<!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/isometry.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>isometry.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>approx::{AbsDiffEq, RelativeEq, UlpsEq};
<span class="kw">use </span>std::fmt;
<span class="kw">use </span>std::hash;
<span class="attr">#[cfg(feature = <span class="string">"serde-serialize-no-std"</span>)]
</span><span class="kw">use </span>serde::{Deserialize, Serialize};
<span class="kw">use </span>simba::scalar::{RealField, SubsetOf};
<span class="kw">use </span>simba::simd::SimdRealField;
<span class="kw">use </span><span class="kw">crate</span>::base::allocator::Allocator;
<span class="kw">use </span><span class="kw">crate</span>::base::dimension::{DimNameAdd, DimNameSum, U1};
<span class="kw">use </span><span class="kw">crate</span>::base::storage::Owned;
<span class="kw">use </span><span class="kw">crate</span>::base::{Const, DefaultAllocator, OMatrix, SVector, Scalar, Unit};
<span class="kw">use </span><span class="kw">crate</span>::geometry::{AbstractRotation, Point, Translation};
<span class="doccomment">/// A direct isometry, i.e., a rotation followed by a translation (aka. a rigid-body motion).
///
/// This is also known as an element of a Special Euclidean (SE) group.
/// The `Isometry` type can either represent a 2D or 3D isometry.
/// A 2D isometry is composed of:
/// - A translation part of type [`Translation2`](crate::Translation2)
/// - A rotation part which can either be a [`UnitComplex`](crate::UnitComplex) or a [`Rotation2`](crate::Rotation2).
///
/// A 3D isometry is composed of:
/// - A translation part of type [`Translation3`](crate::Translation3)
/// - A rotation part which can either be a [`UnitQuaternion`](crate::UnitQuaternion) or a [`Rotation3`](crate::Rotation3).
///
/// Note that instead of using the [`Isometry`](crate::Isometry) type in your code directly, you should use one
/// of its aliases: [`Isometry2`](crate::Isometry2), [`Isometry3`](crate::Isometry3),
/// [`IsometryMatrix2`](crate::IsometryMatrix2), [`IsometryMatrix3`](crate::IsometryMatrix3). Though
/// keep in mind that all the documentation of all the methods of these aliases will also appears on
/// this page.
///
/// # Construction
/// * [From a 2D vector and/or an angle <span style="float:right;">`new`, `translation`, `rotation`…</span>](#construction-from-a-2d-vector-andor-a-rotation-angle)
/// * [From a 3D vector and/or an axis-angle <span style="float:right;">`new`, `translation`, `rotation`…</span>](#construction-from-a-3d-vector-andor-an-axis-angle)
/// * [From a 3D eye position and target point <span style="float:right;">`look_at`, `look_at_lh`, `face_towards`…</span>](#construction-from-a-3d-eye-position-and-target-point)
/// * [From the translation and rotation parts <span style="float:right;">`from_parts`…</span>](#from-the-translation-and-rotation-parts)
///
/// # Transformation and composition
/// Note that transforming vectors and points can be done by multiplication, e.g., `isometry * point`.
/// Composing an isometry with another transformation can also be done by multiplication or division.
