<!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 to the Rust file `/home/mrh/.cargo/registry/src/github.com-1ecc6299db9ec823/nalgebra-0.18.0/src/geometry/isometry_construction.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>isometry_construction.rs.html -- source</title><link rel="stylesheet" type="text/css" href="../../../normalize.css"><link rel="stylesheet" type="text/css" href="../../../rustdoc.css" id="mainThemeStyle"><link rel="stylesheet" type="text/css" href="../../../dark.css"><link rel="stylesheet" type="text/css" href="../../../light.css" id="themeStyle"><script src="../../../storage.js"></script><noscript><link rel="stylesheet" href="../../../noscript.css"></noscript><link rel="shortcut icon" href="http://nalgebra.org/img/favicon.ico"><style type="text/css">#crate-search{background-image:url("../../../down-arrow.svg");}</style></head><body class="rustdoc source"><!--[if lte IE 8]><div class="warning">This old browser is unsupported and will most likely display funky things.</div><![endif]--><nav class="sidebar"><div class="sidebar-menu">&#9776;</div><a href='../../../nalgebra/index.html'><div class='logo-container'><img src='../../../rust-logo.png' alt='logo'></div></a></nav><div class="theme-picker"><button id="theme-picker" aria-label="Pick another theme!"><img src="../../../brush.svg" width="18" alt="Pick another theme!"></button><div id="theme-choices"></div></div><script src="../../../theme.js"></script><nav class="sub"><form class="search-form js-only"><div class="search-container"><div><select id="crate-search"><option value="All crates">All crates</option></select><input class="search-input" name="search" autocomplete="off" spellcheck="false" placeholder="Click or press ‘S’ to search, ‘?’ for more options…" type="search"></div><a id="settings-menu" href="../../../settings.html"><img src="../../../wheel.svg" width="18" alt="Change settings"></a></div></form></nav><section id="main" class="content"><pre class="line-numbers"><span id="1">  1</span>
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</pre><div class="example-wrap"><pre class="rust ">
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;arbitrary&quot;</span>)]</span>
<span class="kw">use</span> <span class="kw">crate</span>::<span class="ident">base</span>::<span class="ident">storage</span>::<span class="ident">Owned</span>;
<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;arbitrary&quot;</span>)]</span>
<span class="kw">use</span> <span class="ident">quickcheck</span>::{<span class="ident">Arbitrary</span>, <span class="ident">Gen</span>};

<span class="kw">use</span> <span class="ident">num</span>::<span class="ident">One</span>;
<span class="kw">use</span> <span class="ident">rand</span>::<span class="ident">distributions</span>::{<span class="ident">Distribution</span>, <span class="ident">Standard</span>};
<span class="kw">use</span> <span class="ident">rand</span>::<span class="ident">Rng</span>;

<span class="kw">use</span> <span class="ident">alga</span>::<span class="ident">general</span>::<span class="ident">RealField</span>;
<span class="kw">use</span> <span class="ident">alga</span>::<span class="ident">linear</span>::<span class="ident">Rotation</span> <span class="kw">as</span> <span class="ident">AlgaRotation</span>;

<span class="kw">use</span> <span class="kw">crate</span>::<span class="ident">base</span>::<span class="ident">allocator</span>::<span class="ident">Allocator</span>;
<span class="kw">use</span> <span class="kw">crate</span>::<span class="ident">base</span>::<span class="ident">dimension</span>::{<span class="ident">DimName</span>, <span class="ident">U2</span>, <span class="ident">U3</span>};
<span class="kw">use</span> <span class="kw">crate</span>::<span class="ident">base</span>::{<span class="ident">DefaultAllocator</span>, <span class="ident">Vector2</span>, <span class="ident">Vector3</span>};

<span class="kw">use</span> <span class="kw">crate</span>::<span class="ident">geometry</span>::{
    <span class="ident">Isometry</span>, <span class="ident">Point</span>, <span class="ident">Point3</span>, <span class="ident">Rotation</span>, <span class="ident">Rotation2</span>, <span class="ident">Rotation3</span>, <span class="ident">Translation</span>, <span class="ident">UnitComplex</span>,
    <span class="ident">UnitQuaternion</span>, <span class="ident">Translation2</span>, <span class="ident">Translation3</span>
};

