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 That&#x27;s why I want to guide and inspire more researchers and engineers to work on them during my academic career.
 To begin with, I&#x27;ve created this tutorial series to help everybody learn my research.
 I&#x27;m looking forward to assisting my collaborators working on the same research topic in the future.</p></div><footer class="theme-doc-footer docusaurus-mt-lg"><div class="theme-doc-footer-edit-meta-row row"><div class="col"><a href="https://github.com/ShenCiao/brush-rendering-tutorial/tree/main/docs/About/About.mdx" target="_blank" rel="noreferrer noopener" class="theme-edit-this-page"><svg fill="currentColor" height="20" width="20" viewBox="0 0 40 40" class="iconEdit_Z9Sw" aria-hidden="true"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div><div class="col lastUpdated_vwxv"></div></div></footer></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="Docs pages"><a class="pagination-nav__link pagination-nav__link--prev" href="/brush-rendering-tutorial/Appendix/Vector-fill/"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">Vector Fill</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#applying-for-phd" class="table-of-contents__link toc-highlight">Applying for Ph.D.</a></li><li><a href="#about-the-tutorial-and-research" class="table-of-contents__link toc-highlight">About the tutorial and research</a></li><li><a href="#sop" class="table-of-contents__link toc-highlight">SoP</a></li></ul></div></div></div></div></main></div></div><footer class="footer"><div class="container container-fluid"><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2023 Brush Rendering Tutorial by Shen Ciao, under CC BY-SA 4.0 License</div></div></div></footer></div>
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 algorithms to locate a point better than the naive solution.
 To dive deeper, you may try using the <a href="https://doc.cgal.org/latest/Arrangement_on_surface_2/index.html" target="_blank" rel="noopener noreferrer">CGAL 2D arrangement library</a>
 and learn the arrangement constructed from 2D polylines, which is slightly different with a naive polygon mesh.</p><p>I hope this &quot;2D mesh metaphor&quot; will help you better understand the problems.</p></div><footer class="theme-doc-footer docusaurus-mt-lg"><div class="theme-doc-footer-edit-meta-row row"><div class="col"><a href="https://github.com/ShenCiao/brush-rendering-tutorial/tree/main/docs/Appendix/Vector-fill/Vector-fill.mdx" target="_blank" rel="noreferrer noopener" class="theme-edit-this-page"><svg fill="currentColor" height="20" width="20" viewBox="0 0 40 40" class="iconEdit_Z9Sw" aria-hidden="true"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div><div class="col lastUpdated_vwxv"></div></div></footer></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="Docs pages"><a class="pagination-nav__link pagination-nav__link--prev" href="/brush-rendering-tutorial/category/appendix/"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">Appendix</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/brush-rendering-tutorial/About/"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">→ I&#x27;m applying for a PhD</div></a></nav></div></div></div></div></main></div></div><footer class="footer"><div class="container container-fluid"><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2023 Brush Rendering Tutorial by Shen Ciao, under CC BY-SA 4.0 License</div></div></div></footer></div>
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 I will elaborate on how to render this stroke in the next section.
 Feel free to change any other parts of the code as long as the function returns the <code>position</code> and <code>radius</code> array correctly.</p><div><div class="tabs-container tabList__CuJ"><ul role="tablist" aria-orientation="horizontal" class="tabs"><li role="tab" tabindex="0" aria-selected="true" class="tabs__item tabItem_LNqP tabs__item--active">geometry.js</li></ul><div class="margin-top--md"><div role="tabpanel" class="tabItem_Ymn6"><section style="display:flex;position:relative;text-align:initial;width:100%;height:40vh"><div style="display:flex;height:100%;width:100%;justify-content:center;align-items:center">Loading...</div><div style="width:100%;display:none"></div></section></div></div></div></div><div style="width:100%"></div><p>Blender Grease Pencil team has developed a lot of novel tools to edit this polyline with radius representation.
 Remember to check out if you were a researcher and want to develop novel techniques for digital painting.</p></div><footer class="theme-doc-footer docusaurus-mt-lg"><div class="theme-doc-footer-edit-meta-row row"><div class="col"><a href="https://github.com/ShenCiao/brush-rendering-tutorial/tree/main/docs/Basics/Basics/Basics.mdx" target="_blank" rel="noreferrer noopener" class="theme-edit-this-page"><svg fill="currentColor" height="20" width="20" viewBox="0 0 40 40" class="iconEdit_Z9Sw" aria-hidden="true"><g><path d="m34.5 11.7l-3 3.1-6.3-6.3 3.1-3q0.5-0.5 1.2-0.5t1.1 0.5l3.9 3.9q0.5 0.4 0.5 1.1t-0.5 1.2z m-29.5 17.1l18.4-18.5 6.3 6.3-18.4 18.4h-6.3v-6.2z"></path></g></svg>Edit this page</a></div><div class="col lastUpdated_vwxv"></div></div></footer></article><nav class="pagination-nav docusaurus-mt-lg" aria-label="Docs pages"><a class="pagination-nav__link pagination-nav__link--prev" href="/brush-rendering-tutorial/category/basics/"><div class="pagination-nav__sublabel">Previous</div><div class="pagination-nav__label">Basics</div></a><a class="pagination-nav__link pagination-nav__link--next" href="/brush-rendering-tutorial/Basics/Vanilla/"><div class="pagination-nav__sublabel">Next</div><div class="pagination-nav__label">Vanilla</div></a></nav></div></div><div class="col col--3"><div class="tableOfContents_bqdL thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#brush-strokes" class="table-of-contents__link toc-highlight">Brush strokes</a></li><li><a href="#geometric-data" class="table-of-contents__link toc-highlight">Geometric data</a></li></ul></div></div></div></div></main></div></div><footer class="footer"><div class="container container-fluid"><div class="footer__bottom text--center"><div class="footer__copyright">Copyright © 2023 Brush Rendering Tutorial by Shen Ciao, under CC BY-SA 4.0 License</div></div></div></footer></div>
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