///
/// * [Transformation of a vector or a point <span style="float:right;">`transform_vector`, `inverse_transform_point`…</span>](#transformation-of-a-vector-or-a-point)
/// * [Inversion and in-place composition <span style="float:right;">`inverse`, `append_rotation_wrt_point_mut`…</span>](#inversion-and-in-place-composition)
/// * [Interpolation <span style="float:right;">`lerp_slerp`…</span>](#interpolation)
///
/// # Conversion to a matrix
/// * [Conversion to a matrix <span style="float:right;">`to_matrix`…</span>](#conversion-to-a-matrix)
///
</span><span class="attr">#[repr(C)]
#[derive(Debug, Copy, Clone)]
#[cfg_attr(feature = <span class="string">"cuda"</span>, derive(cust_core::DeviceCopy))]
#[cfg_attr(feature = <span class="string">"serde-serialize-no-std"</span>, derive(Serialize, Deserialize))]
#[cfg_attr(
feature = <span class="string">"serde-serialize-no-std"</span>,
serde(bound(serialize = <span class="string">"R: Serialize,
DefaultAllocator: Allocator<T, Const<D>>,
Owned<T, Const<D>>: Serialize,
T: Scalar"</span>))
)]
#[cfg_attr(
feature = <span class="string">"serde-serialize-no-std"</span>,
serde(bound(deserialize = <span class="string">"R: Deserialize<'de>,
DefaultAllocator: Allocator<T, Const<D>>,
Owned<T, Const<D>>: Deserialize<'de>,
T: Scalar"</span>))
)]
#[cfg_attr(feature = <span class="string">"rkyv-serialize"</span>, derive(bytecheck::CheckBytes))]
#[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">"Isometry<T::Archived, R::Archived, D>"</span>,
bound(archive = <span class="string">"
T: rkyv::Archive,
R: rkyv::Archive,
Translation<T, D>: rkyv::Archive<Archived = Translation<T::Archived, D>>
"</span>)
)
)]
</span><span class="kw">pub struct </span>Isometry<T, R, <span class="kw">const </span>D: usize> {
<span class="doccomment">/// The pure rotational part of this isometry.
</span><span class="kw">pub </span>rotation: R,
<span class="doccomment">/// The pure translational part of this isometry.
</span><span class="kw">pub </span>translation: Translation<T, D>,
}
<span class="kw">impl</span><T: Scalar + hash::Hash, R: hash::Hash, <span class="kw">const </span>D: usize> hash::Hash <span class="kw">for </span>Isometry<T, R, D>
<span class="kw">where
</span>Owned<T, Const<D>>: hash::Hash,
{
<span class="kw">fn </span>hash<H: hash::Hasher>(<span class="kw-2">&</span><span class="self">self</span>, state: <span class="kw-2">&mut </span>H) {
<span class="self">self</span>.translation.hash(state);
<span class="self">self</span>.rotation.hash(state);
}
}
<span class="doccomment">/// # From the translation and rotation parts
</span><span class="kw">impl</span><T: Scalar, R: AbstractRotation<T, D>, <span class="kw">const </span>D: usize> Isometry<T, R, D> {
<span class="doccomment">/// Creates a new isometry from its rotational and translational parts.
///
/// # Example
///
/// ```
/// # #[macro_use] extern crate approx;
/// # use std::f32;
/// # use nalgebra::{Isometry3, Translation3, UnitQuaternion, Vector3, Point3};
/// let tra = Translation3::new(0.0, 0.0, 3.0);
/// let rot = UnitQuaternion::from_scaled_axis(Vector3::y() * f32::consts::PI);
/// let iso = Isometry3::from_parts(tra, rot);
///
/// assert_relative_eq!(iso * Point3::new(1.0, 2.0, 3.0), Point3::new(-1.0, 2.0, 0.0), epsilon = 1.0e-6);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>from_parts(translation: Translation<T, D>, rotation: R) -> <span class="self">Self </span>{
<span class="self">Self </span>{
rotation,
translation,
}
}
}
<span class="doccomment">/// # Inversion and in-place composition
</span><span class="kw">impl</span><T: SimdRealField, R: AbstractRotation<T, D>, <span class="kw">const </span>D: usize> Isometry<T, R, D>
<span class="kw">where
</span>T::Element: SimdRealField,
{
<span class="doccomment">/// Inverts `self`.
///
/// # Example
///
/// ```
/// # use std::f32;
/// # use nalgebra::{Isometry2, Point2, Vector2};
/// let iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);
/// let inv = iso.inverse();
/// let pt = Point2::new(1.0, 2.0);
///
/// assert_eq!(inv * (iso * pt), pt);
/// ```
</span><span class="attr">#[inline]
#[must_use = <span class="string">"Did you mean to use inverse_mut()?"</span>]
</span><span class="kw">pub fn </span>inverse(<span class="kw-2">&</span><span class="self">self</span>) -> <span class="self">Self </span>{
<span class="kw">let </span><span class="kw-2">mut </span>res = <span class="self">self</span>.clone();
res.inverse_mut();
res
}
<span class="doccomment">/// Inverts `self` in-place.
