<!DOCTYPE html><html lang="en"><head><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1.0"><meta name="generator" content="rustdoc"><meta name="description" content="Source of the Rust file `/Users/erlendbasso/.cargo/registry/src/github.com-1ecc6299db9ec823/nalgebra-0.32.1/src/geometry/perspective.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>perspective.rs - source</title><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceSerif4-Regular-1f7d512b176f0f72.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/FiraSans-Regular-018c141bf0843ffd.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/FiraSans-Medium-8f9a781e4970d388.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceCodePro-Regular-562dcc5011b6de7d.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceSerif4-Bold-124a1ca42af929b6.ttf.woff2"><link rel="preload" as="font" type="font/woff2" crossorigin href="../../../static.files/SourceCodePro-Semibold-d899c5a5c4aeb14a.ttf.woff2"><link rel="stylesheet" href="../../../static.files/normalize-76eba96aa4d2e634.css"><link rel="stylesheet" href="../../../static.files/rustdoc-6827029ac823cab7.css" id="mainThemeStyle"><link rel="stylesheet" id="themeStyle" href="../../../static.files/light-ebce58d0a40c3431.css"><link rel="stylesheet" disabled href="../../../static.files/dark-f23faae4a2daf9a6.css"><link rel="stylesheet" disabled href="../../../static.files/ayu-8af5e100b21cd173.css"><script id="default-settings" ></script><script src="../../../static.files/storage-d43fa987303ecbbb.js"></script><script defer src="../../../static.files/source-script-5cf2e01a42cc9858.js"></script><script defer src="../../../source-files.js"></script><script defer src="../../../static.files/main-c55e1eb52e1886b4.js"></script><noscript><link rel="stylesheet" href="../../../static.files/noscript-13285aec31fa243e.css"></noscript><link rel="icon" href="https://nalgebra.org/img/favicon.ico"></head><body class="rustdoc source"><!--[if lte IE 11]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"></nav><main><div class="width-limiter"><nav class="sub"><a class="sub-logo-container" href="../../../nalgebra/index.html"><img class="rust-logo" src="../../../static.files/rust-logo-151179464ae7ed46.svg" alt="logo"></a><form class="search-form"><span></span><input class="search-input" name="search" aria-label="Run search in the documentation" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"><div id="help-button" title="help" tabindex="-1"><a href="../../../help.html">?</a></div><div id="settings-menu" tabindex="-1"><a href="../../../settings.html" title="settings"><img width="22" height="22" alt="Change settings" src="../../../static.files/wheel-5ec35bf9ca753509.svg"></a></div></form></nav><section id="main-content" class="content"><div class="example-wrap"><pre class="src-line-numbers"><a href="#1" id="1">1</a>
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</pre><pre class="rust"><code><span class="attr">#[cfg(feature = <span class="string">"arbitrary"</span>)]
</span><span class="kw">use </span>quickcheck::{Arbitrary, Gen};
<span class="attr">#[cfg(feature = <span class="string">"rand-no-std"</span>)]
</span><span class="kw">use </span>rand::{
distributions::{Distribution, Standard},
Rng,
};
<span class="attr">#[cfg(feature = <span class="string">"serde-serialize-no-std"</span>)]
</span><span class="kw">use </span>serde::{Deserialize, Deserializer, Serialize, Serializer};
<span class="kw">use </span>std::fmt;
<span class="kw">use </span>simba::scalar::RealField;
<span class="kw">use </span><span class="kw">crate</span>::base::dimension::U3;
<span class="kw">use </span><span class="kw">crate</span>::base::storage::Storage;
<span class="kw">use </span><span class="kw">crate</span>::base::{Matrix4, Vector, Vector3};
<span class="kw">use </span><span class="kw">crate</span>::geometry::{Point3, Projective3};
<span class="doccomment">/// A 3D perspective projection stored as a homogeneous 4x4 matrix.
