N, znear: N, zfar: N) -> 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/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));

pub fn from_matrix_unchecked(matrix: Matrix4<N>) -> 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));

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

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

pub fn inverse(&self) -> Matrix4<N>

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());

pub fn to_homogeneous(&self) -> Matrix4<N>

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);

pub fn as_matrix(&self) -> &Matrix4<N>

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);

pub fn as_projective(&self) -> &Projective3<N>

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());

pub fn to_projective(&self) -> Projective3<N>

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());

pub fn into_inner(self) -> Matrix4<N>

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);

pub fn unwrap(self) -> Matrix4<N>

👎 Deprecated:

use .into_inner() instead

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

pub fn left(&self) -> N

The left offset of the view cuboid.

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);

pub fn right(&self) -> N

The right offset of the view cuboid.

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);

pub fn bottom(&self) -> N

The bottom offset of the view cuboid.

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);

pub fn top(&self) -> N

The top offset of the view cuboid.

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);

pub fn znear(&self) -> N

The near plane offset of the view cuboid.

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);

pub fn zfar(&self) -> N

The far plane offset of the view cuboid.

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);

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

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));

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

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);

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

pub fn set_left(&mut self, left: N)

Sets the left offset of the view cuboid.

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);

pub fn set_right(&mut self, right: N)

Sets the right offset of the view cuboid.

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);

pub fn set_bottom(&mut self, bottom: N)

Sets the bottom offset of the view cuboid.

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);

pub fn set_top(&mut self, top: N)

Sets the top offset of the view cuboid.

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);

pub fn set_znear(&mut self, znear: N)

Sets the near plane offset of the view cuboid.

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);

pub fn set_zfar(&mut self, zfar: N)

Sets the far plane offset of the view cuboid.

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);

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

Sets the view cuboid offsets along the x axis.

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);

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

Sets the view cuboid offsets along the y axis.

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);

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

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

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

impl<N: RealField> Clone for Orthographic3<N>

fn clone(&self) -> Self

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<N: RealField> Debug for Orthographic3<N>

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

Formats the value using the given formatter.

impl<N: RealField> From<Orthographic3<N>> for Matrix4<N>

fn from(orth: Orthographic3<N>) -> Self

Performs the conversion.

impl<N: RealField> PartialEq<Orthographic3<N>> for Orthographic3<N>

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

This method tests for self and other values to be equal, and is used by ==.

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

This method tests for !=.

impl<N: RealField> Copy for Orthographic3<N>