///
/// # Example
///
/// ```
/// # use std::f32;
/// # use nalgebra::{Isometry2, Point2, Vector2};
/// let mut iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);
/// let pt = Point2::new(1.0, 2.0);
/// let transformed_pt = iso * pt;
/// iso.inverse_mut();
///
/// assert_eq!(iso * transformed_pt, pt);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>inverse_mut(<span class="kw-2">&mut </span><span class="self">self</span>) {
<span class="self">self</span>.rotation.inverse_mut();
<span class="self">self</span>.translation.inverse_mut();
<span class="self">self</span>.translation.vector = <span class="self">self</span>.rotation.transform_vector(<span class="kw-2">&</span><span class="self">self</span>.translation.vector);
}
<span class="doccomment">/// Computes `self.inverse() * rhs` in a more efficient way.
///
/// # Example
///
/// ```
/// # use std::f32;
/// # use nalgebra::{Isometry2, Point2, Vector2};
/// let mut iso1 = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);
/// let mut iso2 = Isometry2::new(Vector2::new(10.0, 20.0), f32::consts::FRAC_PI_4);
///
/// assert_eq!(iso1.inverse() * iso2, iso1.inv_mul(&iso2));
/// ```
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>inv_mul(<span class="kw-2">&</span><span class="self">self</span>, rhs: <span class="kw-2">&</span>Isometry<T, R, D>) -> <span class="self">Self </span>{
<span class="kw">let </span>inv_rot1 = <span class="self">self</span>.rotation.inverse();
<span class="kw">let </span>tr_12 = <span class="kw-2">&</span>rhs.translation.vector - <span class="kw-2">&</span><span class="self">self</span>.translation.vector;
Isometry::from_parts(
inv_rot1.transform_vector(<span class="kw-2">&</span>tr_12).into(),
inv_rot1 * rhs.rotation.clone(),
)
}
<span class="doccomment">/// Appends to `self` the given translation in-place.
///
/// # Example
///
/// ```
/// # use std::f32;
/// # use nalgebra::{Isometry2, Translation2, Vector2};
/// let mut iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);
/// let tra = Translation2::new(3.0, 4.0);
/// // Same as `iso = tra * iso`.
/// iso.append_translation_mut(&tra);
///
/// assert_eq!(iso.translation, Translation2::new(4.0, 6.0));
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>append_translation_mut(<span class="kw-2">&mut </span><span class="self">self</span>, t: <span class="kw-2">&</span>Translation<T, D>) {
<span class="self">self</span>.translation.vector += <span class="kw-2">&</span>t.vector
}
<span class="doccomment">/// Appends to `self` the given rotation in-place.
///
/// # Example
///
/// ```
/// # #[macro_use] extern crate approx;
/// # use std::f32;
/// # use nalgebra::{Isometry2, Translation2, UnitComplex, Vector2};
/// let mut iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::PI / 6.0);
/// let rot = UnitComplex::new(f32::consts::PI / 2.0);
/// // Same as `iso = rot * iso`.
/// iso.append_rotation_mut(&rot);
///
/// assert_relative_eq!(iso, Isometry2::new(Vector2::new(-2.0, 1.0), f32::consts::PI * 2.0 / 3.0), epsilon = 1.0e-6);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>append_rotation_mut(<span class="kw-2">&mut </span><span class="self">self</span>, r: <span class="kw-2">&</span>R) {
<span class="self">self</span>.rotation = r.clone() * <span class="self">self</span>.rotation.clone();
<span class="self">self</span>.translation.vector = r.transform_vector(<span class="kw-2">&</span><span class="self">self</span>.translation.vector);
}
<span class="doccomment">/// Appends in-place to `self` a rotation centered at the point `p`, i.e., the rotation that
/// lets `p` invariant.
