<!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_conversion.rs`."><meta name="keywords" content="rust, rustlang, rust-lang"><title>isometry_conversion.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="kw">use</span> <span class="ident">alga</span>::<span class="ident">general</span>::{<span class="ident">RealField</span>, <span class="ident">SubsetOf</span>, <span class="ident">SupersetOf</span>};
<span class="kw">use</span> <span class="ident">alga</span>::<span class="ident">linear</span>::<span class="ident">Rotation</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">DimMin</span>, <span class="ident">DimName</span>, <span class="ident">DimNameAdd</span>, <span class="ident">DimNameSum</span>, <span class="ident">U1</span>};
<span class="kw">use</span> <span class="kw">crate</span>::<span class="ident">base</span>::{<span class="ident">DefaultAllocator</span>, <span class="ident">MatrixN</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">Similarity</span>, <span class="ident">SuperTCategoryOf</span>, <span class="ident">TAffine</span>, <span class="ident">Transform</span>, <span class="ident">Translation</span>};

<span class="comment">/*
 * This file provides the following conversions:
 * =============================================
 *
 * Isometry -&gt; Isometry
 * Isometry -&gt; Similarity
 * Isometry -&gt; Transform
 * Isometry -&gt; Matrix (homogeneous)
 */</span>

<span class="kw">impl</span><span class="op">&lt;</span><span class="ident">N1</span>, <span class="ident">N2</span>, <span class="ident">D</span>: <span class="ident">DimName</span>, <span class="ident">R1</span>, <span class="ident">R2</span><span class="op">&gt;</span> <span class="ident">SubsetOf</span><span class="op">&lt;</span><span class="ident">Isometry</span><span class="op">&lt;</span><span class="ident">N2</span>, <span class="ident">D</span>, <span class="ident">R2</span><span class="op">&gt;</span><span class="op">&gt;</span> <span class="kw">for</span> <span class="ident">Isometry</span><span class="op">&lt;</span><span class="ident">N1</span>, <span class="ident">D</span>, <span class="ident">R1</span><span class="op">&gt;</span>
<span class="kw">where</span>
    <span class="ident">N1</span>: <span class="ident">RealField</span>,
    <span class="ident">N2</span>: <span class="ident">RealField</span> <span class="op">+</span> <span class="ident">SupersetOf</span><span class="op">&lt;</span><span class="ident">N1</span><span class="op">&gt;</span>,
    <span class="ident">R1</span>: <span class="ident">Rotation</span><span class="op">&lt;</span><span class="ident">Point</span><span class="op">&lt;</span><span class="ident">N1</span>, <span class="ident">D</span><span class="op">&gt;</span><span class="op">&gt;</span> <span class="op">+</span> <span class="ident">SubsetOf</span><span class="op">&lt;</span><span class="ident">R2</span><span class="op">&gt;</span>,
    <span class="ident">R2</span>: <span class="ident">Rotation</span><span class="op">&lt;</span><span class="ident">Point</span><span class="op">&lt;</span><span class="ident">N2</span>, <span class="ident">D</span><span class="op">&gt;</span><span class="op">&gt;</span>,
    <span class="ident">DefaultAllocator</span>: <span class="ident">Allocator</span><span class="op">&lt;</span><span class="ident">N1</span>, <span class="ident">D</span><span class="op">&gt;</span> <span class="op">+</span> <span class="ident">Allocator</span><span class="op">&lt;</span><span class="ident">N2</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">to_superset</span>(<span class="kw-2">&amp;</span><span class="self">self</span>) <span class="op">-</span><span class="op">&gt;</span> <span class="ident">Isometry</span><span class="op">&lt;</span><span class="ident">N2</span>, <span class="ident">D</span>, <span class="ident">R2</span><span class="op">&gt;</span> {
        <span class="ident">Isometry</span>::<span class="ident">from_parts</span>(<span class="self">self</span>.<span class="ident">translation</span>.<span class="ident">to_superset</span>(), <span class="self">self</span>.<span class="ident">rotation</span>.<span class="ident">to_superset</span>())
    }

