<!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/base/interpolation.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>interpolation.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="kw">use </span><span class="kw">crate</span>::storage::Storage;
<span class="kw">use crate</span>::{
Allocator, DefaultAllocator, Dim, OVector, One, RealField, Scalar, Unit, Vector, Zero,
};
<span class="kw">use </span>simba::scalar::{ClosedAdd, ClosedMul, ClosedSub};
<span class="doccomment">/// # Interpolation
</span><span class="kw">impl</span><T: Scalar + Zero + One + ClosedAdd + ClosedSub + ClosedMul, D: Dim, S: Storage<T, D>>
Vector<T, D, S>
{
<span class="doccomment">/// Returns `self * (1.0 - t) + rhs * t`, i.e., the linear blend of the vectors x and y using the scalar value a.
///
/// The value for a is not restricted to the range `[0, 1]`.
///
/// # Examples:
///
/// ```
/// # use nalgebra::Vector3;
/// let x = Vector3::new(1.0, 2.0, 3.0);
/// let y = Vector3::new(10.0, 20.0, 30.0);
/// assert_eq!(x.lerp(&y, 0.1), Vector3::new(1.9, 3.8, 5.7));
/// ```
</span><span class="attr">#[must_use]
</span><span class="kw">pub fn </span>lerp<S2: Storage<T, D>>(<span class="kw-2">&</span><span class="self">self</span>, rhs: <span class="kw-2">&</span>Vector<T, D, S2>, t: T) -> OVector<T, D>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, D>,
{
<span class="kw">let </span><span class="kw-2">mut </span>res = <span class="self">self</span>.clone_owned();
res.axpy(t.clone(), rhs, T::one() - t);
res
}
<span class="doccomment">/// Computes the spherical linear interpolation between two non-zero vectors.
///
/// The result is a unit vector.
///
/// # Examples:
///
/// ```
/// # use nalgebra::{Unit, Vector2};
///
/// let v1 =Vector2::new(1.0, 2.0);
/// let v2 = Vector2::new(2.0, -3.0);
///
/// let v = v1.slerp(&v2, 1.0);
///
/// assert_eq!(v, v2.normalize());
/// ```
</span><span class="attr">#[must_use]
</span><span class="kw">pub fn </span>slerp<S2: Storage<T, D>>(<span class="kw-2">&</span><span class="self">self</span>, rhs: <span class="kw-2">&</span>Vector<T, D, S2>, t: T) -> OVector<T, D>
<span class="kw">where
</span>T: RealField,
DefaultAllocator: Allocator<T, D>,
{
<span class="kw">let </span>me = Unit::new_normalize(<span class="self">self</span>.clone_owned());
<span class="kw">let </span>rhs = Unit::new_normalize(rhs.clone_owned());
me.slerp(<span class="kw-2">&</span>rhs, t).into_inner()
}
}
<span class="doccomment">/// # Interpolation between two unit vectors
</span><span class="kw">impl</span><T: RealField, D: Dim, S: Storage<T, D>> Unit<Vector<T, D, S>> {
<span class="doccomment">/// Computes the spherical linear interpolation between two unit vectors.
///
/// # Examples:
///
/// ```
/// # use nalgebra::{Unit, Vector2};
///
/// let v1 = Unit::new_normalize(Vector2::new(1.0, 2.0));
/// let v2 = Unit::new_normalize(Vector2::new(2.0, -3.0));
///
/// let v = v1.slerp(&v2, 1.0);
///
/// assert_eq!(v, v2);
/// ```
</span><span class="attr">#[must_use]
</span><span class="kw">pub fn </span>slerp<S2: Storage<T, D>>(
<span class="kw-2">&</span><span class="self">self</span>,
rhs: <span class="kw-2">&</span>Unit<Vector<T, D, S2>>,
t: T,
) -> Unit<OVector<T, D>>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, D>,
{
<span class="comment">// TODO: the result is wrong when self and rhs are collinear with opposite direction.
</span><span class="self">self</span>.try_slerp(rhs, t, T::default_epsilon())
.unwrap_or_else(|| Unit::new_unchecked(<span class="self">self</span>.clone_owned()))
}
<span class="doccomment">/// Computes the spherical linear interpolation between two unit vectors.
///
/// Returns `None` if the two vectors are almost collinear and with opposite direction
/// (in this case, there is an infinity of possible results).
</span><span class="attr">#[must_use]
</span><span class="kw">pub fn </span>try_slerp<S2: Storage<T, D>>(
<span class="kw-2">&</span><span class="self">self</span>,
rhs: <span class="kw-2">&</span>Unit<Vector<T, D, S2>>,
t: T,
epsilon: T,
) -> <span class="prelude-ty">Option</span><Unit<OVector<T, D>>>
<span class="kw">where
</span>DefaultAllocator: Allocator<T, D>,
{
<span class="kw">let </span>c_hang = <span class="self">self</span>.dot(rhs);
<span class="comment">// self == other
</span><span class="kw">if </span>c_hang >= T::one() {
<span class="kw">return </span><span class="prelude-val">Some</span>(Unit::new_unchecked(<span class="self">self</span>.clone_owned()));
}
<span class="kw">let </span>hang = c_hang.clone().acos();
<span class="kw">let </span>s_hang = (T::one() - c_hang.clone() * c_hang).sqrt();
<span class="comment">// TODO: what if s_hang is 0.0 ? The result is not well-defined.
</span><span class="kw">if </span><span class="macro">relative_eq!</span>(s_hang, T::zero(), epsilon = epsilon) {
<span class="prelude-val">None
</span>} <span class="kw">else </span>{
<span class="kw">let </span>ta = ((T::one() - t.clone()) * hang.clone()).sin() / s_hang.clone();
<span class="kw">let </span>tb = (t * hang).sin() / s_hang;
<span class="kw">let </span><span class="kw-2">mut </span>res = <span class="self">self</span>.scale(ta);
res.axpy(tb, <span class="kw-2">&**</span>rhs, T::one());
<span class="prelude-val">Some</span>(Unit::new_unchecked(res))
}
}
}
</code></pre></div>
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