///
/// # Example
///
/// ```
/// # #[macro_use] extern crate approx;
/// # use std::f32;
/// # use nalgebra::{Isometry2, Translation2, UnitComplex, Vector2, Point2};
/// let mut iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);
/// let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
/// let pt = Point2::new(1.0, 0.0);
/// iso.append_rotation_wrt_point_mut(&rot, &pt);
///
/// assert_relative_eq!(iso * pt, Point2::new(-2.0, 0.0), epsilon = 1.0e-6);
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>append_rotation_wrt_point_mut(<span class="kw-2">&mut </span><span class="self">self</span>, r: <span class="kw-2">&</span>R, p: <span class="kw-2">&</span>Point<T, D>) {
<span class="self">self</span>.translation.vector -= <span class="kw-2">&</span>p.coords;
<span class="self">self</span>.append_rotation_mut(r);
<span class="self">self</span>.translation.vector += <span class="kw-2">&</span>p.coords;
}
<span class="doccomment">/// Appends in-place to `self` a rotation centered at the point with coordinates
/// `self.translation`.
///
/// # Example
///
/// ```
/// # use std::f32;
/// # use nalgebra::{Isometry2, Translation2, UnitComplex, Vector2, Point2};
/// let mut iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);
/// let rot = UnitComplex::new(f32::consts::FRAC_PI_2);
/// iso.append_rotation_wrt_center_mut(&rot);
///
/// // The translation part should not have changed.
/// assert_eq!(iso.translation.vector, Vector2::new(1.0, 2.0));
/// assert_eq!(iso.rotation, UnitComplex::new(f32::consts::PI));
/// ```
</span><span class="attr">#[inline]
</span><span class="kw">pub fn </span>append_rotation_wrt_center_mut(<span class="kw-2">&mut </span><span class="self">self</span>, r: <span class="kw-2">&</span>R) {
<span class="self">self</span>.rotation = r.clone() * <span class="self">self</span>.rotation.clone();
}
}
<span class="doccomment">/// # Transformation of a vector or a point
</span><span class="kw">impl</span><T: SimdRealField, R: AbstractRotation<T, D>, <span class="kw">const </span>D: usize> Isometry<T, R, D>
<span class="kw">where
</span>T::Element: SimdRealField,
{
<span class="doccomment">/// Transform the given point by this isometry.
///
/// This is the same as the multiplication `self * pt`.
///
/// # Example
///
/// ```
/// # #[macro_use] extern crate approx;
/// # use std::f32;
/// # use nalgebra::{Isometry3, Translation3, UnitQuaternion, Vector3, Point3};
/// let tra = Translation3::new(0.0, 0.0, 3.0);
/// let rot = UnitQuaternion::from_scaled_axis(Vector3::y() * f32::consts::FRAC_PI_2);
/// let iso = Isometry3::from_parts(tra, rot);
///
/// let transformed_point = iso.transform_point(&Point3::new(1.0, 2.0, 3.0));
/// assert_relative_eq!(transformed_point, Point3::new(3.0, 2.0, 2.0), epsilon = 1.0e-6);
/// ```
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>transform_point(<span class="kw-2">&</span><span class="self">self</span>, pt: <span class="kw-2">&</span>Point<T, D>) -> Point<T, D> {
<span class="self">self </span>* pt
}
<span class="doccomment">/// Transform the given vector by this isometry, ignoring the translation
/// component of the isometry.
///
/// This is the same as the multiplication `self * v`.