    <span class="attribute">#[<span class="ident">inline</span>]</span>
    <span class="kw">fn</span> <span class="ident">is_in_subset</span>(<span class="ident">iso</span>: <span class="kw-2">&amp;</span><span class="ident">Isometry</span><span class="op">&lt;</span><span class="ident">N2</span>, <span class="ident">D</span>, <span class="ident">R2</span><span class="op">&gt;</span>) <span class="op">-</span><span class="op">&gt;</span> <span class="ident">bool</span> {
        <span class="kw">crate</span>::<span class="ident">is_convertible</span>::<span class="op">&lt;</span><span class="kw">_</span>, <span class="ident">Translation</span><span class="op">&lt;</span><span class="ident">N1</span>, <span class="ident">D</span><span class="op">&gt;</span><span class="op">&gt;</span>(<span class="kw-2">&amp;</span><span class="ident">iso</span>.<span class="ident">translation</span>)
            <span class="kw-2">&amp;</span><span class="op">&amp;</span> <span class="kw">crate</span>::<span class="ident">is_convertible</span>::<span class="op">&lt;</span><span class="kw">_</span>, <span class="ident">R1</span><span class="op">&gt;</span>(<span class="kw-2">&amp;</span><span class="ident">iso</span>.<span class="ident">rotation</span>)
    }

    <span class="attribute">#[<span class="ident">inline</span>]</span>
    <span class="kw">unsafe</span> <span class="kw">fn</span> <span class="ident">from_superset_unchecked</span>(<span class="ident">iso</span>: <span class="kw-2">&amp;</span><span class="ident">Isometry</span><span class="op">&lt;</span><span class="ident">N2</span>, <span class="ident">D</span>, <span class="ident">R2</span><span class="op">&gt;</span>) <span class="op">-</span><span class="op">&gt;</span> <span class="self">Self</span> {
        <span class="ident">Isometry</span>::<span class="ident">from_parts</span>(
            <span class="ident">iso</span>.<span class="ident">translation</span>.<span class="ident">to_subset_unchecked</span>(),
            <span class="ident">iso</span>.<span class="ident">rotation</span>.<span class="ident">to_subset_unchecked</span>(),
        )
    }
}

<span class="kw">impl</span><span class="op">&lt;</span><span class="ident">N1</span>, <span class="ident">N2</span>, <span class="ident">D</span>: <span class="ident">DimName</span>, <span class="ident">R1</span>, <span class="ident">R2</span><span class="op">&gt;</span> <span class="ident">SubsetOf</span><span class="op">&lt;</span><span class="ident">Similarity</span><span class="op">&lt;</span><span class="ident">N2</span>, <span class="ident">D</span>, <span class="ident">R2</span><span class="op">&gt;</span><span class="op">&gt;</span> <span class="kw">for</span> <span class="ident">Isometry</span><span class="op">&lt;</span><span class="ident">N1</span>, <span class="ident">D</span>, <span class="ident">R1</span><span class="op">&gt;</span>
<span class="kw">where</span>
    <span class="ident">N1</span>: <span class="ident">RealField</span>,
    <span class="ident">N2</span>: <span class="ident">RealField</span> <span class="op">+</span> <span class="ident">SupersetOf</span><span class="op">&lt;</span><span class="ident">N1</span><span class="op">&gt;</span>,
    <span class="ident">R1</span>: <span class="ident">Rotation</span><span class="op">&lt;</span><span class="ident">Point</span><span class="op">&lt;</span><span class="ident">N1</span>, <span class="ident">D</span><span class="op">&gt;</span><span class="op">&gt;</span> <span class="op">+</span> <span class="ident">SubsetOf</span><span class="op">&lt;</span><span class="ident">R2</span><span class="op">&gt;</span>,
    <span class="ident">R2</span>: <span class="ident">Rotation</span><span class="op">&lt;</span><span class="ident">Point</span><span class="op">&lt;</span><span class="ident">N2</span>, <span class="ident">D</span><span class="op">&gt;</span><span class="op">&gt;</span>,
    <span class="ident">DefaultAllocator</span>: <span class="ident">Allocator</span><span class="op">&lt;</span><span class="ident">N1</span>, <span class="ident">D</span><span class="op">&gt;</span> <span class="op">+</span> <span class="ident">Allocator</span><span class="op">&lt;</span><span class="ident">N2</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">to_superset</span>(<span class="kw-2">&amp;</span><span class="self">self</span>) <span class="op">-</span><span class="op">&gt;</span> <span class="ident">Similarity</span><span class="op">&lt;</span><span class="ident">N2</span>, <span class="ident">D</span>, <span class="ident">R2</span><span class="op">&gt;</span> {
        <span class="ident">Similarity</span>::<span class="ident">from_isometry</span>(<span class="self">self</span>.<span class="ident">to_superset</span>(), <span class="ident">N2</span>::<span class="ident">one</span>())
    }

