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lx, ly = trace(u, v, startx, starty, x, y, maxstep=20)
linex[1:length(lx),i] = lx
liney[1:length(ly),i] = ly
end</code></pre><h2 id="Arrow"><a class="docs-heading-anchor" href="#Arrow">Arrow</a><a id="Arrow-1"></a><a class="docs-heading-anchor-permalink" href="#Arrow" title="Permalink"></a></h2><p>When plotting, it is usually convenient to display an arrow along the line for showing the direction. Currently we provide a function <a href="https://henry2004y.github.io/FieldTracer.jl/dev/internal/#FieldTracer.add_arrow">add_arrow</a> which acts on a Matplotlib Line2D object and adds an arrow for it.<sup class="footnote-reference"><a id="citeref-3" href="#footnote-3">[3]</a></sup></p><h2 id="Gallery"><a class="docs-heading-anchor" href="#Gallery">Gallery</a><a id="Gallery-1"></a><a class="docs-heading-anchor-permalink" href="#Gallery" title="Permalink"></a></h2><ul><li>Tracing in an analytic asymptotic field</li></ul><p><img src="../figures/trace_asymptote.png" alt/></p><ul><li>Tracing in a analytic 3D dipole field</li></ul><p><img src="../figures/trace_dipole.png" alt/></p><ul><li>Tracing in a numerical 2D magnetic field</li></ul><p><img src="../figures/BxBz_y0cut.png" alt/></p><ul><li>Tracing in a 2D equatorial plane Earth magnetosphere simulation</li></ul><p><img src="../figures/trace_streamline_2Dmagnetosphere.png" alt/></p><ul><li>Streamline tracing in a 2D triangular mesh around an airfoil</li></ul><p><img src="../figures/trace_streamline_2Dunstructured.png" alt/></p><p>An example is shown for the 2D streamline tracing in the unstructured triangular mesh for the famous airfoil problem. The blue lines are the analytic stream functions derived from incompressible Euler equations which are calculated numerically. Three colored lines are displayed with dots representing the footprints inside each cell.</p><ul><li>Fieldline tracing near the magnetic null points, compared to the <code>streamplot</code> function in Matplotlib</li></ul><p><img src="../figures/x_o_point.png" alt/></p><ul><li>Fieldline tracing near Ganymede&#39;s upstream magnetopause</li></ul><p><img src="../figures/trace_magnetopause_ganymede.png" alt/></p><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-1"><a class="tag is-link" href="#citeref-1">1</a>Currently 3D tracing is only limited to structured mesh.</li><li class="footnote" id="footnote-2"><a class="tag is-link" href="#citeref-2">2</a>The scheme switch currently only works for Cartesian grid.</li><li class="footnote" id="footnote-3"><a class="tag is-link" href="#citeref-3">3</a>3D arrow is not supported due to the limitation of Matplotlib. It is possible, but tedious.</li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../log/">Log »</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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Sunday 6 August 2023 09:04">Sunday 6 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
end</code></pre><h2 id="Arrow"><a class="docs-heading-anchor" href="#Arrow">Arrow</a><a id="Arrow-1"></a><a class="docs-heading-anchor-permalink" href="#Arrow" title="Permalink"></a></h2><p>When plotting, it is usually convenient to display an arrow along the line for showing the direction. Currently we provide a function <a href="https://henry2004y.github.io/FieldTracer.jl/dev/internal/#FieldTracer.add_arrow">add_arrow</a> which acts on a Matplotlib Line2D object and adds an arrow for it.<sup class="footnote-reference"><a id="citeref-3" href="#footnote-3">[3]</a></sup></p><h2 id="Gallery"><a class="docs-heading-anchor" href="#Gallery">Gallery</a><a id="Gallery-1"></a><a class="docs-heading-anchor-permalink" href="#Gallery" title="Permalink"></a></h2><ul><li>Tracing in an analytic asymptotic field</li></ul><p><img src="../figures/trace_asymptote.png" alt/></p><ul><li>Tracing in a analytic 3D dipole field</li></ul><p><img src="../figures/trace_dipole.png" alt/></p><ul><li>Tracing in a numerical 2D magnetic field</li></ul><p><img src="../figures/BxBz_y0cut.png" alt/></p><ul><li>Tracing in a 2D equatorial plane Earth magnetosphere simulation</li></ul><p><img src="../figures/trace_streamline_2Dmagnetosphere.png" alt/></p><ul><li>Streamline tracing in a 2D triangular mesh around an airfoil</li></ul><p><img src="../figures/trace_streamline_2Dunstructured.png" alt/></p><p>An example is shown for the 2D streamline tracing in the unstructured triangular mesh for the famous airfoil problem. The blue lines are the analytic stream functions derived from incompressible Euler equations which are calculated numerically. Three colored lines are displayed with dots representing the footprints inside each cell.</p><ul><li>Fieldline tracing near the magnetic null points, compared to the <code>streamplot</code> function in Matplotlib</li></ul><p><img src="../figures/x_o_point.png" alt/></p><ul><li>Fieldline tracing near Ganymede&#39;s upstream magnetopause</li></ul><p><img src="../figures/trace_magnetopause_ganymede.png" alt/></p><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-1"><a class="tag is-link" href="#citeref-1">1</a>Currently 3D tracing is only limited to structured mesh.</li><li class="footnote" id="footnote-2"><a class="tag is-link" href="#citeref-2">2</a>The scheme switch currently only works for Cartesian grid.</li><li class="footnote" id="footnote-3"><a class="tag is-link" href="#citeref-3">3</a>3D arrow is not supported due to the limitation of Matplotlib. It is possible, but tedious.</li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../log/">Log »</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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Tuesday 5 September 2023 02:53">Tuesday 5 September 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