///
/// # Example
///
/// ```
/// # #[macro_use] extern crate approx;
/// # use std::f32;
/// # use nalgebra::{Isometry3, Translation3, UnitQuaternion, Vector3};
/// let tra = Translation3::new(0.0, 0.0, 3.0);
/// let rot = UnitQuaternion::from_scaled_axis(Vector3::y() * f32::consts::FRAC_PI_2);
/// let iso = Isometry3::from_parts(tra, rot);
///
/// let transformed_point = iso.transform_vector(&Vector3::new(1.0, 2.0, 3.0));
/// assert_relative_eq!(transformed_point, Vector3::new(3.0, 2.0, -1.0), epsilon = 1.0e-6);
/// ```
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>transform_vector(<span class="kw-2">&</span><span class="self">self</span>, v: <span class="kw-2">&</span>SVector<T, D>) -> SVector<T, D> {
<span class="self">self </span>* v
}
<span class="doccomment">/// Transform the given point by the inverse of this isometry. This may be
/// less expensive than computing the entire isometry inverse and then
/// transforming the point.
///
/// # Example
///
/// ```
/// # #[macro_use] extern crate approx;
/// # use std::f32;
/// # use nalgebra::{Isometry3, Translation3, UnitQuaternion, Vector3, Point3};
/// let tra = Translation3::new(0.0, 0.0, 3.0);
/// let rot = UnitQuaternion::from_scaled_axis(Vector3::y() * f32::consts::FRAC_PI_2);
/// let iso = Isometry3::from_parts(tra, rot);
///
/// let transformed_point = iso.inverse_transform_point(&Point3::new(1.0, 2.0, 3.0));
/// assert_relative_eq!(transformed_point, Point3::new(0.0, 2.0, 1.0), epsilon = 1.0e-6);
/// ```
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>inverse_transform_point(<span class="kw-2">&</span><span class="self">self</span>, pt: <span class="kw-2">&</span>Point<T, D>) -> Point<T, D> {
<span class="self">self</span>.rotation
.inverse_transform_point(<span class="kw-2">&</span>(pt - <span class="kw-2">&</span><span class="self">self</span>.translation.vector))
}
<span class="doccomment">/// Transform the given vector by the inverse of this isometry, ignoring the
/// translation component of the isometry. This may be
/// less expensive than computing the entire isometry inverse and then
/// transforming the point.
///
/// # Example
///
/// ```
/// # #[macro_use] extern crate approx;
/// # use std::f32;
/// # use nalgebra::{Isometry3, Translation3, UnitQuaternion, Vector3};
/// let tra = Translation3::new(0.0, 0.0, 3.0);
/// let rot = UnitQuaternion::from_scaled_axis(Vector3::y() * f32::consts::FRAC_PI_2);
/// let iso = Isometry3::from_parts(tra, rot);
///
/// let transformed_point = iso.inverse_transform_vector(&Vector3::new(1.0, 2.0, 3.0));
/// assert_relative_eq!(transformed_point, Vector3::new(-3.0, 2.0, 1.0), epsilon = 1.0e-6);
/// ```
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>inverse_transform_vector(<span class="kw-2">&</span><span class="self">self</span>, v: <span class="kw-2">&</span>SVector<T, D>) -> SVector<T, D> {
<span class="self">self</span>.rotation.inverse_transform_vector(v)
}
<span class="doccomment">/// Transform the given unit vector by the inverse of this isometry, ignoring the
/// translation component of the isometry. This may be
/// less expensive than computing the entire isometry inverse and then
/// transforming the point.
///
/// # Example
///
/// ```
/// # #[macro_use] extern crate approx;
/// # use std::f32;
/// # use nalgebra::{Isometry3, Translation3, UnitQuaternion, Vector3};
/// let tra = Translation3::new(0.0, 0.0, 3.0);
/// let rot = UnitQuaternion::from_scaled_axis(Vector3::z() * f32::consts::FRAC_PI_2);
/// let iso = Isometry3::from_parts(tra, rot);
///
/// let transformed_point = iso.inverse_transform_unit_vector(&Vector3::x_axis());
/// assert_relative_eq!(transformed_point, -Vector3::y_axis(), epsilon = 1.0e-6);
/// ```
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>inverse_transform_unit_vector(<span class="kw-2">&</span><span class="self">self</span>, v: <span class="kw-2">&</span>Unit<SVector<T, D>>) -> Unit<SVector<T, D>> {
<span class="self">self</span>.rotation.inverse_transform_unit_vector(v)
}
}
<span class="comment">// NOTE: we don't require `R: Rotation<...>` here because this is not useful for the implementation
// and makes it hard to use it, e.g., for Transform × Isometry implementation.