    <span class="attribute">#[<span class="ident">inline</span>]</span>
    <span class="kw">fn</span> <span class="ident">is_in_subset</span>(<span class="ident">sim</span>: <span class="kw-2">&amp;</span><span class="ident">Similarity</span><span class="op">&lt;</span><span class="ident">N2</span>, <span class="ident">D</span>, <span class="ident">R2</span><span class="op">&gt;</span>) <span class="op">-</span><span class="op">&gt;</span> <span class="ident">bool</span> {
        <span class="kw">crate</span>::<span class="ident">is_convertible</span>::<span class="op">&lt;</span><span class="kw">_</span>, <span class="ident">Isometry</span><span class="op">&lt;</span><span class="ident">N1</span>, <span class="ident">D</span>, <span class="ident">R1</span><span class="op">&gt;</span><span class="op">&gt;</span>(<span class="kw-2">&amp;</span><span class="ident">sim</span>.<span class="ident">isometry</span>) <span class="kw-2">&amp;</span><span class="op">&amp;</span> <span class="ident">sim</span>.<span class="ident">scaling</span>() <span class="op">=</span><span class="op">=</span> <span class="ident">N2</span>::<span class="ident">one</span>()
    }

    <span class="attribute">#[<span class="ident">inline</span>]</span>
    <span class="kw">unsafe</span> <span class="kw">fn</span> <span class="ident">from_superset_unchecked</span>(<span class="ident">sim</span>: <span class="kw-2">&amp;</span><span class="ident">Similarity</span><span class="op">&lt;</span><span class="ident">N2</span>, <span class="ident">D</span>, <span class="ident">R2</span><span class="op">&gt;</span>) <span class="op">-</span><span class="op">&gt;</span> <span class="self">Self</span> {
        <span class="kw">crate</span>::<span class="ident">convert_ref_unchecked</span>(<span class="kw-2">&amp;</span><span class="ident">sim</span>.<span class="ident">isometry</span>)
    }
}