2 changes: 1 addition & 1 deletion dev/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>Home · FieldTracer.jl</title><script data-outdated-warner src="assets/warner.js"></script><link rel="canonical" href="https://henry2004y.github.io/FieldTracer.jl/"/><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/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/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="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></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href>FieldTracer.jl</a></span></div><form class="docs-search" action="search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li class="is-active"><a class="tocitem" href>Home</a></li><li><a class="tocitem" href="example/">Example</a></li><li><a class="tocitem" href="log/">Log</a></li><li><a class="tocitem" href="internal/">Internal</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"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Home</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Home</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/henry2004y/FieldTracer.jl/blob/master/docs/src/index.md#L" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="FieldTracer"><a class="docs-heading-anchor" href="#FieldTracer">FieldTracer</a><a id="FieldTracer-1"></a><a class="docs-heading-anchor-permalink" href="#FieldTracer" title="Permalink"></a></h1><p>Vector field tracing on common types of meshes.</p><p>This package supports 2nd and 4th order field line tracing on</p><ul><li>2D/3D regular Cartesian mesh</li><li>2D unstructured quadrilateral mesh</li><li>2D unstructured triangular mesh</li></ul><p>It can be used for</p><ul><li>generating streamlines and fieldlines;</li><li>checking field connectivity between spatial cells.</li></ul></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="example/">Example »</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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Sunday 6 August 2023 09:04">Sunday 6 August 2023</span>. Using Julia version 1.9.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Home · FieldTracer.jl</title><script data-outdated-warner src="assets/warner.js"></script><link rel="canonical" href="https://henry2004y.github.io/FieldTracer.jl/"/><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/0.045/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.15.4/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.13.24/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="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></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href>FieldTracer.jl</a></span></div><form class="docs-search" action="search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li class="is-active"><a class="tocitem" href>Home</a></li><li><a class="tocitem" href="example/">Example</a></li><li><a class="tocitem" href="log/">Log</a></li><li><a class="tocitem" href="internal/">Internal</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"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Home</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Home</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/henry2004y/FieldTracer.jl/blob/master/docs/src/index.md#L" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="FieldTracer"><a class="docs-heading-anchor" href="#FieldTracer">FieldTracer</a><a id="FieldTracer-1"></a><a class="docs-heading-anchor-permalink" href="#FieldTracer" title="Permalink"></a></h1><p>Vector field tracing on common types of meshes.</p><p>This package supports 2nd and 4th order field line tracing on</p><ul><li>2D/3D regular Cartesian mesh</li><li>2D unstructured quadrilateral mesh</li><li>2D unstructured triangular mesh</li></ul><p>It can be used for</p><ul><li>generating streamlines and fieldlines;</li><li>checking field connectivity between spatial cells.</li></ul></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="example/">Example »</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></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 0.27.25 on <span class="colophon-date" title="Tuesday 5 September 2023 02:53">Tuesday 5 September 2023</span>. Using Julia version 1.9.3.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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