</span><span class="attr">#[repr(C)]
#[cfg_attr(
feature = <span class="string">"rkyv-serialize-no-std"</span>,
derive(rkyv::Archive, rkyv::Serialize, rkyv::Deserialize),
archive(
<span class="kw">as </span>= <span class="string">"Perspective3<T::Archived>"</span>,
bound(archive = <span class="string">"
T: rkyv::Archive,
Matrix4<T>: rkyv::Archive<Archived = Matrix4<T::Archived>>
"</span>)
)
)]
#[cfg_attr(feature = <span class="string">"rkyv-serialize"</span>, derive(bytecheck::CheckBytes))]
#[cfg_attr(feature = <span class="string">"cuda"</span>, derive(cust_core::DeviceCopy))]
#[derive(Copy, Clone)]
</span><span class="kw">pub struct </span>Perspective3<T> {
matrix: Matrix4<T>,
}
<span class="kw">impl</span><T: RealField> fmt::Debug <span class="kw">for </span>Perspective3<T> {
<span class="kw">fn </span>fmt(<span class="kw-2">&</span><span class="self">self</span>, f: <span class="kw-2">&mut </span>fmt::Formatter<<span class="lifetime">'_</span>>) -> <span class="prelude-ty">Result</span><(), fmt::Error> {
<span class="self">self</span>.matrix.fmt(f)
}
}
<span class="kw">impl</span><T: RealField> PartialEq <span class="kw">for </span>Perspective3<T> {
<span class="attr">#[inline]
</span><span class="kw">fn </span>eq(<span class="kw-2">&</span><span class="self">self</span>, right: <span class="kw-2">&</span><span class="self">Self</span>) -> bool {
<span class="self">self</span>.matrix == right.matrix
}
}
<span class="attr">#[cfg(feature = <span class="string">"bytemuck"</span>)]
</span><span class="kw">unsafe impl</span><T> bytemuck::Zeroable <span class="kw">for </span>Perspective3<T>
<span class="kw">where
</span>T: RealField + bytemuck::Zeroable,
Matrix4<T>: bytemuck::Zeroable,
{
}
<span class="attr">#[cfg(feature = <span class="string">"bytemuck"</span>)]
</span><span class="kw">unsafe impl</span><T> bytemuck::Pod <span class="kw">for </span>Perspective3<T>
<span class="kw">where
</span>T: RealField + bytemuck::Pod,
Matrix4<T>: bytemuck::Pod,
{
}
<span class="attr">#[cfg(feature = <span class="string">"serde-serialize-no-std"</span>)]
</span><span class="kw">impl</span><T: RealField + Serialize> Serialize <span class="kw">for </span>Perspective3<T> {
<span class="kw">fn </span>serialize<S>(<span class="kw-2">&</span><span class="self">self</span>, serializer: S) -> <span class="prelude-ty">Result</span><S::Ok, S::Error>
<span class="kw">where
</span>S: Serializer,
{
<span class="self">self</span>.matrix.serialize(serializer)
}
}
<span class="attr">#[cfg(feature = <span class="string">"serde-serialize-no-std"</span>)]
</span><span class="kw">impl</span><<span class="lifetime">'a</span>, T: RealField + Deserialize<<span class="lifetime">'a</span>>> Deserialize<<span class="lifetime">'a</span>> <span class="kw">for </span>Perspective3<T> {
<span class="kw">fn </span>deserialize<Des>(deserializer: Des) -> <span class="prelude-ty">Result</span><<span class="self">Self</span>, Des::Error>
<span class="kw">where
</span>Des: Deserializer<<span class="lifetime">'a</span>>,
{
<span class="kw">let </span>matrix = Matrix4::<T>::deserialize(deserializer)<span class="question-mark">?</span>;
<span class="prelude-val">Ok</span>(<span class="self">Self</span>::from_matrix_unchecked(matrix))
}
}
<span class="kw">impl</span><T> Perspective3<T> {
<span class="doccomment">/// Wraps the given matrix to interpret it as a 3D perspective matrix.
///
/// It is not checked whether or not the given matrix actually represents a perspective
/// projection.
</span><span class="attr">#[inline]
</span><span class="kw">pub const fn </span>from_matrix_unchecked(matrix: Matrix4<T>) -> <span class="self">Self </span>{
<span class="self">Self </span>{ matrix }
}
}
<span class="kw">impl</span><T: RealField> Perspective3<T> {
<span class="doccomment">/// Creates a new perspective matrix from the aspect ratio, y field of view, and near/far planes.
</span><span class="kw">pub fn </span>new(aspect: T, fovy: T, znear: T, zfar: T) -> <span class="self">Self </span>{
<span class="macro">assert!</span>(
<span class="macro">relative_ne!</span>(zfar, znear),
<span class="string">"The near-plane and far-plane must not be superimposed."
</span>);
<span class="macro">assert!</span>(
!<span class="macro">relative_eq!</span>(aspect, T::zero()),
<span class="string">"The aspect ratio must not be zero."