<span class="kw">impl</span><span class="op">&lt;</span><span class="ident">N1</span>, <span class="ident">N2</span>, <span class="ident">D</span>, <span class="ident">R</span>, <span class="ident">C</span><span class="op">&gt;</span> <span class="ident">SubsetOf</span><span class="op">&lt;</span><span class="ident">Transform</span><span class="op">&lt;</span><span class="ident">N2</span>, <span class="ident">D</span>, <span class="ident">C</span><span class="op">&gt;</span><span class="op">&gt;</span> <span class="kw">for</span> <span class="ident">Isometry</span><span class="op">&lt;</span><span class="ident">N1</span>, <span class="ident">D</span>, <span class="ident">R</span><span class="op">&gt;</span>
<span class="kw">where</span>
    <span class="ident">N1</span>: <span class="ident">RealField</span>,
    <span class="ident">N2</span>: <span class="ident">RealField</span> <span class="op">+</span> <span class="ident">SupersetOf</span><span class="op">&lt;</span><span class="ident">N1</span><span class="op">&gt;</span>,
    <span class="ident">C</span>: <span class="ident">SuperTCategoryOf</span><span class="op">&lt;</span><span class="ident">TAffine</span><span class="op">&gt;</span>,
    <span class="ident">R</span>: <span class="ident">Rotation</span><span class="op">&lt;</span><span class="ident">Point</span><span class="op">&lt;</span><span class="ident">N1</span>, <span class="ident">D</span><span class="op">&gt;</span><span class="op">&gt;</span>
        <span class="op">+</span> <span class="ident">SubsetOf</span><span class="op">&lt;</span><span class="ident">MatrixN</span><span class="op">&lt;</span><span class="ident">N1</span>, <span class="ident">DimNameSum</span><span class="op">&lt;</span><span class="ident">D</span>, <span class="ident">U1</span><span class="op">&gt;</span><span class="op">&gt;</span><span class="op">&gt;</span>
        <span class="op">+</span> <span class="ident">SubsetOf</span><span class="op">&lt;</span><span class="ident">MatrixN</span><span class="op">&lt;</span><span class="ident">N2</span>, <span class="ident">DimNameSum</span><span class="op">&lt;</span><span class="ident">D</span>, <span class="ident">U1</span><span class="op">&gt;</span><span class="op">&gt;</span><span class="op">&gt;</span>,
    <span class="ident">D</span>: <span class="ident">DimNameAdd</span><span class="op">&lt;</span><span class="ident">U1</span><span class="op">&gt;</span> <span class="op">+</span> <span class="ident">DimMin</span><span class="op">&lt;</span><span class="ident">D</span>, <span class="ident">Output</span> <span class="op">=</span> <span class="ident">D</span><span class="op">&gt;</span>, <span class="comment">// needed by .is_special_orthogonal()</span>
    <span class="ident">DefaultAllocator</span>: <span class="ident">Allocator</span><span class="op">&lt;</span><span class="ident">N1</span>, <span class="ident">D</span><span class="op">&gt;</span>
        <span class="op">+</span> <span class="ident">Allocator</span><span class="op">&lt;</span><span class="ident">N1</span>, <span class="ident">D</span>, <span class="ident">D</span><span class="op">&gt;</span>
        <span class="op">+</span> <span class="ident">Allocator</span><span class="op">&lt;</span><span class="ident">N1</span>, <span class="ident">DimNameSum</span><span class="op">&lt;</span><span class="ident">D</span>, <span class="ident">U1</span><span class="op">&gt;</span>, <span class="ident">DimNameSum</span><span class="op">&lt;</span><span class="ident">D</span>, <span class="ident">U1</span><span class="op">&gt;</span><span class="op">&gt;</span>
        <span class="op">+</span> <span class="ident">Allocator</span><span class="op">&lt;</span><span class="ident">N2</span>, <span class="ident">DimNameSum</span><span class="op">&lt;</span><span class="ident">D</span>, <span class="ident">U1</span><span class="op">&gt;</span>, <span class="ident">DimNameSum</span><span class="op">&lt;</span><span class="ident">D</span>, <span class="ident">U1</span><span class="op">&gt;</span><span class="op">&gt;</span>
        <span class="op">+</span> <span class="ident">Allocator</span><span class="op">&lt;</span><span class="ident">N2</span>, <span class="ident">DimNameSum</span><span class="op">&lt;</span><span class="ident">D</span>, <span class="ident">U1</span><span class="op">&gt;</span>, <span class="ident">DimNameSum</span><span class="op">&lt;</span><span class="ident">D</span>, <span class="ident">U1</span><span class="op">&gt;</span><span class="op">&gt;</span>
        <span class="op">+</span> <span class="ident">Allocator</span><span class="op">&lt;</span>(<span class="ident">usize</span>, <span class="ident">usize</span>), <span class="ident">D</span><span class="op">&gt;</span>
        <span class="op">+</span> <span class="ident">Allocator</span><span class="op">&lt;</span><span class="ident">N2</span>, <span class="ident">D</span>, <span class="ident">D</span><span class="op">&gt;</span>
        <span class="op">+</span> <span class="ident">Allocator</span><span class="op">&lt;</span><span class="ident">N2</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">to_superset</span>(<span class="kw-2">&amp;</span><span class="self">self</span>) <span class="op">-</span><span class="op">&gt;</span> <span class="ident">Transform</span><span class="op">&lt;</span><span class="ident">N2</span>, <span class="ident">D</span>, <span class="ident">C</span><span class="op">&gt;</span> {
        <span class="ident">Transform</span>::<span class="ident">from_matrix_unchecked</span>(<span class="self">self</span>.<span class="ident">to_homogeneous</span>().<span class="ident">to_superset</span>())
    }

