nalgebra/src/geometry/perspective.rs

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#[cfg(feature = "arbitrary")]
use quickcheck::{Arbitrary, Gen};
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use rand::distributions::{Distribution, Standard};
use rand::Rng;
#[cfg(feature = "serde-serialize")]
use serde::{Deserialize, Deserializer, Serialize, Serializer};
use std::fmt;
use std::mem;
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use alga::general::RealField;
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use crate::base::dimension::U3;
use crate::base::helper;
use crate::base::storage::Storage;
use crate::base::{Matrix4, Scalar, Vector, Vector3};
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use crate::geometry::{Point3, Projective3};
/// A 3D perspective projection stored as an homogeneous 4x4 matrix.
pub struct Perspective3<N: Scalar + Clone> {
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matrix: Matrix4<N>,
}
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impl<N: RealField> Copy for Perspective3<N> {}
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impl<N: RealField> Clone for Perspective3<N> {
#[inline]
fn clone(&self) -> Self {
Self::from_matrix_unchecked(self.matrix.clone())
}
}
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impl<N: RealField> fmt::Debug for Perspective3<N> {
fn fmt(&self, f: &mut fmt::Formatter) -> Result<(), fmt::Error> {
self.matrix.fmt(f)
}
}
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impl<N: RealField> PartialEq for Perspective3<N> {
#[inline]
fn eq(&self, right: &Self) -> bool {
self.matrix == right.matrix
}
}
#[cfg(feature = "serde-serialize")]
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impl<N: RealField + Serialize> Serialize for Perspective3<N> {
fn serialize<S>(&self, serializer: S) -> Result<S::Ok, S::Error>
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where S: Serializer {
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self.matrix.serialize(serializer)
}
}
#[cfg(feature = "serde-serialize")]
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impl<'a, N: RealField + Deserialize<'a>> Deserialize<'a> for Perspective3<N> {
fn deserialize<Des>(deserializer: Des) -> Result<Self, Des::Error>
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where Des: Deserializer<'a> {
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let matrix = Matrix4::<N>::deserialize(deserializer)?;
Ok(Self::from_matrix_unchecked(matrix))
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}
}
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impl<N: RealField> Perspective3<N> {
/// Creates a new perspective matrix from the aspect ratio, y field of view, and near/far planes.
pub fn new(aspect: N, fovy: N, znear: N, zfar: N) -> Self {
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assert!(
!relative_eq!(zfar - znear, N::zero()),
"The near-plane and far-plane must not be superimposed."
);
assert!(
!relative_eq!(aspect, N::zero()),
"The apsect ratio must not be zero."
);
let matrix = Matrix4::identity();
let mut res = Self::from_matrix_unchecked(matrix);
res.set_fovy(fovy);
res.set_aspect(aspect);
res.set_znear_and_zfar(znear, zfar);
res.matrix[(3, 3)] = N::zero();
res.matrix[(3, 2)] = -N::one();
res
}
/// Wraps the given matrix to interpret it as a 3D perspective matrix.
///
/// It is not checked whether or not the given matrix actually represents an orthographic
/// projection.
#[inline]
pub fn from_matrix_unchecked(matrix: Matrix4<N>) -> Self {
Self { matrix: matrix }
}
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/// Retrieves the inverse of the underlying homogeneous matrix.
#[inline]
pub fn inverse(&self) -> Matrix4<N> {
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let mut res = self.to_homogeneous();
res[(0, 0)] = N::one() / self.matrix[(0, 0)];
res[(1, 1)] = N::one() / self.matrix[(1, 1)];
res[(2, 2)] = N::zero();
let m23 = self.matrix[(2, 3)];
let m32 = self.matrix[(3, 2)];
res[(2, 3)] = N::one() / m32;
res[(3, 2)] = N::one() / m23;
res[(3, 3)] = -self.matrix[(2, 2)] / (m23 * m32);
res
}
/// Computes the corresponding homogeneous matrix.
#[inline]
pub fn to_homogeneous(&self) -> Matrix4<N> {
self.matrix.clone_owned()
}
/// A reference to the underlying homogeneous transformation matrix.
#[inline]
pub fn as_matrix(&self) -> &Matrix4<N> {
&self.matrix
}
/// A reference to this transformation seen as a `Projective3`.
#[inline]
pub fn as_projective(&self) -> &Projective3<N> {
unsafe { mem::transmute(self) }
}
/// This transformation seen as a `Projective3`.
#[inline]
pub fn to_projective(&self) -> Projective3<N> {
Projective3::from_matrix_unchecked(self.matrix)
}
/// Retrieves the underlying homogeneous matrix.
#[inline]
pub fn into_inner(self) -> Matrix4<N> {
self.matrix
}
/// Retrieves the underlying homogeneous matrix.
/// Deprecated: Use [Perspective3::into_inner] instead.
#[deprecated(note="use `.into_inner()` instead")]
#[inline]
pub fn unwrap(self) -> Matrix4<N> {
self.matrix
}
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/// Gets the `width / height` aspect ratio of the view frustum.
#[inline]
pub fn aspect(&self) -> N {
self.matrix[(1, 1)] / self.matrix[(0, 0)]
}
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/// Gets the y field of view of the view frustum.
