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</footer></div><divclass="main"id="top"><divid="main-header"class="main-header"><divclass="search"><divclass="search-input-wrap"><inputtype="text"id="search-input"class="search-input"tabindex="0"placeholder="Search "aria-label="Search "autocomplete="off"><labelfor="search-input"class="search-label"><svgviewBox="0 0 24 24"class="search-icon"><usexlink:href="#svg-search"></use></svg></label></div><divid="search-results"class="search-results"></div></div></div><divid="main-content-wrap"class="main-content-wrap"><navaria-label="Breadcrumb"class="breadcrumb-nav"><olclass="breadcrumb-nav-list"><liclass="breadcrumb-nav-list-item"><ahref="/meshedit/">A2: MeshEdit</a></li><liclass="breadcrumb-nav-list-item"><ahref="/meshedit/global/">Global Operations</a></li><liclass="breadcrumb-nav-list-item"><span>Triangulation</span></li></ol></nav><divid="main-content"class="main-content"role="main"><h1id="triangulation"><ahref="#triangulation"class="anchor-heading"aria-labelledby="triangulation"><svgviewBox="0 0 16 16"aria-hidden="true"><usexlink:href="#svg-link"></use></svg></a> Triangulation </h1><p>For an in-practice example, see the <ahref="/Scotty3D/guide/model">User Guide</a>.</p><p>A variety of geometry processing algorithms become easier to implement (or are only well defined) when the input consists purely of triangles. The method <codeclass="language-plaintext highlighter-rouge">Halfedge_Mesh::triangulate</code> converts any polygon mesh into a triangle mesh by splitting each polygon into triangles.</p><p>This transformation is performed in-place, i.e., the original mesh data is replaced with the new, triangulated data (rather than making a copy). The implementation of this method will look much like the implementation of the local mesh operations, with the addition of looping over every face in the mesh.</p><p>There is more than one way to split a polygon into triangles. Two common patterns are to connect every vertex to a single vertex, or to “zig-zag” the triangulation across the polygon:</p><center><imgsrc="triangulate.png"style="height:300px"/></center><p>The <codeclass="language-plaintext highlighter-rouge">triangulate</code> routine is not required to produce any particular triangulation so long as:</p><ul><li>all polygons in the output are triangles,</li><li>the vertex positions remain unchanged, and</li><li>the output is a valid, manifold halfedge mesh.</li></ul><p>Note that triangulation of nonconvex or nonplanar polygons may lead to geometry that is unattractive or difficult to interpret. However, the purpose of this method is simply to produce triangular <em>connectivity</em> for a given polygon mesh, and correct halfedge connectivity is the only invariant that must be preserved by the implementation. The <em>geometric</em> quality of the triangulation can later be improved by running other global algorithms (e.g., isotropic remeshing); ambitious developers may also wish to consult the following reference:</p><ul><li>Zou et al, <ahref="http://www.cs.wustl.edu/~taoju/research/triangulate_final.pdf">“An Algorithm for Triangulating Multiple 3D Polygons”</a></li></ul></div></div><divclass="search-overlay"></div></div></body></html>