    <span class="attribute">#[<span class="ident">inline</span>]</span>
    <span class="kw">fn</span> <span class="ident">is_in_subset</span>(<span class="ident">t</span>: <span class="kw-2">&amp;</span><span class="ident">Transform</span><span class="op">&lt;</span><span class="ident">N2</span>, <span class="ident">D</span>, <span class="ident">C</span><span class="op">&gt;</span>) <span class="op">-</span><span class="op">&gt;</span> <span class="ident">bool</span> {
        <span class="op">&lt;</span><span class="self">Self</span> <span class="kw">as</span> <span class="ident">SubsetOf</span><span class="op">&lt;</span><span class="kw">_</span><span class="op">&gt;</span><span class="op">&gt;</span>::<span class="ident">is_in_subset</span>(<span class="ident">t</span>.<span class="ident">matrix</span>())
    }

    <span class="attribute">#[<span class="ident">inline</span>]</span>
    <span class="kw">unsafe</span> <span class="kw">fn</span> <span class="ident">from_superset_unchecked</span>(<span class="ident">t</span>: <span class="kw-2">&amp;</span><span class="ident">Transform</span><span class="op">&lt;</span><span class="ident">N2</span>, <span class="ident">D</span>, <span class="ident">C</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_superset_unchecked</span>(<span class="ident">t</span>.<span class="ident">matrix</span>())
    }
}

<span class="kw">impl</span><span class="op">&lt;</span><span class="ident">N1</span>, <span class="ident">N2</span>, <span class="ident">D</span>, <span class="ident">R</span><span class="op">&gt;</span> <span class="ident">SubsetOf</span><span class="op">&lt;</span><span class="ident">MatrixN</span><span class="op">&lt;</span><span class="ident">N2</span>, <span class="ident">DimNameSum</span><span class="op">&lt;</span><span class="ident">D</span>, <span class="ident">U1</span><span class="op">&gt;</span><span class="op">&gt;</span><span class="op">&gt;</span> <span class="kw">for</span> <span class="ident">Isometry</span><span class="op">&lt;</span><span class="ident">N1</span>, <span class="ident">D</span>, <span class="ident">R</span><span class="op">&gt;</span>
<span class="kw">where</span>
    <span class="ident">N1</span>: <span class="ident">RealField</span>,
    <span class="ident">N2</span>: <span class="ident">RealField</span> <span class="op">+</span> <span class="ident">SupersetOf</span><span class="op">&lt;</span><span class="ident">N1</span><span class="op">&gt;</span>,
    <span class="ident">R</span>: <span class="ident">Rotation</span><span class="op">&lt;</span><span class="ident">Point</span><span class="op">&lt;</span><span class="ident">N1</span>, <span class="ident">D</span><span class="op">&gt;</span><span class="op">&gt;</span>
        <span class="op">+</span> <span class="ident">SubsetOf</span><span class="op">&lt;</span><span class="ident">MatrixN</span><span class="op">&lt;</span><span class="ident">N1</span>, <span class="ident">DimNameSum</span><span class="op">&lt;</span><span class="ident">D</span>, <span class="ident">U1</span><span class="op">&gt;</span><span class="op">&gt;</span><span class="op">&gt;</span>
        <span class="op">+</span> <span class="ident">SubsetOf</span><span class="op">&lt;</span><span class="ident">MatrixN</span><span class="op">&lt;</span><span class="ident">N2</span>, <span class="ident">DimNameSum</span><span class="op">&lt;</span><span class="ident">D</span>, <span class="ident">U1</span><span class="op">&gt;</span><span class="op">&gt;</span><span class="op">&gt;</span>,
    <span class="ident">D</span>: <span class="ident">DimNameAdd</span><span class="op">&lt;</span><span class="ident">U1</span><span class="op">&gt;</span> <span class="op">+</span> <span class="ident">DimMin</span><span class="op">&lt;</span><span class="ident">D</span>, <span class="ident">Output</span> <span class="op">=</span> <span class="ident">D</span><span class="op">&gt;</span>, <span class="comment">// needed by .is_special_orthogonal()</span>
    <span class="ident">DefaultAllocator</span>: <span class="ident">Allocator</span><span class="op">&lt;</span><span class="ident">N1</span>, <span class="ident">D</span><span class="op">&gt;</span>
        <span class="op">+</span> <span class="ident">Allocator</span><span class="op">&lt;</span><span class="ident">N1</span>, <span class="ident">D</span>, <span class="ident">D</span><span class="op">&gt;</span>
        <span class="op">+</span> <span class="ident">Allocator</span><span class="op">&lt;</span><span class="ident">N1</span>, <span class="ident">DimNameSum</span><span class="op">&lt;</span><span class="ident">D</span>, <span class="ident">U1</span><span class="op">&gt;</span>, <span class="ident">DimNameSum</span><span class="op">&lt;</span><span class="ident">D</span>, <span class="ident">U1</span><span class="op">&gt;</span><span class="op">&gt;</span>
        <span class="op">+</span> <span class="ident">Allocator</span><span class="op">&lt;</span><span class="ident">N2</span>, <span class="ident">DimNameSum</span><span class="op">&lt;</span><span class="ident">D</span>, <span class="ident">U1</span><span class="op">&gt;</span>, <span class="ident">DimNameSum</span><span class="op">&lt;</span><span class="ident">D</span>, <span class="ident">U1</span><span class="op">&gt;</span><span class="op">&gt;</span>
        <span class="op">+</span> <span class="ident">Allocator</span><span class="op">&lt;</span><span class="ident">N2</span>, <span class="ident">DimNameSum</span><span class="op">&lt;</span><span class="ident">D</span>, <span class="ident">U1</span><span class="op">&gt;</span>, <span class="ident">DimNameSum</span><span class="op">&lt;</span><span class="ident">D</span>, <span class="ident">U1</span><span class="op">&gt;</span><span class="op">&gt;</span>
        <span class="op">+</span> <span class="ident">Allocator</span><span class="op">&lt;</span>(<span class="ident">usize</span>, <span class="ident">usize</span>), <span class="ident">D</span><span class="op">&gt;</span>
        <span class="op">+</span> <span class="ident">Allocator</span><span class="op">&lt;</span><span class="ident">N2</span>, <span class="ident">D</span>, <span class="ident">D</span><span class="op">&gt;</span>
        <span class="op">+</span> <span class="ident">Allocator</span><span class="op">&lt;</span><span class="ident">N2</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">to_superset</span>(<span class="kw-2">&amp;</span><span class="self">self</span>) <span class="op">-</span><span class="op">&gt;</span> <span class="ident">MatrixN</span><span class="op">&lt;</span><span class="ident">N2</span>, <span class="ident">DimNameSum</span><span class="op">&lt;</span><span class="ident">D</span>, <span class="ident">U1</span><span class="op">&gt;</span><span class="op">&gt;</span> {
        <span class="self">self</span>.<span class="ident">to_homogeneous</span>().<span class="ident">to_superset</span>()
    }