// This is OK since all constructors of the isometry enforce the Rotation bound already (and
// explicit struct construction is prevented by the dummy ZST field).
</span><span class="doccomment">/// # Conversion to a matrix
</span><span class="kw">impl</span><T: SimdRealField, R, <span class="kw">const </span>D: usize> Isometry<T, R, D> {
<span class="doccomment">/// Converts this isometry into its equivalent homogeneous transformation matrix.
///
/// This is the same as `self.to_matrix()`.
///
/// # Example
///
/// ```
/// # #[macro_use] extern crate approx;
/// # use std::f32;
/// # use nalgebra::{Isometry2, Vector2, Matrix3};
/// let iso = Isometry2::new(Vector2::new(10.0, 20.0), f32::consts::FRAC_PI_6);
/// let expected = Matrix3::new(0.8660254, -0.5, 10.0,
/// 0.5, 0.8660254, 20.0,
/// 0.0, 0.0, 1.0);
///
/// assert_relative_eq!(iso.to_homogeneous(), expected, epsilon = 1.0e-6);
/// ```
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>to_homogeneous(<span class="kw-2">&</span><span class="self">self</span>) -> OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
<span class="kw">where
</span>Const<D>: DimNameAdd<U1>,
R: SubsetOf<OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
{
<span class="kw">let </span><span class="kw-2">mut </span>res: OMatrix<T, <span class="kw">_</span>, <span class="kw">_</span>> = <span class="kw">crate</span>::convert_ref(<span class="kw-2">&</span><span class="self">self</span>.rotation);
res.fixed_view_mut::<D, <span class="number">1</span>>(<span class="number">0</span>, D)
.copy_from(<span class="kw-2">&</span><span class="self">self</span>.translation.vector);
res
}
<span class="doccomment">/// Converts this isometry into its equivalent homogeneous transformation matrix.
///
/// This is the same as `self.to_homogeneous()`.
///
/// # Example
///
/// ```
/// # #[macro_use] extern crate approx;
/// # use std::f32;
/// # use nalgebra::{Isometry2, Vector2, Matrix3};
/// let iso = Isometry2::new(Vector2::new(10.0, 20.0), f32::consts::FRAC_PI_6);
/// let expected = Matrix3::new(0.8660254, -0.5, 10.0,
/// 0.5, 0.8660254, 20.0,
/// 0.0, 0.0, 1.0);
///
/// assert_relative_eq!(iso.to_matrix(), expected, epsilon = 1.0e-6);
/// ```
</span><span class="attr">#[inline]
#[must_use]
</span><span class="kw">pub fn </span>to_matrix(<span class="kw-2">&</span><span class="self">self</span>) -> OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>
<span class="kw">where
</span>Const<D>: DimNameAdd<U1>,
R: SubsetOf<OMatrix<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>>,
DefaultAllocator: Allocator<T, DimNameSum<Const<D>, U1>, DimNameSum<Const<D>, U1>>,
{
<span class="self">self</span>.to_homogeneous()
}
}
<span class="kw">impl</span><T: SimdRealField, R, <span class="kw">const </span>D: usize> Eq <span class="kw">for </span>Isometry<T, R, D> <span class="kw">where
</span>R: AbstractRotation<T, D> + Eq
{
}
<span class="kw">impl</span><T: SimdRealField, R, <span class="kw">const </span>D: usize> PartialEq <span class="kw">for </span>Isometry<T, R, D>
<span class="kw">where
</span>R: AbstractRotation<T, D> + PartialEq,
{
<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>.translation == right.translation && <span class="self">self</span>.rotation == right.rotation
}
}
<span class="kw">impl</span><T: RealField, R, <span class="kw">const </span>D: usize> AbsDiffEq <span class="kw">for </span>Isometry<T, R, D>
<span class="kw">where
</span>R: AbstractRotation<T, D> + AbsDiffEq<Epsilon = T::Epsilon>,
T::Epsilon: Clone,
