nalgebra/src/geometry/perspective.rs

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#[cfg(feature="arbitrary")]
use quickcheck::{Arbitrary, Gen};
use rand::{Rand, Rng};
use alga::general::Real;
use core::{Scalar, SquareMatrix, OwnedSquareMatrix, ColumnVector, OwnedColumnVector, MatrixArray};
use core::dimension::{U1, U3, U4};
use core::storage::{OwnedStorage, Storage, StorageMut};
use core::allocator::OwnedAllocator;
use core::helper;
use geometry::{PointBase, OwnedPoint};
/// A 3D perspective projection stored as an homogeneous 4x4 matrix.
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#[derive(Debug, Clone, Copy, Serialize, Deserialize)] // FIXME: Hash
pub struct PerspectiveBase<N: Scalar, S: Storage<N, U4, U4>> {
matrix: SquareMatrix<N, U4, S>
}
/// A 3D perspective projection stored as a static homogeneous 4x4 matrix.
pub type Perspective3<N> = PerspectiveBase<N, MatrixArray<N, U4, U4>>;
impl<N, S> Eq for PerspectiveBase<N, S>
where N: Scalar + Eq,
S: Storage<N, U4, U4> { }
impl<N, S> PartialEq for PerspectiveBase<N, S>
where N: Scalar,
S: Storage<N, U4, U4> {
#[inline]
fn eq(&self, right: &Self) -> bool {
self.matrix == right.matrix
}
}
impl<N, S> PerspectiveBase<N, S>
where N: Real,
S: OwnedStorage<N, U4, U4>,
S::Alloc: OwnedAllocator<N, U4, U4, S> {
/// 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 {
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 = SquareMatrix::<N, U4, S>::identity();
let mut res = PerspectiveBase::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: SquareMatrix<N, U4, S>) -> Self {
PerspectiveBase {
matrix: matrix
}
}
}
impl<N, S> PerspectiveBase<N, S>
where N: Real,
S: Storage<N, U4, U4> {
/// A reference to the underlying homogeneous transformation matrix.
#[inline]
pub fn as_matrix(&self) -> &SquareMatrix<N, U4, S> {
&self.matrix
}
/// Retrieves the underlying homogeneous matrix.
#[inline]
pub fn unwrap(self) -> SquareMatrix<N, U4, S> {
self.matrix
}
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/// Retrieves the inverse of the underlying homogeneous matrix.
#[inline]
pub fn inverse(&self) -> OwnedSquareMatrix<N, U4, S::Alloc> {
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) -> OwnedSquareMatrix<N, U4, S::Alloc> {
self.matrix.clone_owned()
}
/// Gets the `width / height` aspect ratio of the view frustrum.
#[inline]
pub fn aspect(&self) -> N {
self.matrix[(1, 1)] / self.matrix[(0, 0)]
}
/// Gets the y field of view of the view frustrum.
#[inline]
pub fn fovy(&self) -> N {
(N::one() / self.matrix[(1, 1)]).atan() * ::convert(2.0)
}
/// Gets the near plane offset of the view frustrum.
#[inline]
pub fn znear(&self) -> N {
let ratio = (-self.matrix[(2, 2)] + N::one()) / (-self.matrix[(2, 2)] - N::one());
self.matrix[(2, 3)] / (ratio * ::convert(2.0)) - self.matrix[(2, 3)] / ::convert(2.0)
}
/// Gets the far plane offset of the view frustrum.
#[inline]
pub fn zfar(&self) -> N {
let ratio = (-self.matrix[(2, 2)] + N::one()) / (-self.matrix[(2, 2)] - N::one());
(self.matrix[(2, 3)] - ratio * self.matrix[(2, 3)]) / ::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<SB>(&self, p: &PointBase<N, U3, SB>) -> OwnedPoint<N, U3, SB::Alloc>
where SB: Storage<N, U3, U1> {
let inverse_denom = -N::one() / p[2];
OwnedPoint::<N, U3, SB::Alloc>::new(
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<SB>(&self, p: &PointBase<N, U3, SB>) -> OwnedPoint<N, U3, SB::Alloc>
where SB: Storage<N, U3, U1> {
let inverse_denom = self.matrix[(2, 3)] / (p[2] + self.matrix[(2, 2)]);
OwnedPoint::<N, U3, SB::Alloc>::new(
p[0] * inverse_denom / self.matrix[(0, 0)],
p[1] * inverse_denom / self.matrix[(1, 1)],
-inverse_denom
)
}
// 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: &ColumnVector<N, U3, SB>) -> OwnedColumnVector<N, U3, SB::Alloc>
where SB: Storage<N, U3, U1> {
let inverse_denom = -N::one() / p[2];
OwnedColumnVector::<N, U3, SB::Alloc>::new(
self.matrix[(0, 0)] * p[0] * inverse_denom,
self.matrix[(1, 1)] * p[1] * inverse_denom,
self.matrix[(2, 2)]
)
}
}
impl<N, S> PerspectiveBase<N, S>
where N: Real,
S: StorageMut<N, U4, U4> {
/// Updates this perspective matrix with a new `width / height` aspect ratio of the view
/// frustrum.
#[inline]
pub fn set_aspect(&mut self, aspect: N) {
assert!(!relative_eq!(aspect, N::zero()), "The aspect ratio must not be zero.");
self.matrix[(0, 0)] = self.matrix[(1, 1)] / aspect;
}
/// Updates this perspective with a new y field of view of the view frustrum.
#[inline]
pub fn set_fovy(&mut self, fovy: N) {
let old_m22 = self.matrix[(1, 1)];
self.matrix[(1, 1)] = N::one() / (fovy / ::convert(2.0)).tan();
self.matrix[(0, 0)] = self.matrix[(0, 0)] * (self.matrix[(1, 1)] / old_m22);
}
/// Updates this perspective matrix with a new near plane offset of the view frustrum.
#[inline]
pub fn set_znear(&mut self, znear: N) {
let zfar = self.zfar();
self.set_znear_and_zfar(znear, zfar);
}
/// Updates this perspective matrix with a new far plane offset of the view frustrum.
#[inline]
pub fn set_zfar(&mut self, zfar: N) {
let znear = self.znear();
self.set_znear_and_zfar(znear, zfar);
}
/// Updates this perspective matrix with new near and far plane offsets of the view frustrum.
#[inline]
pub fn set_znear_and_zfar(&mut self, znear: N, zfar: N) {
self.matrix[(2, 2)] = (zfar + znear) / (znear - zfar);
self.matrix[(2, 3)] = zfar * znear * ::convert(2.0) / (znear - zfar);
}
}
impl<N, S> Rand for PerspectiveBase<N, S>
where N: Real + Rand,
S: OwnedStorage<N, U4, U4>,
S::Alloc: OwnedAllocator<N, U4, U4, S> {
fn rand<R: Rng>(r: &mut R) -> Self {
let znear = Rand::rand(r);
let zfar = helper::reject_rand(r, |&x: &N| !(x - znear).is_zero());
let aspect = helper::reject_rand(r, |&x: &N| !x.is_zero());
Self::new(aspect, Rand::rand(r), znear, zfar)
}
}
#[cfg(feature="arbitrary")]
impl<N, S> Arbitrary for PerspectiveBase<N, S>
where N: Real + Arbitrary,
S: OwnedStorage<N, U4, U4> + Send,
S::Alloc: OwnedAllocator<N, U4, U4, S> {
fn arbitrary<G: Gen>(g: &mut G) -> Self {
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)
}
}