    <span class="attribute">#[<span class="ident">inline</span>]</span>
    <span class="kw">fn</span> <span class="ident">is_in_subset</span>(<span class="ident">m</span>: <span class="kw-2">&amp;</span><span class="ident">MatrixN</span><span class="op">&lt;</span><span class="ident">N2</span>, <span class="ident">DimNameSum</span><span class="op">&lt;</span><span class="ident">D</span>, <span class="ident">U1</span><span class="op">&gt;</span><span class="op">&gt;</span>) <span class="op">-</span><span class="op">&gt;</span> <span class="ident">bool</span> {
        <span class="kw">let</span> <span class="ident">rot</span> <span class="op">=</span> <span class="ident">m</span>.<span class="ident">fixed_slice</span>::<span class="op">&lt;</span><span class="ident">D</span>, <span class="ident">D</span><span class="op">&gt;</span>(<span class="number">0</span>, <span class="number">0</span>);
        <span class="kw">let</span> <span class="ident">bottom</span> <span class="op">=</span> <span class="ident">m</span>.<span class="ident">fixed_slice</span>::<span class="op">&lt;</span><span class="ident">U1</span>, <span class="ident">D</span><span class="op">&gt;</span>(<span class="ident">D</span>::<span class="ident">dim</span>(), <span class="number">0</span>);