<span class="kw">impl</span><span class="op">&lt;</span><span class="ident">N</span>: <span class="ident">RealField</span>, <span class="ident">D</span>: <span class="ident">DimName</span>, <span class="ident">R</span>: <span class="ident">AlgaRotation</span><span class="op">&lt;</span><span class="ident">Point</span><span class="op">&lt;</span><span class="ident">N</span>, <span class="ident">D</span><span class="op">&gt;</span><span class="op">&gt;</span><span class="op">&gt;</span> <span class="ident">Isometry</span><span class="op">&lt;</span><span class="ident">N</span>, <span class="ident">D</span>, <span class="ident">R</span><span class="op">&gt;</span>
<span class="kw">where</span> <span class="ident">DefaultAllocator</span>: <span class="ident">Allocator</span><span class="op">&lt;</span><span class="ident">N</span>, <span class="ident">D</span><span class="op">&gt;</span>
{
    <span class="doccomment">/// Creates a new identity isometry.</span>
    <span class="doccomment">///</span>
    <span class="doccomment">/// # Example</span>
    <span class="doccomment">///</span>
    <span class="doccomment">/// ```</span>
    <span class="doccomment">/// # use nalgebra::{Isometry2, Point2, Isometry3, Point3};</span>
    <span class="doccomment">///</span>
    <span class="doccomment">/// let iso = Isometry2::identity();</span>
    <span class="doccomment">/// let pt = Point2::new(1.0, 2.0);</span>
    <span class="doccomment">/// assert_eq!(iso * pt, pt);</span>
    <span class="doccomment">///</span>
    <span class="doccomment">/// let iso = Isometry3::identity();</span>
    <span class="doccomment">/// let pt = Point3::new(1.0, 2.0, 3.0);</span>
    <span class="doccomment">/// assert_eq!(iso * pt, pt);</span>
    <span class="doccomment">/// ```</span>
    <span class="attribute">#[<span class="ident">inline</span>]</span>
    <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">identity</span>() <span class="op">-</span><span class="op">&gt;</span> <span class="self">Self</span> {
        <span class="self">Self</span>::<span class="ident">from_parts</span>(<span class="ident">Translation</span>::<span class="ident">identity</span>(), <span class="ident">R</span>::<span class="ident">identity</span>())
    }

    <span class="doccomment">/// The isometry that applies the rotation `r` with its axis passing through the point `p`.</span>
    <span class="doccomment">/// This effectively lets `p` invariant.</span>
    <span class="doccomment">///</span>
    <span class="doccomment">/// # Example</span>
    <span class="doccomment">///</span>
    <span class="doccomment">/// ```</span>
    <span class="doccomment">/// # #[macro_use] extern crate approx;</span>
    <span class="doccomment">/// # use std::f32;</span>
    <span class="doccomment">/// # use nalgebra::{Isometry2, Point2, UnitComplex};</span>
    <span class="doccomment">/// let rot = UnitComplex::new(f32::consts::PI);</span>
    <span class="doccomment">/// let pt = Point2::new(1.0, 0.0);</span>
    <span class="doccomment">/// let iso = Isometry2::rotation_wrt_point(rot, pt);</span>
    <span class="doccomment">///</span>
    <span class="doccomment">/// assert_eq!(iso * pt, pt); // The rotation center is not affected.</span>
    <span class="doccomment">/// assert_relative_eq!(iso * Point2::new(1.0, 2.0), Point2::new(1.0, -2.0), epsilon = 1.0e-6);</span>
    <span class="doccomment">/// ```</span>
    <span class="attribute">#[<span class="ident">inline</span>]</span>
    <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">rotation_wrt_point</span>(<span class="ident">r</span>: <span class="ident">R</span>, <span class="ident">p</span>: <span class="ident">Point</span><span class="op">&lt;</span><span class="ident">N</span>, <span class="ident">D</span><span class="op">&gt;</span>) <span class="op">-</span><span class="op">&gt;</span> <span class="self">Self</span> {
        <span class="kw">let</span> <span class="ident">shift</span> <span class="op">=</span> <span class="ident">r</span>.<span class="ident">transform_vector</span>(<span class="kw-2">&amp;</span><span class="op">-</span><span class="kw-2">&amp;</span><span class="ident">p</span>.<span class="ident">coords</span>);
        <span class="self">Self</span>::<span class="ident">from_parts</span>(<span class="ident">Translation</span>::<span class="ident">from</span>(<span class="ident">shift</span> <span class="op">+</span> <span class="ident">p</span>.<span class="ident">coords</span>), <span class="ident">r</span>)
    }
}

<span class="kw">impl</span><span class="op">&lt;</span><span class="ident">N</span>: <span class="ident">RealField</span>, <span class="ident">D</span>: <span class="ident">DimName</span>, <span class="ident">R</span>: <span class="ident">AlgaRotation</span><span class="op">&lt;</span><span class="ident">Point</span><span class="op">&lt;</span><span class="ident">N</span>, <span class="ident">D</span><span class="op">&gt;</span><span class="op">&gt;</span><span class="op">&gt;</span> <span class="ident">One</span> <span class="kw">for</span> <span class="ident">Isometry</span><span class="op">&lt;</span><span class="ident">N</span>, <span class="ident">D</span>, <span class="ident">R</span><span class="op">&gt;</span>
<span class="kw">where</span> <span class="ident">DefaultAllocator</span>: <span class="ident">Allocator</span><span class="op">&lt;</span><span class="ident">N</span>, <span class="ident">D</span><span class="op">&gt;</span>
{
    <span class="doccomment">/// Creates a new identity isometry.</span>
    <span class="attribute">#[<span class="ident">inline</span>]</span>
    <span class="kw">fn</span> <span class="ident">one</span>() <span class="op">-</span><span class="op">&gt;</span> <span class="self">Self</span> {
        <span class="self">Self</span>::<span class="ident">identity</span>()
    }
}