#[inline]
pub fn fovy(&self) -> N {
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(N::one() / self.matrix[(1, 1)]).atan() * crate::convert(2.0)
}
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/// Gets the near plane offset of the view frustum.
#[inline]
pub fn znear(&self) -> N {
let ratio = (-self.matrix[(2, 2)] + N::one()) / (-self.matrix[(2, 2)] - N::one());
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self.matrix[(2, 3)] / (ratio * crate::convert(2.0)) - self.matrix[(2, 3)] / crate::convert(2.0)
}
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/// Gets the far plane offset of the view frustum.
#[inline]
pub fn zfar(&self) -> N {
let ratio = (-self.matrix[(2, 2)] + N::one()) / (-self.matrix[(2, 2)] - N::one());
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(self.matrix[(2, 3)] - ratio * self.matrix[(2, 3)]) / crate::convert(2.0)
}
// FIXME: add a method to retrieve znear and zfar simultaneously?
// FIXME: when we get specialization, specialize the Mul impl instead.
/// Projects a point. Faster than matrix multiplication.
#[inline]
pub fn project_point(&self, p: &Point3<N>) -> Point3<N> {
let inverse_denom = -N::one() / p[2];
Point3::new(
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self.matrix[(0, 0)] * p[0] * inverse_denom,
self.matrix[(1, 1)] * p[1] * inverse_denom,
(self.matrix[(2, 2)] * p[2] + self.matrix[(2, 3)]) * inverse_denom,
)
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}
/// Un-projects a point. Faster than multiplication by the matrix inverse.
#[inline]
pub fn unproject_point(&self, p: &Point3<N>) -> Point3<N> {
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let inverse_denom = self.matrix[(2, 3)] / (p[2] + self.matrix[(2, 2)]);
Point3::new(
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p[0] * inverse_denom / self.matrix[(0, 0)],
p[1] * inverse_denom / self.matrix[(1, 1)],
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-inverse_denom,
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)
}
// FIXME: when we get specialization, specialize the Mul impl instead.
/// Projects a vector. Faster than matrix multiplication.
#[inline]
pub fn project_vector<SB>(&self, p: &Vector<N, U3, SB>) -> Vector3<N>
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where SB: Storage<N, U3> {
let inverse_denom = -N::one() / p[2];
Vector3::new(
self.matrix[(0, 0)] * p[0] * inverse_denom,
self.matrix[(1, 1)] * p[1] * inverse_denom,
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self.matrix[(2, 2)],
)
}
/// Updates this perspective matrix with a new `width / height` aspect ratio of the view
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/// frustum.
#[inline]
pub fn set_aspect(&mut self, aspect: N) {
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assert!(
!relative_eq!(aspect, N::zero()),
"The aspect ratio must not be zero."
);
self.matrix[(0, 0)] = self.matrix[(1, 1)] / aspect;
}
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/// Updates this perspective with a new y field of view of the view frustum.
#[inline]
pub fn set_fovy(&mut self, fovy: N) {
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let old_m22 = self.matrix[(1, 1)];
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self.matrix[(1, 1)] = N::one() / (fovy / crate::convert(2.0)).tan();
self.matrix[(0, 0)] = self.matrix[(0, 0)] * (self.matrix[(1, 1)] / old_m22);
}
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/// Updates this perspective matrix with a new near plane offset of the view frustum.
#[inline]
pub fn set_znear(&mut self, znear: N) {
let zfar = self.zfar();
self.set_znear_and_zfar(znear, zfar);
}
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/// Updates this perspective matrix with a new far plane offset of the view frustum.
#[inline]
pub fn set_zfar(&mut self, zfar: N) {
let znear = self.znear();
self.set_znear_and_zfar(znear, zfar);
}
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/// Updates this perspective matrix with new near and far plane offsets of the view frustum.
#[inline]
pub fn set_znear_and_zfar(&mut self, znear: N, zfar: N) {
self.matrix[(2, 2)] = (zfar + znear) / (znear - zfar);
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self.matrix[(2, 3)] = zfar * znear * crate::convert(2.0) / (znear - zfar);
}
}
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impl<N: RealField> Distribution<Perspective3<N>> for Standard
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where Standard: Distribution<N>
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{
fn sample<'a, R: Rng + ?Sized>(&self, r: &'a mut R) -> Perspective3<N> {
let znear = r.gen();
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let zfar = helper::reject_rand(r, |&x: &N| !(x - znear).is_zero());
let aspect = helper::reject_rand(r, |&x: &N| !x.is_zero());
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Perspective3::new(aspect, r.gen(), znear, zfar)
}
}
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#[cfg(feature = "arbitrary")]
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impl<N: RealField + Arbitrary> Arbitrary for Perspective3<N> {
fn arbitrary<G: Gen>(g: &mut G) -> Self {
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let znear = Arbitrary::arbitrary(g);
let zfar = helper::reject(g, |&x: &N| !(x - znear).is_zero());
let aspect = helper::reject(g, |&x: &N| !x.is_zero());
Self::new(aspect, Arbitrary::arbitrary(g), znear, zfar)
}
}
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impl<N: RealField> From<Perspective3<N>> for Matrix4<N> {
#[inline]
fn from(orth: Perspective3<N>) -> Self {
orth.into_inner()
}
}