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{"documenter":{"julia_version":"1.10.0","generation_timestamp":"2024-02-06T16:08:29","documenter_version":"1.2.1"}}
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<!DOCTYPE html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Angle · Rotations.jl</title><meta name="title" content="Angle · Rotations.jl"/><meta property="og:title" content="Angle · Rotations.jl"/><meta property="twitter:title" content="Angle · Rotations.jl"/><meta name="description" content="Documentation for Rotations.jl."/><meta property="og:description" content="Documentation for Rotations.jl."/><meta property="twitter:description" content="Documentation for Rotations.jl."/><meta property="og:url" content="https://JuliaGeometry.github.io/Rotations.jl/2d_angle/"/><meta property="twitter:url" content="https://JuliaGeometry.github.io/Rotations.jl/2d_angle/"/><link rel="canonical" href="https://JuliaGeometry.github.io/Rotations.jl/2d_angle/"/><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../search_index.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script><link href="../assets/custom.css" rel="stylesheet" type="text/css"/><link href="../assets/favicon.ico" rel="icon" type="image/x-icon"/></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../"><img src="../assets/logo.svg" alt="Rotations.jl logo"/></a><div class="docs-package-name"><span class="docs-autofit"><a href="../">Rotations.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><a class="tocitem" href="../">Home</a></li><li><a class="tocitem" href="../rotation_types/">Rotation Types</a></li><li><span class="tocitem">2D Rotations</span><ul><li><a class="tocitem" href="../2d_matrix/">Matrix</a></li><li class="is-active"><a class="tocitem" href>Angle</a><ul class="internal"><li><a class="tocitem" href="#Angle2d"><span><code>Angle2d</code></span></a></li></ul></li></ul></li><li><span class="tocitem">3D Rotations</span><ul><li><a class="tocitem" href="../3d_matrix/">Matrix</a></li><li><a class="tocitem" href="../3d_euler/">Euler Angles</a></li><li><a class="tocitem" href="../3d_angleaxis/">Angle and Axis</a></li><li><a class="tocitem" href="../3d_quaternion/">Quaternion and Related Parameters</a></li></ul></li><li><span class="tocitem">Rotation Generators</span><ul><li><a class="tocitem" href="../rotation_generator_types/">Rotation Generator Types</a></li><li><a class="tocitem" href="../2d_rotation_generator/">2D Rotation Generators</a></li><li><a class="tocitem" href="../3d_rotation_generator/">3D Rotation Generators</a></li></ul></li><li><a class="tocitem" href="../general_dimensional_rotations/">General Dimensional Rotations</a></li><li><a class="tocitem" href="../functions/">Common Methods for Rotations</a></li><li><a class="tocitem" href="../visualizing/">Visualizing Rotations</a></li><li><a class="tocitem" href="../functionreference/">Function Reference</a></li><li><a class="tocitem" href="../reference/">References</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">2D Rotations</a></li><li class="is-active"><a href>Angle</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Angle</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/JuliaGeometry/Rotations.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/JuliaGeometry/Rotations.jl/blob/master/docs/src/2d_angle.md#" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="2D-Rotation-by-Angle"><a class="docs-heading-anchor" href="#2D-Rotation-by-Angle">2D Rotation by Angle</a><a id="2D-Rotation-by-Angle-1"></a><a class="docs-heading-anchor-permalink" href="#2D-Rotation-by-Angle" title="Permalink"></a></h1><p><code>Angle2d</code> is a type that internally has an angle as a parameter, and can be thought of as a lazy version of <code>RotMatrix{2}</code>.</p><h2 id="Angle2d"><a class="docs-heading-anchor" href="#Angle2d"><code>Angle2d</code></a><a id="Angle2d-1"></a><a class="docs-heading-anchor-permalink" href="#Angle2d" title="Permalink"></a></h2><p><strong>example</strong></p><pre><code class="language-julia-repl hljs" style="display:block;">julia&gt; t = 1.2 # rotation angle</code><code class="nohighlight hljs ansi" style="display:block;">1.2</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; m = [cos(t) -sin(t);sin(t) cos(t)]</code><code class="nohighlight hljs ansi" style="display:block;">2×2 Matrix{Float64}:
0.362358 -0.932039
0.932039 0.362358</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; Angle2d(t) # construct from matrix</code><code class="nohighlight hljs ansi" style="display:block;">2×2 Angle2d{Float64} with indices SOneTo(2)×SOneTo(2)(1.2):
0.362358 -0.932039
0.932039 0.362358</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; RotMatrix{2}(t)</code><code class="nohighlight hljs ansi" style="display:block;">2×2 RotMatrix2{Float64} with indices SOneTo(2)×SOneTo(2):
0.362358 -0.932039
0.932039 0.362358</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; dump(Angle2d(t))</code><code class="nohighlight hljs ansi" style="display:block;">Angle2d{Float64}
theta: Float64 1.2</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; dump(RotMatrix{2}(t))</code><code class="nohighlight hljs ansi" style="display:block;">RotMatrix2{Float64}
mat: StaticArraysCore.SMatrix{2, 2, Float64, 4}
data: NTuple{4, Float64}
1: Float64 0.3623577544766736
2: Float64 0.9320390859672263
3: Float64 -0.9320390859672263
4: Float64 0.3623577544766736</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../2d_matrix/">« Matrix</a><a class="docs-footer-nextpage" href="../3d_matrix/">Matrix »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Tuesday 6 February 2024 16:08">Tuesday 6 February 2024</span>. Using Julia version 1.10.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
8 changes: 8 additions & 0 deletions v1.7.0/2d_matrix/index.html