<span class="kw">impl</span><span class="op">&lt;</span><span class="ident">N</span>: <span class="ident">RealField</span>, <span class="ident">D</span>: <span class="ident">DimName</span>, <span class="ident">R</span><span class="op">&gt;</span> <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">Isometry</span><span class="op">&lt;</span><span class="ident">N</span>, <span class="ident">D</span>, <span class="ident">R</span><span class="op">&gt;</span><span class="op">&gt;</span> <span class="kw">for</span> <span class="ident">Standard</span>
<span class="kw">where</span>
    <span class="ident">R</span>: <span class="ident">AlgaRotation</span><span class="op">&lt;</span><span class="ident">Point</span><span class="op">&lt;</span><span class="ident">N</span>, <span class="ident">D</span><span class="op">&gt;</span><span class="op">&gt;</span>,
    <span class="ident">Standard</span>: <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">N</span><span class="op">&gt;</span> <span class="op">+</span> <span class="ident">Distribution</span><span class="op">&lt;</span><span class="ident">R</span><span class="op">&gt;</span>,
    <span class="ident">DefaultAllocator</span>: <span class="ident">Allocator</span><span class="op">&lt;</span><span class="ident">N</span>, <span class="ident">D</span><span class="op">&gt;</span>,
{
    <span class="attribute">#[<span class="ident">inline</span>]</span>
    <span class="kw">fn</span> <span class="ident">sample</span><span class="op">&lt;</span><span class="lifetime">&#39;a</span>, <span class="ident">G</span>: <span class="ident">Rng</span> <span class="op">+</span> <span class="question-mark">?</span><span class="ident">Sized</span><span class="op">&gt;</span>(<span class="kw-2">&amp;</span><span class="self">self</span>, <span class="ident">rng</span>: <span class="kw-2">&amp;</span><span class="lifetime">&#39;a</span> <span class="kw-2">mut</span> <span class="ident">G</span>) <span class="op">-</span><span class="op">&gt;</span> <span class="ident">Isometry</span><span class="op">&lt;</span><span class="ident">N</span>, <span class="ident">D</span>, <span class="ident">R</span><span class="op">&gt;</span> {
        <span class="ident">Isometry</span>::<span class="ident">from_parts</span>(<span class="ident">rng</span>.<span class="ident">gen</span>(), <span class="ident">rng</span>.<span class="ident">gen</span>())
    }
}

<span class="attribute">#[<span class="ident">cfg</span>(<span class="ident">feature</span> <span class="op">=</span> <span class="string">&quot;arbitrary&quot;</span>)]</span>
<span class="kw">impl</span><span class="op">&lt;</span><span class="ident">N</span>, <span class="ident">D</span>: <span class="ident">DimName</span>, <span class="ident">R</span><span class="op">&gt;</span> <span class="ident">Arbitrary</span> <span class="kw">for</span> <span class="ident">Isometry</span><span class="op">&lt;</span><span class="ident">N</span>, <span class="ident">D</span>, <span class="ident">R</span><span class="op">&gt;</span>
<span class="kw">where</span>
    <span class="ident">N</span>: <span class="ident">RealField</span> <span class="op">+</span> <span class="ident">Arbitrary</span> <span class="op">+</span> <span class="ident">Send</span>,
    <span class="ident">R</span>: <span class="ident">AlgaRotation</span><span class="op">&lt;</span><span class="ident">Point</span><span class="op">&lt;</span><span class="ident">N</span>, <span class="ident">D</span><span class="op">&gt;</span><span class="op">&gt;</span> <span class="op">+</span> <span class="ident">Arbitrary</span> <span class="op">+</span> <span class="ident">Send</span>,
    <span class="ident">Owned</span><span class="op">&lt;</span><span class="ident">N</span>, <span class="ident">D</span><span class="op">&gt;</span>: <span class="ident">Send</span>,
    <span class="ident">DefaultAllocator</span>: <span class="ident">Allocator</span><span class="op">&lt;</span><span class="ident">N</span>, <span class="ident">D</span><span class="op">&gt;</span>,
{
    <span class="attribute">#[<span class="ident">inline</span>]</span>
    <span class="kw">fn</span> <span class="ident">arbitrary</span><span class="op">&lt;</span><span class="ident">G</span>: <span class="ident">Gen</span><span class="op">&gt;</span>(<span class="ident">rng</span>: <span class="kw-2">&amp;</span><span class="kw-2">mut</span> <span class="ident">G</span>) <span class="op">-</span><span class="op">&gt;</span> <span class="self">Self</span> {
        <span class="self">Self</span>::<span class="ident">from_parts</span>(<span class="ident">Arbitrary</span>::<span class="ident">arbitrary</span>(<span class="ident">rng</span>), <span class="ident">Arbitrary</span>::<span class="ident">arbitrary</span>(<span class="ident">rng</span>))
    }
}

<span class="comment">/*
 *
 * Constructors for various static dimensions.
 *
 */</span>

