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2005-11-28 14:57:47 +05:00
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<h1>About meshes</h1>
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<p><img src="../i_blue.jpg" x-maintain-ratio="TRUE" width="30px" height="30px" border="0" class="img_whs1"> <span style="font-weight: bold;"><B>MESH</B></span> represents
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a discretization of a geometrical CAD model into a set of entities with
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a simple topology. In MESH there are two options of creation of meshes,
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you can:</p>
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<p> </p>
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<ul type="disc" class="whs2">
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<li class=kadov-p><p>generate meshes on the basis of geometrical shapes
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produced in the GEOM module, </p></li>
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<li class=kadov-p><p>create your own meshes using the MESH functions
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destined for modification of generated meshes. </p></li>
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2004-06-18 14:55:35 +06:00
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</ul>
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<p> </p>
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<p>The topology of a mesh is described by the relationships between its
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entities including:</p>
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<p class="whs3"> </p>
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<ul type="disc" class="whs2">
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<li class=kadov-p><p class="whs3"><span style="font-weight: bold;"><B>Node</B></span>
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<20> 0D element of a mesh presented by a point with coordinates (x, y, z).</p></li>
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<li class=kadov-p><p class="whs3"><span style="font-weight: bold;"><B>Edge</B></span>
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<20> 1D element of a mesh defined by two nodes.</p></li>
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<li class=kadov-p><p class="whs3"><span style="font-weight: bold;"><B>Face</B></span>
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<20> 2D element of a mesh defined by three or four edges (closed contour).</p></li>
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<li class=kadov-p><p class="whs3"><span style="font-weight: bold;"><B>Volume</B></span>
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<20> 3D element of a mesh defined by several faces.</p></li>
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</ul>
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<p class="whs3"> </p>
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<p class="whs4">These entities are considered as topological
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entities and they don't imply any geometric representation. Only <span
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style="font-weight: bold;"><B>Nodes</B></span> reference geometric
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representations of points with definite coordinates. <span style="text-indent: 8px;">The
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node entity will contain additional
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information about its position in the space and its relations with the
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meshed CAD model. Its position could be described in the following way:</span></p>
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<p class="whs4"> </p>
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<ul type="disc" class="whs2">
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<li class=kadov-p><p class="whs3"><span style="font-weight: bold;"><B>2D
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position</B></span>. It is a free position defined by only two coordinates
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x,y.</p></li>
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<li class=kadov-p><p class="whs3"><span style="font-weight: bold;"><B>3D
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position</B></span>. It is a free position defined by three coordinates x,y
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and z.</p></li>
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<li class=kadov-p><p class="whs3"><span style="font-weight: bold;"><B>Surface
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position</B></span>. It characterizes the position of a node on a geometric
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surface and is defined by the u,v position in the parametric space of
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the corresponding surface.</p></li>
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<li class=kadov-p><p class="whs3"><span style="font-weight: bold;"><B>Line
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position</B></span>. It characterizes the position of a node on a geometric
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curve and is defined by the u parameter and the corresponding curve.</p></li>
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<li class=kadov-p><p class="whs3"><span style="font-weight: bold;"><B>Vertex
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position</B></span>. It characterizes the position of a node on a geometric
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point of the meshed CAD model and is defined by the x,y,z coordinates
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of the corresponding vertex.</p></li>
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</ul>
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<p class="whs3"> </p>
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<p class="whs3"> </p>
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<h4 class="whs5">Connections</h4>
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<p class="whs6">Each mesh entity bounds 0 or more mesh entities
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of higher dimension. In the same way each mesh entity is bounded by 0
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or more mesh entities of lower dimension:</p>
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<p class="whs6"> </p>
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<ul type="disc" class="whs2">
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<li class=kadov-p><p class="whs6">A node bounds edges,
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faces and volumes</p></li>
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<li class=kadov-p><p class="whs6">An edge bounds faces,
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and volumes</p></li>
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<li class=kadov-p><p class="whs6">A face bounds volumes</p></li>
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<li class=kadov-p><p class="whs6">A volume is bounded
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by faces, edges and nodes</p></li>
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<li class=kadov-p><p class="whs6">A face is bounded by
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edges, and nodes</p></li>
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<li class=kadov-p><p class="whs6">An edge is bounded by
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nodes</p></li>
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</ul>
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<p class="whs6"> </p>
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<p class="whs6">You can notice that there are two types of
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connections: <span style="font-weight: bold;"><B>inverse</B></span> and <span
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style="font-weight: bold;"><B>direct</B></span> connections.</p>
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<p class="whs6"> </p>
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<h4 class="whs5">Inverse connections</h4>
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<p class="whs6"> </p>
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<p class="whs6">This relationship has a particularity that
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the order of bounded entities has not a direct meaning. Also the number
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of bounded entities is not fixed.</p>
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<p class="whs6"> </p>
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<p class="whs6"><img src="../pics/exemple.gif" x-maintain-ratio="TRUE" width="36px" height="38px" border="0" class="img_whs7"> The edges surrounding a node.
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The 3rd edge has no more sense that the 5th one.</p>
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<p class="whs6"> </p>
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<p class="whs8">Direct connections</p>
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<p class="whs6"> </p>
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<p class="whs6">This relationship has a particularity that
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the order of bounding entities is meaningful. The number of bounding entities
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is fixed and depends on the type of the entity (hexahedron, tetrahedron,<2C>).</p>
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<p class="whs6"> </p>
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<p class="whs6"><img src="../pics/exemple.gif" x-maintain-ratio="TRUE" width="36px" height="38px" border="0" class="img_whs7"> An edge is composed of two
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nodes. A face is composed of 3 or 4 edges depending if we are dealing
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with triangles or quadrangles.</p>
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<p class="whs6"> </p>
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<p class="whs6">The connections are not only restricted to
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entities of one dimension higher or lower. For example some algorithms
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may be interested to retrieve all the faces surrounding a node.</p>
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<p class="whs6"> </p>
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<p class="whs6"> </p>
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<p class="whs6"> </p>
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