        <span class="comment">// Scalar types agree.</span>
        <span class="ident">m</span>.<span class="ident">iter</span>().<span class="ident">all</span>(<span class="op">|</span><span class="ident">e</span><span class="op">|</span> <span class="ident">SupersetOf</span>::<span class="op">&lt;</span><span class="ident">N1</span><span class="op">&gt;</span>::<span class="ident">is_in_subset</span>(<span class="ident">e</span>)) <span class="kw-2">&amp;</span><span class="op">&amp;</span>
        <span class="comment">// The block part is a rotation.</span>
        <span class="ident">rot</span>.<span class="ident">is_special_orthogonal</span>(<span class="ident">N2</span>::<span class="ident">default_epsilon</span>() <span class="op">*</span> <span class="kw">crate</span>::<span class="ident">convert</span>(<span class="number">100.0</span>)) <span class="kw-2">&amp;</span><span class="op">&amp;</span>
        <span class="comment">// The bottom row is (0, 0, ..., 1)</span>
        <span class="ident">bottom</span>.<span class="ident">iter</span>().<span class="ident">all</span>(<span class="op">|</span><span class="ident">e</span><span class="op">|</span> <span class="ident">e</span>.<span class="ident">is_zero</span>()) <span class="kw-2">&amp;</span><span class="op">&amp;</span> <span class="ident">m</span>[(<span class="ident">D</span>::<span class="ident">dim</span>(), <span class="ident">D</span>::<span class="ident">dim</span>())] <span class="op">=</span><span class="op">=</span> <span class="ident">N2</span>::<span class="ident">one</span>()
    }

    <span class="attribute">#[<span class="ident">inline</span>]</span>
    <span class="kw">unsafe</span> <span class="kw">fn</span> <span class="ident">from_superset_unchecked</span>(<span class="ident">m</span>: <span class="kw-2">&amp;</span><span class="ident">MatrixN</span><span class="op">&lt;</span><span class="ident">N2</span>, <span class="ident">DimNameSum</span><span class="op">&lt;</span><span class="ident">D</span>, <span class="ident">U1</span><span class="op">&gt;</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">t</span> <span class="op">=</span> <span class="ident">m</span>.<span class="ident">fixed_slice</span>::<span class="op">&lt;</span><span class="ident">D</span>, <span class="ident">U1</span><span class="op">&gt;</span>(<span class="number">0</span>, <span class="ident">D</span>::<span class="ident">dim</span>()).<span class="ident">into_owned</span>();
        <span class="kw">let</span> <span class="ident">t</span> <span class="op">=</span> <span class="ident">Translation</span> {
            <span class="ident">vector</span>: <span class="kw">crate</span>::<span class="ident">convert_unchecked</span>(<span class="ident">t</span>),
        };

        <span class="self">Self</span>::<span class="ident">from_parts</span>(<span class="ident">t</span>, <span class="kw">crate</span>::<span class="ident">convert_unchecked</span>(<span class="ident">m</span>.<span class="ident">clone_owned</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">From</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">MatrixN</span><span class="op">&lt;</span><span class="ident">N</span>, <span class="ident">DimNameSum</span><span class="op">&lt;</span><span class="ident">D</span>, <span class="ident">U1</span><span class="op">&gt;</span><span class="op">&gt;</span>
<span class="kw">where</span>
    <span class="ident">D</span>: <span class="ident">DimNameAdd</span><span class="op">&lt;</span><span class="ident">U1</span><span class="op">&gt;</span>,
    <span class="ident">R</span>: <span class="ident">SubsetOf</span><span class="op">&lt;</span><span class="ident">MatrixN</span><span class="op">&lt;</span><span class="ident">N</span>, <span class="ident">DimNameSum</span><span class="op">&lt;</span><span class="ident">D</span>, <span class="ident">U1</span><span class="op">&gt;</span><span class="op">&gt;</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">DimNameSum</span><span class="op">&lt;</span><span class="ident">D</span>, <span class="ident">U1</span><span class="op">&gt;</span>, <span class="ident">DimNameSum</span><span class="op">&lt;</span><span class="ident">D</span>, <span class="ident">U1</span><span class="op">&gt;</span><span class="op">&gt;</span> <span class="op">+</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">from</span>(<span class="ident">iso</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">-</span><span class="op">&gt;</span> <span class="self">Self</span> {
        <span class="ident">iso</span>.<span class="ident">to_homogeneous</span>()
    }
}
</pre></div>
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