<span class="comment">// 2D rotation.</span>
<span class="kw">impl</span><span class="op">&lt;</span><span class="ident">N</span>: <span class="ident">RealField</span><span class="op">&gt;</span> <span class="ident">Isometry</span><span class="op">&lt;</span><span class="ident">N</span>, <span class="ident">U2</span>, <span class="ident">Rotation2</span><span class="op">&lt;</span><span class="ident">N</span><span class="op">&gt;</span><span class="op">&gt;</span> {
    <span class="doccomment">/// Creates a new 2D isometry from a translation and a rotation angle.</span>
    <span class="doccomment">///</span>
    <span class="doccomment">/// Its rotational part is represented as a 2x2 rotation matrix.</span>
    <span class="doccomment">///</span>
    <span class="doccomment">/// # Example</span>
    <span class="doccomment">///</span>
    <span class="doccomment">/// ```</span>
    <span class="doccomment">/// # use std::f32;</span>
    <span class="doccomment">/// # use nalgebra::{Isometry2, Vector2, Point2};</span>
    <span class="doccomment">/// let iso = Isometry2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);</span>
    <span class="doccomment">///</span>
    <span class="doccomment">/// assert_eq!(iso * Point2::new(3.0, 4.0), Point2::new(-3.0, 5.0));</span>
    <span class="doccomment">/// ```</span>
    <span class="attribute">#[<span class="ident">inline</span>]</span>
    <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">new</span>(<span class="ident">translation</span>: <span class="ident">Vector2</span><span class="op">&lt;</span><span class="ident">N</span><span class="op">&gt;</span>, <span class="ident">angle</span>: <span class="ident">N</span>) <span class="op">-</span><span class="op">&gt;</span> <span class="self">Self</span> {
        <span class="self">Self</span>::<span class="ident">from_parts</span>(
            <span class="ident">Translation</span>::<span class="ident">from</span>(<span class="ident">translation</span>),
            <span class="ident">Rotation</span>::<span class="op">&lt;</span><span class="ident">N</span>, <span class="ident">U2</span><span class="op">&gt;</span>::<span class="ident">new</span>(<span class="ident">angle</span>),
        )
    }

    <span class="doccomment">/// Creates a new isometry from the given translation coordinates.</span>
    <span class="attribute">#[<span class="ident">inline</span>]</span>
    <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">translation</span>(<span class="ident">x</span>: <span class="ident">N</span>, <span class="ident">y</span>: <span class="ident">N</span>) <span class="op">-</span><span class="op">&gt;</span> <span class="self">Self</span> {
        <span class="self">Self</span>::<span class="ident">new</span>(<span class="ident">Vector2</span>::<span class="ident">new</span>(<span class="ident">x</span>, <span class="ident">y</span>), <span class="ident">N</span>::<span class="ident">zero</span>())
    }

    <span class="doccomment">/// Creates a new isometry from the given rotation angle.</span>
    <span class="attribute">#[<span class="ident">inline</span>]</span>
    <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">rotation</span>(<span class="ident">angle</span>: <span class="ident">N</span>) <span class="op">-</span><span class="op">&gt;</span> <span class="self">Self</span> {
        <span class="self">Self</span>::<span class="ident">new</span>(<span class="ident">Vector2</span>::<span class="ident">zeros</span>(), <span class="ident">angle</span>)
    }
}

<span class="kw">impl</span><span class="op">&lt;</span><span class="ident">N</span>: <span class="ident">RealField</span><span class="op">&gt;</span> <span class="ident">Isometry</span><span class="op">&lt;</span><span class="ident">N</span>, <span class="ident">U2</span>, <span class="ident">UnitComplex</span><span class="op">&lt;</span><span class="ident">N</span><span class="op">&gt;</span><span class="op">&gt;</span> {
    <span class="doccomment">/// Creates a new 2D isometry from a translation and a rotation angle.</span>
    <span class="doccomment">///</span>
    <span class="doccomment">/// Its rotational part is represented as an unit complex number.</span>
    <span class="doccomment">///</span>
    <span class="doccomment">/// # Example</span>
    <span class="doccomment">///</span>
    <span class="doccomment">/// ```</span>
    <span class="doccomment">/// # use std::f32;</span>
    <span class="doccomment">/// # use nalgebra::{IsometryMatrix2, Point2, Vector2};</span>
    <span class="doccomment">/// let iso = IsometryMatrix2::new(Vector2::new(1.0, 2.0), f32::consts::FRAC_PI_2);</span>
    <span class="doccomment">///</span>
    <span class="doccomment">/// assert_eq!(iso * Point2::new(3.0, 4.0), Point2::new(-3.0, 5.0));</span>
    <span class="doccomment">/// ```</span>
    <span class="attribute">#[<span class="ident">inline</span>]</span>
    <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">new</span>(<span class="ident">translation</span>: <span class="ident">Vector2</span><span class="op">&lt;</span><span class="ident">N</span><span class="op">&gt;</span>, <span class="ident">angle</span>: <span class="ident">N</span>) <span class="op">-</span><span class="op">&gt;</span> <span class="self">Self</span> {
        <span class="self">Self</span>::<span class="ident">from_parts</span>(
            <span class="ident">Translation</span>::<span class="ident">from</span>(<span class="ident">translation</span>),
            <span class="ident">UnitComplex</span>::<span class="ident">from_angle</span>(<span class="ident">angle</span>),
        )
    }