</span>);
<span class="kw">let </span>matrix = Matrix4::identity();
<span class="kw">let </span><span class="kw-2">mut </span>res = <span class="self">Self</span>::from_matrix_unchecked(matrix);
res.set_fovy(fovy);
res.set_aspect(aspect);
res.set_znear_and_zfar(znear, zfar);
res.matrix[(<span class="number">3</span>, <span class="number">3</span>)] = T::zero();
res.matrix[(<span class="number">3</span>, <span class="number">2</span>)] = -T::one();
res
}
<span class="doccomment">/// Retrieves the inverse of the underlying homogeneous matrix.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>inverse(<span class="kw-2">&</span><span class="self">self</span>) -> Matrix4<T> {
<span class="kw">let </span><span class="kw-2">mut </span>res = <span class="self">self</span>.clone().to_homogeneous();
res[(<span class="number">0</span>, <span class="number">0</span>)] = T::one() / <span class="self">self</span>.matrix[(<span class="number">0</span>, <span class="number">0</span>)].clone();
res[(<span class="number">1</span>, <span class="number">1</span>)] = T::one() / <span class="self">self</span>.matrix[(<span class="number">1</span>, <span class="number">1</span>)].clone();
res[(<span class="number">2</span>, <span class="number">2</span>)] = T::zero();
<span class="kw">let </span>m23 = <span class="self">self</span>.matrix[(<span class="number">2</span>, <span class="number">3</span>)].clone();
<span class="kw">let </span>m32 = <span class="self">self</span>.matrix[(<span class="number">3</span>, <span class="number">2</span>)].clone();
res[(<span class="number">2</span>, <span class="number">3</span>)] = T::one() / m32.clone();
res[(<span class="number">3</span>, <span class="number">2</span>)] = T::one() / m23.clone();
res[(<span class="number">3</span>, <span class="number">3</span>)] = -<span class="self">self</span>.matrix[(<span class="number">2</span>, <span class="number">2</span>)].clone() / (m23 * m32);
res
}
<span class="doccomment">/// Computes the corresponding homogeneous matrix.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>to_homogeneous(<span class="self">self</span>) -> Matrix4<T> {
<span class="self">self</span>.matrix.clone_owned()
}
<span class="doccomment">/// A reference to the underlying homogeneous transformation matrix.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>as_matrix(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="kw-2">&</span>Matrix4<T> {
<span class="kw-2">&</span><span class="self">self</span>.matrix
}
<span class="doccomment">/// A reference to this transformation seen as a `Projective3`.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>as_projective(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="kw-2">&</span>Projective3<T> {
<span class="kw">unsafe </span>{ <span class="kw-2">&*</span>(<span class="self">self </span><span class="kw">as </span><span class="kw-2">*const </span>Perspective3<T> <span class="kw">as </span><span class="kw-2">*const </span>Projective3<T>) }
}
<span class="doccomment">/// This transformation seen as a `Projective3`.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>to_projective(<span class="self">self</span>) -> Projective3<T> {
Projective3::from_matrix_unchecked(<span class="self">self</span>.matrix)
}
<span class="doccomment">/// Retrieves the underlying homogeneous matrix.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>into_inner(<span class="self">self</span>) -> Matrix4<T> {
<span class="self">self</span>.matrix
}
<span class="doccomment">/// Retrieves the underlying homogeneous matrix.
/// Deprecated: Use [`Perspective3::into_inner`] instead.
</span><span class="attr">#[deprecated(note = <span class="string">"use `.into_inner()` instead"</span>)]
#[inline]
</span><span class="kw">pub fn </span>unwrap(<span class="self">self</span>) -> Matrix4<T> {
<span class="self">self</span>.matrix
}
<span class="doccomment">/// Gets the `width / height` aspect ratio of the view frustum.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>aspect(<span class="kw-2">&</span><span class="self">self</span>) -> T {
<span class="self">self</span>.matrix[(<span class="number">1</span>, <span class="number">1</span>)].clone() / <span class="self">self</span>.matrix[(<span class="number">0</span>, <span class="number">0</span>)].clone()
}
<span class="doccomment">/// Gets the y field of view of the view frustum.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>fovy(<span class="kw-2">&</span><span class="self">self</span>) -> T {
(T::one() / <span class="self">self</span>.matrix[(<span class="number">1</span>, <span class="number">1</span>)].clone()).atan() * <span class="kw">crate</span>::convert(<span class="number">2.0</span>)
}
<span class="doccomment">/// Gets the near plane offset of the view frustum.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>znear(<span class="kw-2">&</span><span class="self">self</span>) -> T {
<span class="kw">let </span>ratio =
(-<span class="self">self</span>.matrix[(<span class="number">2</span>, <span class="number">2</span>)].clone() + T::one()) / (-<span class="self">self</span>.matrix[(<span class="number">2</span>, <span class="number">2</span>)].clone() - T::one());
<span class="self">self</span>.matrix[(<span class="number">2</span>, <span class="number">3</span>)].clone() / (ratio * <span class="kw">crate</span>::convert(<span class="number">2.0</span>))
- <span class="self">self</span>.matrix[(<span class="number">2</span>, <span class="number">3</span>)].clone() / <span class="kw">crate</span>::convert(<span class="number">2.0</span>)
}
<span class="doccomment">/// Gets the far plane offset of the view frustum.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>zfar(<span class="kw-2">&</span><span class="self">self</span>) -> T {
<span class="kw">let </span>ratio =
(-<span class="self">self</span>.matrix[(<span class="number">2</span>, <span class="number">2</span>)].clone() + T::one()) / (-<span class="self">self</span>.matrix[(<span class="number">2</span>, <span class="number">2</span>)].clone() - T::one());
(<span class="self">self</span>.matrix[(<span class="number">2</span>, <span class="number">3</span>)].clone() - ratio * <span class="self">self</span>.matrix[(<span class="number">2</span>, <span class="number">3</span>)].clone()) / <span class="kw">crate</span>::convert(<span class="number">2.0</span>)
}
<span class="comment">// TODO: add a method to retrieve znear and zfar simultaneously?