{
<span class="kw">type </span>Epsilon = T::Epsilon;
<span class="attr">#[inline]
</span><span class="kw">fn </span>default_epsilon() -> <span class="self">Self</span>::Epsilon {
T::default_epsilon()
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>abs_diff_eq(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>, epsilon: <span class="self">Self</span>::Epsilon) -> bool {
<span class="self">self</span>.translation
.abs_diff_eq(<span class="kw-2">&</span>other.translation, epsilon.clone())
&& <span class="self">self</span>.rotation.abs_diff_eq(<span class="kw-2">&</span>other.rotation, epsilon)
}
}
<span class="kw">impl</span><T: RealField, R, <span class="kw">const </span>D: usize> RelativeEq <span class="kw">for </span>Isometry<T, R, D>
<span class="kw">where
</span>R: AbstractRotation<T, D> + RelativeEq<Epsilon = T::Epsilon>,
T::Epsilon: Clone,
{
<span class="attr">#[inline]
</span><span class="kw">fn </span>default_max_relative() -> <span class="self">Self</span>::Epsilon {
T::default_max_relative()
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>relative_eq(
<span class="kw-2">&</span><span class="self">self</span>,
other: <span class="kw-2">&</span><span class="self">Self</span>,
epsilon: <span class="self">Self</span>::Epsilon,
max_relative: <span class="self">Self</span>::Epsilon,
) -> bool {
<span class="self">self</span>.translation
.relative_eq(<span class="kw-2">&</span>other.translation, epsilon.clone(), max_relative.clone())
&& <span class="self">self
</span>.rotation
.relative_eq(<span class="kw-2">&</span>other.rotation, epsilon, max_relative)
}
}
<span class="kw">impl</span><T: RealField, R, <span class="kw">const </span>D: usize> UlpsEq <span class="kw">for </span>Isometry<T, R, D>
<span class="kw">where
</span>R: AbstractRotation<T, D> + UlpsEq<Epsilon = T::Epsilon>,
T::Epsilon: Clone,
{
<span class="attr">#[inline]
</span><span class="kw">fn </span>default_max_ulps() -> u32 {
T::default_max_ulps()
}
<span class="attr">#[inline]
</span><span class="kw">fn </span>ulps_eq(<span class="kw-2">&</span><span class="self">self</span>, other: <span class="kw-2">&</span><span class="self">Self</span>, epsilon: <span class="self">Self</span>::Epsilon, max_ulps: u32) -> bool {
<span class="self">self</span>.translation
.ulps_eq(<span class="kw-2">&</span>other.translation, epsilon.clone(), max_ulps)
&& <span class="self">self</span>.rotation.ulps_eq(<span class="kw-2">&</span>other.rotation, epsilon, max_ulps)
}
}
<span class="comment">/*
*
* Display
*
*/
</span><span class="kw">impl</span><T: RealField + fmt::Display, R, <span class="kw">const </span>D: usize> fmt::Display <span class="kw">for </span>Isometry<T, R, D>
<span class="kw">where
</span>R: fmt::Display,
{
<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>>) -> fmt::Result {
<span class="kw">let </span>precision = f.precision().unwrap_or(<span class="number">3</span>);
<span class="macro">writeln!</span>(f, <span class="string">"Isometry {{"</span>)<span class="question-mark">?</span>;
<span class="macro">write!</span>(f, <span class="string">"{:.*}"</span>, precision, <span class="self">self</span>.translation)<span class="question-mark">?</span>;
<span class="macro">write!</span>(f, <span class="string">"{:.*}"</span>, precision, <span class="self">self</span>.rotation)<span class="question-mark">?</span>;
<span class="macro">writeln!</span>(f, <span class="string">"}}"</span>)
}
}
</code></pre></div>
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