    <span class="doccomment">/// Creates a new isometry from the given translation coordinates.</span>
    <span class="attribute">#[<span class="ident">inline</span>]</span>
    <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">translation</span>(<span class="ident">x</span>: <span class="ident">N</span>, <span class="ident">y</span>: <span class="ident">N</span>) <span class="op">-</span><span class="op">&gt;</span> <span class="self">Self</span> {
        <span class="self">Self</span>::<span class="ident">from_parts</span>(<span class="ident">Translation2</span>::<span class="ident">new</span>(<span class="ident">x</span>, <span class="ident">y</span>), <span class="ident">UnitComplex</span>::<span class="ident">identity</span>())
    }

    <span class="doccomment">/// Creates a new isometry from the given rotation angle.</span>
    <span class="attribute">#[<span class="ident">inline</span>]</span>
    <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">rotation</span>(<span class="ident">angle</span>: <span class="ident">N</span>) <span class="op">-</span><span class="op">&gt;</span> <span class="self">Self</span> {
        <span class="self">Self</span>::<span class="ident">new</span>(<span class="ident">Vector2</span>::<span class="ident">zeros</span>(), <span class="ident">angle</span>)
    }
}

<span class="comment">// 3D rotation.</span>
<span class="macro">macro_rules</span><span class="macro">!</span> <span class="ident">isometry_construction_impl</span>(
    (<span class="macro-nonterminal">$</span><span class="macro-nonterminal">RotId</span>: <span class="ident">ident</span> <span class="op">&lt;</span> $(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">RotParams</span>: <span class="ident">ident</span>),<span class="kw-2">*</span><span class="op">&gt;</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">RRDim</span>: <span class="ident">ty</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">RCDim</span>: <span class="ident">ty</span>) <span class="op">=</span><span class="op">&gt;</span> {
        <span class="kw">impl</span><span class="op">&lt;</span><span class="ident">N</span>: <span class="ident">RealField</span><span class="op">&gt;</span> <span class="ident">Isometry</span><span class="op">&lt;</span><span class="ident">N</span>, <span class="ident">U3</span>, <span class="macro-nonterminal">$</span><span class="macro-nonterminal">RotId</span><span class="op">&lt;</span>$(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">RotParams</span>),<span class="kw-2">*</span><span class="op">&gt;</span><span class="op">&gt;</span> {
            <span class="doccomment">/// Creates a new isometry from a translation and a rotation axis-angle.</span>
            <span class="doccomment">///</span>
            <span class="doccomment">/// # Example</span>
            <span class="doccomment">///</span>
            <span class="doccomment">/// ```</span>
            <span class="doccomment">/// # #[macro_use] extern crate approx;</span>
            <span class="doccomment">/// # use std::f32;</span>
            <span class="doccomment">/// # use nalgebra::{Isometry3, IsometryMatrix3, Point3, Vector3};</span>
            <span class="doccomment">/// let axisangle = Vector3::y() * f32::consts::FRAC_PI_2;</span>
            <span class="doccomment">/// let translation = Vector3::new(1.0, 2.0, 3.0);</span>
            <span class="doccomment">/// // Point and vector being transformed in the tests.</span>
            <span class="doccomment">/// let pt = Point3::new(4.0, 5.0, 6.0);</span>
            <span class="doccomment">/// let vec = Vector3::new(4.0, 5.0, 6.0);</span>
            <span class="doccomment">///</span>
            <span class="doccomment">/// // Isometry with its rotation part represented as a UnitQuaternion</span>
            <span class="doccomment">/// let iso = Isometry3::new(translation, axisangle);</span>
            <span class="doccomment">/// assert_relative_eq!(iso * pt, Point3::new(7.0, 7.0, -1.0), epsilon = 1.0e-6);</span>
            <span class="doccomment">/// assert_relative_eq!(iso * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);</span>
            <span class="doccomment">///</span>
            <span class="doccomment">/// // Isometry with its rotation part represented as a Rotation3 (a 3x3 rotation matrix).</span>
            <span class="doccomment">/// let iso = IsometryMatrix3::new(translation, axisangle);</span>
            <span class="doccomment">/// assert_relative_eq!(iso * pt, Point3::new(7.0, 7.0, -1.0), epsilon = 1.0e-6);</span>
            <span class="doccomment">/// assert_relative_eq!(iso * vec, Vector3::new(6.0, 5.0, -4.0), epsilon = 1.0e-6);</span>
            <span class="doccomment">/// ```</span>
            <span class="attribute">#[<span class="ident">inline</span>]</span>
            <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">new</span>(<span class="ident">translation</span>: <span class="ident">Vector3</span><span class="op">&lt;</span><span class="ident">N</span><span class="op">&gt;</span>, <span class="ident">axisangle</span>: <span class="ident">Vector3</span><span class="op">&lt;</span><span class="ident">N</span><span class="op">&gt;</span>) <span class="op">-</span><span class="op">&gt;</span> <span class="self">Self</span> {
                <span class="self">Self</span>::<span class="ident">from_parts</span>(
                    <span class="ident">Translation</span>::<span class="ident">from</span>(<span class="ident">translation</span>),
                    <span class="macro-nonterminal">$</span><span class="macro-nonterminal">RotId</span>::<span class="op">&lt;</span>$(<span class="macro-nonterminal">$</span><span class="macro-nonterminal">RotParams</span>),<span class="kw-2">*</span><span class="op">&gt;</span>::<span class="ident">from_scaled_axis</span>(<span class="ident">axisangle</span>))
            }