// TODO: when we get specialization, specialize the Mul impl instead.
</span><span class="doccomment">/// Projects a point. Faster than matrix multiplication.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>project_point(<span class="kw-2">&</span><span class="self">self</span>, p: <span class="kw-2">&</span>Point3<T>) -> Point3<T> {
<span class="kw">let </span>inverse_denom = -T::one() / p[<span class="number">2</span>].clone();
Point3::new(
<span class="self">self</span>.matrix[(<span class="number">0</span>, <span class="number">0</span>)].clone() * p[<span class="number">0</span>].clone() * inverse_denom.clone(),
<span class="self">self</span>.matrix[(<span class="number">1</span>, <span class="number">1</span>)].clone() * p[<span class="number">1</span>].clone() * inverse_denom.clone(),
(<span class="self">self</span>.matrix[(<span class="number">2</span>, <span class="number">2</span>)].clone() * p[<span class="number">2</span>].clone() + <span class="self">self</span>.matrix[(<span class="number">2</span>, <span class="number">3</span>)].clone())
* inverse_denom,
)
}
<span class="doccomment">/// Un-projects a point. Faster than multiplication by the matrix inverse.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>unproject_point(<span class="kw-2">&</span><span class="self">self</span>, p: <span class="kw-2">&</span>Point3<T>) -> Point3<T> {
<span class="kw">let </span>inverse_denom =
<span class="self">self</span>.matrix[(<span class="number">2</span>, <span class="number">3</span>)].clone() / (p[<span class="number">2</span>].clone() + <span class="self">self</span>.matrix[(<span class="number">2</span>, <span class="number">2</span>)].clone());
Point3::new(
p[<span class="number">0</span>].clone() * inverse_denom.clone() / <span class="self">self</span>.matrix[(<span class="number">0</span>, <span class="number">0</span>)].clone(),
p[<span class="number">1</span>].clone() * inverse_denom.clone() / <span class="self">self</span>.matrix[(<span class="number">1</span>, <span class="number">1</span>)].clone(),
-inverse_denom,
)
}
<span class="comment">// TODO: when we get specialization, specialize the Mul impl instead.
</span><span class="doccomment">/// Projects a vector. Faster than matrix multiplication.
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>project_vector<SB>(<span class="kw-2">&</span><span class="self">self</span>, p: <span class="kw-2">&</span>Vector<T, U3, SB>) -> Vector3<T>
<span class="kw">where
</span>SB: Storage<T, U3>,
{
<span class="kw">let </span>inverse_denom = -T::one() / p[<span class="number">2</span>].clone();
Vector3::new(
<span class="self">self</span>.matrix[(<span class="number">0</span>, <span class="number">0</span>)].clone() * p[<span class="number">0</span>].clone() * inverse_denom.clone(),
<span class="self">self</span>.matrix[(<span class="number">1</span>, <span class="number">1</span>)].clone() * p[<span class="number">1</span>].clone() * inverse_denom,
<span class="self">self</span>.matrix[(<span class="number">2</span>, <span class="number">2</span>)].clone(),
)
}
<span class="doccomment">/// Updates this perspective matrix with a new `width / height` aspect ratio of the view
/// frustum.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>set_aspect(<span class="kw-2">&mut </span><span class="self">self</span>, aspect: T) {
<span class="macro">assert!</span>(
!<span class="macro">relative_eq!</span>(aspect, T::zero()),
<span class="string">"The aspect ratio must not be zero."
