build based on 455b592

JuliaGeometry · Sep 30, 2024 · 0123aac · 0123aac
1 parent 37258a5
commit 0123aac
Show file tree

Hide file tree

Showing 149 changed files with 366 additions and 366 deletions.
diff --git a/dev/.documenter-siteinfo.json b/dev/.documenter-siteinfo.json
@@ -1 +1 @@
-{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-09-28T10:50:43","documenter_version":"1.7.0"}}
+{"documenter":{"julia_version":"1.10.5","generation_timestamp":"2024-09-30T18:54:08","documenter_version":"1.7.0"}}
diff --git a/dev/api/convex_hull/index.html b/dev/api/convex_hull/index.html
diff --git a/dev/api/curves/index.html b/dev/api/curves/index.html
diff --git a/dev/api/data_structures/index.html b/dev/api/data_structures/index.html
diff --git a/dev/api/iterators/index.html b/dev/api/iterators/index.html
diff --git a/dev/api/operations/index.html b/dev/api/operations/index.html
diff --git a/dev/api/other/index.html b/dev/api/other/index.html
diff --git a/dev/api/overview/index.html b/dev/api/overview/index.html
diff --git a/dev/api/point_location/index.html b/dev/api/point_location/index.html
diff --git a/dev/api/predicates/index.html b/dev/api/predicates/index.html
diff --git a/dev/api/primitives/index.html b/dev/api/primitives/index.html
diff --git a/dev/api/statistics/index.html b/dev/api/statistics/index.html
diff --git a/dev/api/triangulation/index.html b/dev/api/triangulation/index.html
diff --git a/dev/api/voronoi/index.html b/dev/api/voronoi/index.html
diff --git a/dev/applications/cell_simulations/index.html b/dev/applications/cell_simulations/index.html
@@ -277,4 +277,4 @@
 record(fig, &quot;cell_simulation.mp4&quot;, 1:10:length(t); framerate = 60) do ii
     i[] = ii
     title_obs[] = L&quot;t = %$(((ii-1) * Δt))&quot;
-end;</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-1"><a class="tag is-link" href="#citeref-1">1</a>If you are interested in how these ideas are applied in one dimension, see also <a href="https://github.com/DanielVandH/EpithelialDynamics1D.jl">EpithelialDynamics1D.jl</a>.</li><li class="footnote" id="footnote-2"><a class="tag is-link" href="#citeref-2">2</a>There are efficient methods for updating the triangulation after small perturbations, e.g. the paper <a href="https://doi.org/10.1145/1064092.1064129"><em>Star splaying: an algorithm for repairing Delaunay triangulations and convex hulls</em></a> by Shewchuk (2005). For this implementation, we do not concern ourselves with being overly efficient, and simply retriangulate.</li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../interpolation/">« Interpolation</a><a class="docs-footer-nextpage" href="../pde_discretisation/">Solving PDEs »</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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Saturday 28 September 2024 10:50">Saturday 28 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+end;</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-1"><a class="tag is-link" href="#citeref-1">1</a>If you are interested in how these ideas are applied in one dimension, see also <a href="https://github.com/DanielVandH/EpithelialDynamics1D.jl">EpithelialDynamics1D.jl</a>.</li><li class="footnote" id="footnote-2"><a class="tag is-link" href="#citeref-2">2</a>There are efficient methods for updating the triangulation after small perturbations, e.g. the paper <a href="https://doi.org/10.1145/1064092.1064129"><em>Star splaying: an algorithm for repairing Delaunay triangulations and convex hulls</em></a> by Shewchuk (2005). For this implementation, we do not concern ourselves with being overly efficient, and simply retriangulate.</li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../interpolation/">« Interpolation</a><a class="docs-footer-nextpage" href="../pde_discretisation/">Solving PDEs »</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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 30 September 2024 18:54">Monday 30 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/applications/interpolation/12e1e94a.png b/dev/applications/interpolation/12e1e94a.png
diff --git a/dev/applications/interpolation/ad3ffc98.png b/dev/applications/interpolation/ad3ffc98.png
diff --git a/dev/applications/interpolation/index.html b/dev/applications/interpolation/index.html
@@ -26,7 +26,7 @@
 triplot!(ax2, tri, show_points = true)
 poly!(ax2, envelope_points, color = (:red, 0.2))
 resize_to_layout!(fig)
-fig</code></pre><img src="ad3ffc98.png" alt="Example block output"/><p>As we can see, the red region we have computed from our envelope is indeed the envelope we need.</p><h3 id="Computing-the-Sibsonian-coordinates"><a class="docs-heading-anchor" href="#Computing-the-Sibsonian-coordinates">Computing the Sibsonian coordinates</a><a id="Computing-the-Sibsonian-coordinates-1"></a><a class="docs-heading-anchor-permalink" href="#Computing-the-Sibsonian-coordinates" title="Permalink"></a></h3><p>When we are interpolating at a point <span>$\vb x$</span>, remember that we need to know the area of the Voronoi polygon that would be produced when <span>$\vb x$</span> is inserted into <span>$\mathcal V(X)$</span>. To compute this area, we need to know how we can compute it using the Bowyer-Watson envelope. Remember that the Voronoi polygons are obtained by drawing lines between the circumcenters of neighbouring triangles. This can be done using the Bowyer-Watson envelope: The edges of the envelope, together with the new point, define the triangles that would be produced if it were to be added into the triangulation, and so we can join the circumcenters of these triangles to compute the new Voronoi polygon. We can then use this polygon, together with the original tessellation, to compute the Sibsonian coordinates.</p><p>Let us first discuss the area of the Voronoi polygons in <span>$N(\vb x)$</span> (<span>$\vb x$</span>&#39;s natural neighbours, i.e. the vertices of the envelope) before <span>$\vb x$</span> is inserted. We only need to compute the part of the area that is contained within the envelope, since everything outside of that envelope is unchanged. If we included the entire area, then the area that we subtract off for the intersection we compute later would just cancel it out anyway. Let&#39;s zoom in on the envelope and consider a specific example of how we can do this computation.</p><pre><code class="language-julia hljs">fig = Figure(fontsize = 24)