            <span class="doccomment">/// Creates a new isometry from the given translation coordinates.</span>
            <span class="attribute">#[<span class="ident">inline</span>]</span>
            <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">translation</span>(<span class="ident">x</span>: <span class="ident">N</span>, <span class="ident">y</span>: <span class="ident">N</span>, <span class="ident">z</span>: <span class="ident">N</span>) <span class="op">-</span><span class="op">&gt;</span> <span class="self">Self</span> {
                <span class="self">Self</span>::<span class="ident">from_parts</span>(<span class="ident">Translation3</span>::<span class="ident">new</span>(<span class="ident">x</span>, <span class="ident">y</span>, <span class="ident">z</span>), <span class="macro-nonterminal">$</span><span class="macro-nonterminal">RotId</span>::<span class="ident">identity</span>())
            }

            <span class="doccomment">/// Creates a new isometry from the given rotation angle.</span>
            <span class="attribute">#[<span class="ident">inline</span>]</span>
            <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">rotation</span>(<span class="ident">axisangle</span>: <span class="ident">Vector3</span><span class="op">&lt;</span><span class="ident">N</span><span class="op">&gt;</span>) <span class="op">-</span><span class="op">&gt;</span> <span class="self">Self</span> {
                <span class="self">Self</span>::<span class="ident">new</span>(<span class="ident">Vector3</span>::<span class="ident">zeros</span>(), <span class="ident">axisangle</span>)
            }

            <span class="doccomment">/// Creates an isometry that corresponds to the local frame of an observer standing at the</span>
            <span class="doccomment">/// point `eye` and looking toward `target`.</span>
            <span class="doccomment">///</span>
            <span class="doccomment">/// It maps the `z` axis to the view direction `target - eye`and the origin to the `eye`.</span>
            <span class="doccomment">///</span>
            <span class="doccomment">/// # Arguments</span>
            <span class="doccomment">///   * eye - The observer position.</span>
            <span class="doccomment">///   * target - The target position.</span>
            <span class="doccomment">///   * up - Vertical direction. The only requirement of this parameter is to not be collinear</span>
            <span class="doccomment">///   to `eye - at`. Non-collinearity is not checked.</span>
            <span class="doccomment">///</span>
            <span class="doccomment">/// # Example</span>
            <span class="doccomment">///</span>
            <span class="doccomment">/// ```</span>
            <span class="doccomment">/// # #[macro_use] extern crate approx;</span>
            <span class="doccomment">/// # use std::f32;</span>
            <span class="doccomment">/// # use nalgebra::{Isometry3, IsometryMatrix3, Point3, Vector3};</span>
            <span class="doccomment">/// let eye = Point3::new(1.0, 2.0, 3.0);</span>
            <span class="doccomment">/// let target = Point3::new(2.0, 2.0, 3.0);</span>
            <span class="doccomment">/// let up = Vector3::y();</span>
            <span class="doccomment">///</span>
            <span class="doccomment">/// // Isometry with its rotation part represented as a UnitQuaternion</span>
            <span class="doccomment">/// let iso = Isometry3::face_towards(&amp;eye, &amp;target, &amp;up);</span>
            <span class="doccomment">/// assert_eq!(iso * Point3::origin(), eye);</span>
            <span class="doccomment">/// assert_relative_eq!(iso * Vector3::z(), Vector3::x());</span>
            <span class="doccomment">///</span>
            <span class="doccomment">/// // Isometry with its rotation part represented as Rotation3 (a 3x3 rotation matrix).</span>
            <span class="doccomment">/// let iso = IsometryMatrix3::face_towards(&amp;eye, &amp;target, &amp;up);</span>
            <span class="doccomment">/// assert_eq!(iso * Point3::origin(), eye);</span>
            <span class="doccomment">/// assert_relative_eq!(iso * Vector3::z(), Vector3::x());</span>
            <span class="doccomment">/// ```</span>
            <span class="attribute">#[<span class="ident">inline</span>]</span>
            <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">face_towards</span>(<span class="ident">eye</span>:    <span class="kw-2">&amp;</span><span class="ident">Point3</span><span class="op">&lt;</span><span class="ident">N</span><span class="op">&gt;</span>,
                                      <span class="ident">target</span>: <span class="kw-2">&amp;</span><span class="ident">Point3</span><span class="op">&lt;</span><span class="ident">N</span><span class="op">&gt;</span>,
                                      <span class="ident">up</span>:     <span class="kw-2">&amp;</span><span class="ident">Vector3</span><span class="op">&lt;</span><span class="ident">N</span><span class="op">&gt;</span>)
                                      <span class="op">-</span><span class="op">&gt;</span> <span class="self">Self</span> {
                <span class="self">Self</span>::<span class="ident">from_parts</span>(
                    <span class="ident">Translation</span>::<span class="ident">from</span>(<span class="ident">eye</span>.<span class="ident">coords</span>.<span class="ident">clone</span>()),
                    <span class="macro-nonterminal">$</span><span class="macro-nonterminal">RotId</span>::<span class="ident">face_towards</span>(<span class="kw-2">&amp;</span>(<span class="ident">target</span> <span class="op">-</span> <span class="ident">eye</span>), <span class="ident">up</span>))
            }