</span>);
<span class="self">self</span>.matrix[(<span class="number">0</span>, <span class="number">0</span>)] = <span class="self">self</span>.matrix[(<span class="number">1</span>, <span class="number">1</span>)].clone() / aspect;
}
<span class="doccomment">/// Updates this perspective with a new y field of view of the view frustum.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>set_fovy(<span class="kw-2">&mut </span><span class="self">self</span>, fovy: T) {
<span class="kw">let </span>old_m22 = <span class="self">self</span>.matrix[(<span class="number">1</span>, <span class="number">1</span>)].clone();
<span class="kw">let </span>new_m22 = T::one() / (fovy / <span class="kw">crate</span>::convert(<span class="number">2.0</span>)).tan();
<span class="self">self</span>.matrix[(<span class="number">1</span>, <span class="number">1</span>)] = new_m22.clone();
<span class="self">self</span>.matrix[(<span class="number">0</span>, <span class="number">0</span>)] <span class="kw-2">*</span>= new_m22 / old_m22;
}
<span class="doccomment">/// Updates this perspective matrix with a new near plane offset of the view frustum.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>set_znear(<span class="kw-2">&mut </span><span class="self">self</span>, znear: T) {
<span class="kw">let </span>zfar = <span class="self">self</span>.zfar();
<span class="self">self</span>.set_znear_and_zfar(znear, zfar);
}
<span class="doccomment">/// Updates this perspective matrix with a new far plane offset of the view frustum.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>set_zfar(<span class="kw-2">&mut </span><span class="self">self</span>, zfar: T) {
<span class="kw">let </span>znear = <span class="self">self</span>.znear();
<span class="self">self</span>.set_znear_and_zfar(znear, zfar);
}
<span class="doccomment">/// Updates this perspective matrix with new near and far plane offsets of the view frustum.
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>set_znear_and_zfar(<span class="kw-2">&mut </span><span class="self">self</span>, znear: T, zfar: T) {
<span class="self">self</span>.matrix[(<span class="number">2</span>, <span class="number">2</span>)] = (zfar.clone() + znear.clone()) / (znear.clone() - zfar.clone());
<span class="self">self</span>.matrix[(<span class="number">2</span>, <span class="number">3</span>)] = zfar.clone() * znear.clone() * <span class="kw">crate</span>::convert(<span class="number">2.0</span>) / (znear - zfar);
}
}
<span class="attr">#[cfg(feature = <span class="string">"rand-no-std"</span>)]
</span><span class="kw">impl</span><T: RealField> Distribution<Perspective3<T>> <span class="kw">for </span>Standard
<span class="kw">where
</span>Standard: Distribution<T>,
{
<span class="doccomment">/// Generate an arbitrary random variate for testing purposes.
</span><span class="kw">fn </span>sample<R: Rng + <span class="question-mark">?</span>Sized>(<span class="kw-2">&</span><span class="self">self</span>, r: <span class="kw-2">&mut </span>R) -> Perspective3<T> {
<span class="kw">use </span><span class="kw">crate</span>::base::helper;
<span class="kw">let </span>znear = r.gen();
<span class="kw">let </span>zfar = helper::reject_rand(r, |x: <span class="kw-2">&</span>T| !(x.clone() - znear.clone()).is_zero());
<span class="kw">let </span>aspect = helper::reject_rand(r, |x: <span class="kw-2">&</span>T| !x.is_zero());
Perspective3::new(aspect, r.gen(), znear, zfar)
}
}
<span class="attr">#[cfg(feature = <span class="string">"arbitrary"</span>)]
</span><span class="kw">impl</span><T: RealField + Arbitrary> Arbitrary <span class="kw">for </span>Perspective3<T> {
<span class="kw">fn </span>arbitrary(g: <span class="kw-2">&mut </span>Gen) -> <span class="self">Self </span>{
<span class="kw">use </span><span class="kw">crate</span>::base::helper;
<span class="kw">let </span>znear: T = Arbitrary::arbitrary(g);
<span class="kw">let </span>zfar = helper::reject(g, |x: <span class="kw-2">&</span>T| !(x.clone() - znear.clone()).is_zero());
<span class="kw">let </span>aspect = helper::reject(g, |x: <span class="kw-2">&</span>T| !x.is_zero());
<span class="self">Self</span>::new(aspect, Arbitrary::arbitrary(g), znear, zfar)
}
}
<span class="kw">impl</span><T: RealField> From<Perspective3<T>> <span class="kw">for </span>Matrix4<T> {
<span class="attr">#[inline]
</span><span class="kw">fn </span>from(pers: Perspective3<T>) -> <span class="self">Self </span>{
pers.into_inner()
}
}
</code></pre></div>
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