+fig</code></pre><img src="12e1e94a.png" alt="Example block output"/><p>As we can see, the red region we have computed from our envelope is indeed the envelope we need.</p><h3 id="Computing-the-Sibsonian-coordinates"><a class="docs-heading-anchor" href="#Computing-the-Sibsonian-coordinates">Computing the Sibsonian coordinates</a><a id="Computing-the-Sibsonian-coordinates-1"></a><a class="docs-heading-anchor-permalink" href="#Computing-the-Sibsonian-coordinates" title="Permalink"></a></h3><p>When we are interpolating at a point <span>$\vb x$</span>, remember that we need to know the area of the Voronoi polygon that would be produced when <span>$\vb x$</span> is inserted into <span>$\mathcal V(X)$</span>. To compute this area, we need to know how we can compute it using the Bowyer-Watson envelope. Remember that the Voronoi polygons are obtained by drawing lines between the circumcenters of neighbouring triangles. This can be done using the Bowyer-Watson envelope: The edges of the envelope, together with the new point, define the triangles that would be produced if it were to be added into the triangulation, and so we can join the circumcenters of these triangles to compute the new Voronoi polygon. We can then use this polygon, together with the original tessellation, to compute the Sibsonian coordinates.</p><p>Let us first discuss the area of the Voronoi polygons in <span>$N(\vb x)$</span> (<span>$\vb x$</span>&#39;s natural neighbours, i.e. the vertices of the envelope) before <span>$\vb x$</span> is inserted. We only need to compute the part of the area that is contained within the envelope, since everything outside of that envelope is unchanged. If we included the entire area, then the area that we subtract off for the intersection we compute later would just cancel it out anyway. Let&#39;s zoom in on the envelope and consider a specific example of how we can do this computation.</p><pre><code class="language-julia hljs">fig = Figure(fontsize = 24)
 ax = Axis(fig[1, 1], width = 400, height = 400)
 triplot!(ax, tri, show_points = true)
 lines!(ax, envelope_points, color = :red)
@@ -303,4 +303,4 @@
 zi = [evaluate_sibson_interpolant(trit, zz, (xᵢ, yᵢ)) for xᵢ in xx, yᵢ in yy]
 contourf!(ax2, xx, yy, zi)
 resize_to_layout!(fig)
-fig</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-1"><a class="tag is-link" href="#citeref-1">1</a>This is more expensive than we need. In NaturalNeighbours.jl, we use the <code>peek</code> keyword in <code>triangulate</code> to avoid making any changes to the triangulation itself, and use the <code>InsertionEventHistory</code> to track all changes made.</li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../overview/">« Overview</a><a class="docs-footer-nextpage" href="../cell_simulations/">Cellular Biology »</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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Saturday 28 September 2024 10:50">Saturday 28 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+fig</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-1"><a class="tag is-link" href="#citeref-1">1</a>This is more expensive than we need. In NaturalNeighbours.jl, we use the <code>peek</code> keyword in <code>triangulate</code> to avoid making any changes to the triangulation itself, and use the <code>InsertionEventHistory</code> to track all changes made.</li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../overview/">« Overview</a><a class="docs-footer-nextpage" href="../cell_simulations/">Cellular Biology »</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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 30 September 2024 18:54">Monday 30 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/applications/overview/index.html b/dev/applications/overview/index.html
diff --git a/dev/applications/pde_discretisation/index.html b/dev/applications/pde_discretisation/index.html
@@ -291,4 +291,4 @@
 D = 6.25e-4
 T = solve_met_problem(tri, D)
 fig, ax, sc = tricontourf(tri, T, levels = 0:5:200, extendhigh = :auto)
-fig</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-1"><a class="tag is-link" href="#citeref-1">1</a>See <a href="https://sciml.github.io/FiniteVolumeMethod.jl/stable/tutorials/mean_exit_time/">this example</a> for more detail.</li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../cell_simulations/">« Cellular Biology</a><a class="docs-footer-nextpage" href="../../terminology/">Terminology »</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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Saturday 28 September 2024 10:50">Saturday 28 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
+fig</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-1"><a class="tag is-link" href="#citeref-1">1</a>See <a href="https://sciml.github.io/FiniteVolumeMethod.jl/stable/tutorials/mean_exit_time/">this example</a> for more detail.</li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../cell_simulations/">« Cellular Biology</a><a class="docs-footer-nextpage" href="../../terminology/">Terminology »</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="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.7.0 on <span class="colophon-date" title="Monday 30 September 2024 18:54">Monday 30 September 2024</span>. Using Julia version 1.10.5.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/dev/extended/algorithms/index.html b/dev/extended/algorithms/index.html
diff --git a/dev/extended/data_structures/index.html b/dev/extended/data_structures/index.html
diff --git a/dev/extended/overview/index.html b/dev/extended/overview/index.html
diff --git a/dev/extended/utils/index.html b/dev/extended/utils/index.html