            <span class="doccomment">/// Deprecated: Use [Isometry::face_towards] instead.</span>
            <span class="attribute">#[<span class="ident">deprecated</span>(<span class="ident">note</span><span class="op">=</span><span class="string">&quot;renamed to `face_towards`&quot;</span>)]</span>
            <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">new_observer_frame</span>(<span class="ident">eye</span>:    <span class="kw-2">&amp;</span><span class="ident">Point3</span><span class="op">&lt;</span><span class="ident">N</span><span class="op">&gt;</span>,
                                      <span class="ident">target</span>: <span class="kw-2">&amp;</span><span class="ident">Point3</span><span class="op">&lt;</span><span class="ident">N</span><span class="op">&gt;</span>,
                                      <span class="ident">up</span>:     <span class="kw-2">&amp;</span><span class="ident">Vector3</span><span class="op">&lt;</span><span class="ident">N</span><span class="op">&gt;</span>)
                                      <span class="op">-</span><span class="op">&gt;</span> <span class="self">Self</span> {
                <span class="self">Self</span>::<span class="ident">face_towards</span>(<span class="ident">eye</span>, <span class="ident">target</span>, <span class="ident">up</span>)
            }

            <span class="doccomment">/// Builds a right-handed look-at view matrix.</span>
            <span class="doccomment">///</span>
            <span class="doccomment">/// It maps the view direction `target - eye` to the **negative** `z` axis to and the `eye` to the origin.</span>
            <span class="doccomment">/// This conforms to the common notion of right handed camera look-at **view matrix** from</span>
            <span class="doccomment">/// the computer graphics community, i.e. the camera is assumed to look toward its local `-z` axis.</span>
            <span class="doccomment">///</span>
            <span class="doccomment">/// # Arguments</span>
            <span class="doccomment">///   * eye - The eye position.</span>
            <span class="doccomment">///   * target - The target position.</span>
            <span class="doccomment">///   * up - A vector approximately aligned with required the vertical axis. The only</span>
            <span class="doccomment">///   requirement of this parameter is to not be collinear to `target - eye`.</span>
            <span class="doccomment">///</span>
            <span class="doccomment">/// # Example</span>
            <span class="doccomment">///</span>
            <span class="doccomment">/// ```</span>
            <span class="doccomment">/// # #[macro_use] extern crate approx;</span>
            <span class="doccomment">/// # use std::f32;</span>
            <span class="doccomment">/// # use nalgebra::{Isometry3, IsometryMatrix3, Point3, Vector3};</span>
            <span class="doccomment">/// let eye = Point3::new(1.0, 2.0, 3.0);</span>
            <span class="doccomment">/// let target = Point3::new(2.0, 2.0, 3.0);</span>
            <span class="doccomment">/// let up = Vector3::y();</span>
            <span class="doccomment">///</span>
            <span class="doccomment">/// // Isometry with its rotation part represented as a UnitQuaternion</span>
            <span class="doccomment">/// let iso = Isometry3::look_at_rh(&amp;eye, &amp;target, &amp;up);</span>
            <span class="doccomment">/// assert_eq!(iso * eye, Point3::origin());</span>
            <span class="doccomment">/// assert_relative_eq!(iso * Vector3::x(), -Vector3::z());</span>
            <span class="doccomment">///</span>
            <span class="doccomment">/// // Isometry with its rotation part represented as Rotation3 (a 3x3 rotation matrix).</span>
            <span class="doccomment">/// let iso = IsometryMatrix3::look_at_rh(&amp;eye, &amp;target, &amp;up);</span>
            <span class="doccomment">/// assert_eq!(iso * eye, Point3::origin());</span>
            <span class="doccomment">/// assert_relative_eq!(iso * Vector3::x(), -Vector3::z());</span>
            <span class="doccomment">/// ```</span>
            <span class="attribute">#[<span class="ident">inline</span>]</span>
            <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">look_at_rh</span>(<span class="ident">eye</span>:    <span class="kw-2">&amp;</span><span class="ident">Point3</span><span class="op">&lt;</span><span class="ident">N</span><span class="op">&gt;</span>,
                              <span class="ident">target</span>: <span class="kw-2">&amp;</span><span class="ident">Point3</span><span class="op">&lt;</span><span class="ident">N</span><span class="op">&gt;</span>,
                              <span class="ident">up</span>:     <span class="kw-2">&amp;</span><span class="ident">Vector3</span><span class="op">&lt;</span><span class="ident">N</span><span class="op">&gt;</span>)
                              <span class="op">-</span><span class="op">&gt;</span> <span class="self">Self</span> {
                <span class="kw">let</span> <span class="ident">rotation</span> <span class="op">=</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">RotId</span>::<span class="ident">look_at_rh</span>(<span class="kw-2">&amp;</span>(<span class="ident">target</span> <span class="op">-</span> <span class="ident">eye</span>), <span class="ident">up</span>);
                <span class="kw">let</span> <span class="ident">trans</span>    <span class="op">=</span> <span class="kw-2">&amp;</span><span class="ident">rotation</span> <span class="op">*</span> (<span class="op">-</span><span class="ident">eye</span>);