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<!DOCTYPE html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Matrix · Rotations.jl</title><meta name="title" content="Matrix · Rotations.jl"/><meta property="og:title" content="Matrix · Rotations.jl"/><meta property="twitter:title" content="Matrix · Rotations.jl"/><meta name="description" content="Documentation for Rotations.jl."/><meta property="og:description" content="Documentation for Rotations.jl."/><meta property="twitter:description" content="Documentation for Rotations.jl."/><meta property="og:url" content="https://JuliaGeometry.github.io/Rotations.jl/2d_matrix/"/><meta property="twitter:url" content="https://JuliaGeometry.github.io/Rotations.jl/2d_matrix/"/><link rel="canonical" href="https://JuliaGeometry.github.io/Rotations.jl/2d_matrix/"/><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../search_index.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark" data-theme-primary-dark/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script><link href="../assets/custom.css" rel="stylesheet" type="text/css"/><link href="../assets/favicon.ico" rel="icon" type="image/x-icon"/></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../"><img src="../assets/logo.svg" alt="Rotations.jl logo"/></a><div class="docs-package-name"><span class="docs-autofit"><a href="../">Rotations.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><a class="tocitem" href="../">Home</a></li><li><a class="tocitem" href="../rotation_types/">Rotation Types</a></li><li><span class="tocitem">2D Rotations</span><ul><li class="is-active"><a class="tocitem" href>Matrix</a><ul class="internal"><li><a class="tocitem" href="#RotMatrix2"><span><code>RotMatrix2</code></span></a></li></ul></li><li><a class="tocitem" href="../2d_angle/">Angle</a></li></ul></li><li><span class="tocitem">3D Rotations</span><ul><li><a class="tocitem" href="../3d_matrix/">Matrix</a></li><li><a class="tocitem" href="../3d_euler/">Euler Angles</a></li><li><a class="tocitem" href="../3d_angleaxis/">Angle and Axis</a></li><li><a class="tocitem" href="../3d_quaternion/">Quaternion and Related Parameters</a></li></ul></li><li><span class="tocitem">Rotation Generators</span><ul><li><a class="tocitem" href="../rotation_generator_types/">Rotation Generator Types</a></li><li><a class="tocitem" href="../2d_rotation_generator/">2D Rotation Generators</a></li><li><a class="tocitem" href="../3d_rotation_generator/">3D Rotation Generators</a></li></ul></li><li><a class="tocitem" href="../general_dimensional_rotations/">General Dimensional Rotations</a></li><li><a class="tocitem" href="../functions/">Common Methods for Rotations</a></li><li><a class="tocitem" href="../visualizing/">Visualizing Rotations</a></li><li><a class="tocitem" href="../functionreference/">Function Reference</a></li><li><a class="tocitem" href="../reference/">References</a></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">2D Rotations</a></li><li class="is-active"><a href>Matrix</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Matrix</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/JuliaGeometry/Rotations.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/JuliaGeometry/Rotations.jl/blob/master/docs/src/2d_matrix.md#" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="2D-Rotation-Matrix"><a class="docs-heading-anchor" href="#2D-Rotation-Matrix">2D Rotation Matrix</a><a id="2D-Rotation-Matrix-1"></a><a class="docs-heading-anchor-permalink" href="#2D-Rotation-Matrix" title="Permalink"></a></h1><p>An <span>$2 \times 2$</span> rotation matrix storing the rotation. This is a simple wrapper for a <a href="https://github.com/JuliaArrays/StaticArrays.jl">StaticArrays</a> <code>SMatrix{2,2,T}</code>. A rotation matrix <span>$R$</span> should have the property <span>$I = R R^\top$</span>, but this isn&#39;t enforced by the constructor. On the other hand, all the types below are guaranteed to be &quot;proper&quot; rotations for all input parameters (equivalently: parity conserving, in <span>$SO(2)$</span>, <span>$\det(R) = 1$</span>, or a rotation without reflection).</p><h2 id="RotMatrix2"><a class="docs-heading-anchor" href="#RotMatrix2"><code>RotMatrix2</code></a><a id="RotMatrix2-1"></a><a class="docs-heading-anchor-permalink" href="#RotMatrix2" title="Permalink"></a></h2><p><strong>example</strong></p><pre><code class="language-julia-repl hljs" style="display:block;">julia&gt; t = 1.2 # rotation angle</code><code class="nohighlight hljs ansi" style="display:block;">1.2</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; m = [cos(t) -sin(t);sin(t) cos(t)]</code><code class="nohighlight hljs ansi" style="display:block;">2×2 Matrix{Float64}:
0.362358 -0.932039
0.932039 0.362358</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; RotMatrix{2}(m) # construct from matrix</code><code class="nohighlight hljs ansi" style="display:block;">2×2 RotMatrix2{Float64} with indices SOneTo(2)×SOneTo(2):
0.362358 -0.932039
0.932039 0.362358</code><br/><code class="language-julia-repl hljs" style="display:block;">julia&gt; RotMatrix{2}(t) # construct from angle</code><code class="nohighlight hljs ansi" style="display:block;">2×2 RotMatrix2{Float64} with indices SOneTo(2)×SOneTo(2):
0.362358 -0.932039
0.932039 0.362358</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../rotation_types/">« Rotation Types</a><a class="docs-footer-nextpage" href="../2d_angle/">Angle »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="auto">Automatic (OS)</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.2.1 on <span class="colophon-date" title="Tuesday 6 February 2024 16:08">Tuesday 6 February 2024</span>. Using Julia version 1.10.0.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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