                <span class="self">Self</span>::<span class="ident">from_parts</span>(<span class="ident">Translation</span>::<span class="ident">from</span>(<span class="ident">trans</span>.<span class="ident">coords</span>), <span class="ident">rotation</span>)
            }

            <span class="doccomment">/// Builds a left-handed look-at view matrix.</span>
            <span class="doccomment">///</span>
            <span class="doccomment">/// It maps the view direction `target - eye` to the **positive** `z` axis and the `eye` to the origin.</span>
            <span class="doccomment">/// This conforms to the common notion of right handed camera look-at **view matrix** from</span>
            <span class="doccomment">/// the computer graphics community, i.e. the camera is assumed to look toward its local `z` axis.</span>
            <span class="doccomment">///</span>
            <span class="doccomment">/// # Arguments</span>
            <span class="doccomment">///   * eye - The eye position.</span>
            <span class="doccomment">///   * target - The target position.</span>
            <span class="doccomment">///   * up - A vector approximately aligned with required the vertical axis. The only</span>
            <span class="doccomment">///   requirement of this parameter is to not be collinear to `target - eye`.</span>
            <span class="doccomment">///</span>
            <span class="doccomment">/// # Example</span>
            <span class="doccomment">///</span>
            <span class="doccomment">/// ```</span>
            <span class="doccomment">/// # #[macro_use] extern crate approx;</span>
            <span class="doccomment">/// # use std::f32;</span>
            <span class="doccomment">/// # use nalgebra::{Isometry3, IsometryMatrix3, Point3, Vector3};</span>
            <span class="doccomment">/// let eye = Point3::new(1.0, 2.0, 3.0);</span>
            <span class="doccomment">/// let target = Point3::new(2.0, 2.0, 3.0);</span>
            <span class="doccomment">/// let up = Vector3::y();</span>
            <span class="doccomment">///</span>
            <span class="doccomment">/// // Isometry with its rotation part represented as a UnitQuaternion</span>
            <span class="doccomment">/// let iso = Isometry3::look_at_lh(&amp;eye, &amp;target, &amp;up);</span>
            <span class="doccomment">/// assert_eq!(iso * eye, Point3::origin());</span>
            <span class="doccomment">/// assert_relative_eq!(iso * Vector3::x(), Vector3::z());</span>
            <span class="doccomment">///</span>
            <span class="doccomment">/// // Isometry with its rotation part represented as Rotation3 (a 3x3 rotation matrix).</span>
            <span class="doccomment">/// let iso = IsometryMatrix3::look_at_lh(&amp;eye, &amp;target, &amp;up);</span>
            <span class="doccomment">/// assert_eq!(iso * eye, Point3::origin());</span>
            <span class="doccomment">/// assert_relative_eq!(iso * Vector3::x(), Vector3::z());</span>
            <span class="doccomment">/// ```</span>
            <span class="attribute">#[<span class="ident">inline</span>]</span>
            <span class="kw">pub</span> <span class="kw">fn</span> <span class="ident">look_at_lh</span>(<span class="ident">eye</span>:    <span class="kw-2">&amp;</span><span class="ident">Point3</span><span class="op">&lt;</span><span class="ident">N</span><span class="op">&gt;</span>,
                              <span class="ident">target</span>: <span class="kw-2">&amp;</span><span class="ident">Point3</span><span class="op">&lt;</span><span class="ident">N</span><span class="op">&gt;</span>,
                              <span class="ident">up</span>:     <span class="kw-2">&amp;</span><span class="ident">Vector3</span><span class="op">&lt;</span><span class="ident">N</span><span class="op">&gt;</span>)
                              <span class="op">-</span><span class="op">&gt;</span> <span class="self">Self</span> {
                <span class="kw">let</span> <span class="ident">rotation</span> <span class="op">=</span> <span class="macro-nonterminal">$</span><span class="macro-nonterminal">RotId</span>::<span class="ident">look_at_lh</span>(<span class="kw-2">&amp;</span>(<span class="ident">target</span> <span class="op">-</span> <span class="ident">eye</span>), <span class="ident">up</span>);
                <span class="kw">let</span> <span class="ident">trans</span>    <span class="op">=</span> <span class="kw-2">&amp;</span><span class="ident">rotation</span> <span class="op">*</span> (<span class="op">-</span><span class="ident">eye</span>);

                <span class="self">Self</span>::<span class="ident">from_parts</span>(<span class="ident">Translation</span>::<span class="ident">from</span>(<span class="ident">trans</span>.<span class="ident">coords</span>), <span class="ident">rotation</span>)
            }
        }
    }
);

<span class="macro">isometry_construction_impl</span><span class="macro">!</span>(<span class="ident">Rotation3</span><span class="op">&lt;</span><span class="ident">N</span><span class="op">&gt;</span>, <span class="ident">U3</span>, <span class="ident">U3</span>);
<span class="macro">isometry_construction_impl</span><span class="macro">!</span>(<span class="ident">UnitQuaternion</span><span class="op">&lt;</span><span class="ident">N</span><span class="op">&gt;</span>, <span class="ident">U4</span>, <span class="ident">U1</span>);
</pre></div>
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