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@ -3,9 +3,7 @@
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\page area_page Area
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\n \b Area mesh quality control is based on the algorithm of area
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calculation of meshing elements. It can be applied to meshes
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consisting of 2D meshing elements with 3 and 4 nodes (triangles and
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quadrangles).
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calculation of mesh faces.
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<em>To apply the Area quality control to your mesh:</em>
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<ol>
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@ -17,7 +15,7 @@ quadrangles).
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\image html image35.png
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<center><em>"Area" button</em></center>
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Your mesh will be displayed in the viewer with its elements colored
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Your mesh will be displayed in the viewer with its faces colored
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according to the applied mesh quality control criterion:
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\image html image5.jpg
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@ -2,9 +2,8 @@
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\page borders_at_multi_connection_page Borders at multi-connection
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\n This mesh quality control highlights borders of faces consisting of
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edges belonging to several faces. The amount of faces is specified by
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user.
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\n This mesh quality control highlights segments according to number
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of elements, faces and volumes, the segment belongs to.
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\image html image151.gif
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@ -2,8 +2,8 @@
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\page borders_at_multi_connection_2d_page Borders at multi-connection 2D
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\n This mesh quality control highlights borders of elements of mesh,
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consisting of edges belonging to several elements of mesh.
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\n This mesh quality control highlights borders of faces (links
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between nodes) according to number of faces the link belongs to.
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\image html image127.gif
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@ -14,7 +14,7 @@ quadratic meshes.
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<em>To produce a conversion:</em>
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<ol>
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<li>Select a mesh or a sub-mesh in the Object Browser or in the
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Viewer.</li>
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Viewer.</li>
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<li>From the Modification menu or from the contextual menu in the
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Object Browser choose <b> Convert to/from Quadratic Mesh</b> item,
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or click <em>"Convert to/from quadratic"</em> button in the
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@ -3,8 +3,9 @@
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\page extrusion_along_path_page Extrusion along Path
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\n In principle, <b>Extrusion along Path</b> works in the same way
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as \ref extrusion_page "Extrusion", the main difference is that we define not a vector,
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but a path of extrusion which must be a 1D mesh or 1D sub-mesh.
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as \ref extrusion_page "Extrusion", the main difference is that we
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define not a vector, but a path of extrusion which must be an 1D mesh
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or 1D sub-mesh.
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To get an idea of how this algorithm works, examine several examples,
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starting from the most simple case of extrusion along a straight edge.
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In the examples the sample mesh will be extruded along different
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@ -66,8 +67,8 @@ six coincident nodes and two coincident faces in the resulting
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mesh.</center>
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\image html circle_angles_after.png
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<center>The same, but using angles {45, -45, 45, -45, 45, -45, 45,
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-45}</center>
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<center>The same, but using angles {45, -45, 45, -45, 45, -45, 45, -45}
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</center>
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<br><em>To use Extrusion along Path:</em>
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<ol>
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@ -93,7 +94,7 @@ The following dialog will appear:
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of following means:
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<ul>
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<li><b>Select the whole mesh, sub-mesh or group</b> activating this
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checkbox.</li>
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check-box.</li>
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<li>Choose mesh elements with the mouse in the 3D Viewer. It is
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possible to select a whole area with a mouse frame.</li>
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<li>Input the element IDs directly in <b>Node IDs</b>, <b>Edge
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@ -107,10 +108,10 @@ The following dialog will appear:
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<li>Define the \b Path along which the elements will be extruded.<br>
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Path definition consists of several elements:
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<ul>
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<li><b>Mesh or submesh</b> - 1D mesh or sub-mesh, along which
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<li><b>Mesh or sub-mesh</b> - 1D mesh or sub-mesh, along which
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proceeds the extrusion.</li>
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<li><b>Start node</b> - the start node. It is used to define
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the direction of extrusion. </li>
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<li><b>Start node</b> - the start node of the Path. It is used
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to define the direction of extrusion. </li>
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</ul>
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</li>
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<li>If you activate <b>Generate Groups</b> check-box, the <em>result elements</em>
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@ -3,7 +3,7 @@
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\page free_borders_page Free borders
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\n This mesh quality control highlights borders of faces consisting of
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edges belonging to one face only.
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1D elements (segments) belonging to one face only.
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\image html free_borders1.png
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@ -2,8 +2,8 @@
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\page free_edges_page Free edges
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\n This mesh quality control highlights borders of elements of mesh
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consisting of edges belonging to one element of mesh only.
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\n This mesh quality control highlights borders of faces
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consisting of node links belonging to one face only.
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\image html free_edges.png
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<center>In this picture some elements of mesh have been deleted and
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@ -3,8 +3,7 @@
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\page length_2d_page Length 2D
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\n This quality control criterion consists of calculation of length of
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the edges combining the meshing elements (triangles and quadrangles)
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of your mesh.
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the links between corner nodes of mesh faces.
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<em>To apply the Length 2D quality criterion to your mesh:</em>
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<ol>
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@ -16,7 +15,8 @@ of your mesh.
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\image html image34.png
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<center><em>"Length 2D" button</em></center>
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Your mesh will be displayed in the viewer with its elements colored according to the applied mesh quality control criterion:
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Your mesh will be displayed in the viewer with links colored according
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to the applied mesh quality control criterion:
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\image html length2d.png
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</li>
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@ -28,8 +28,8 @@ the type of operation you would like to perform.</li>
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\n "Create boundary elements" dialog allows creation of boundary elements
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of two types.
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<ul>
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<li><b>2D from 3D</b> creates mesh faces on free facets of volume elements</li>
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<li><b>1D from 2D</b> creates mesh edges on free edges of mesh faces</li>
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<li><b>2D from 3D</b> creates missing mesh faces on free facets of volume elements</li>
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<li><b>1D from 2D</b> creates missing mesh edges on free edges of mesh faces</li>
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</ul>
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Here a <em>free facet</em> means a facet shared by only one volume, a <em>free edge</em>
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means an edge shared by only one mesh face.
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@ -14,17 +14,19 @@ The smp file contains 4 sections:
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-# The first line indicates the total number of pattern nodes (N).
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-# The next N lines describe nodes coordinates. Each line contains 2
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node coordinates for a 2D pattern or 3 node coordinates for a 3D pattern.
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Note, that node coordinates of a 3D pattern can be defined only by relative values in range [0;1].
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node coordinates for a 2D pattern or 3 node coordinates for a 3D pattern.
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Note, that node coordinates of a 3D pattern can be defined only by
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relative values in range [0;1].
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-# The key-points line contains the indices of the nodes to be mapped on geometrical
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vertices (for a 2D pattern only). Index n refers to the node described
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on the n-th line of section 2. The index of the first node zero. For a 3D pattern the key points are not specified.
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vertices (for a 2D pattern only). Index n refers to the node described
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on the n-th line of section 2. The index of the first node is
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zero. For a 3D pattern the key points are not specified.
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-# The remaining lines describe nodal connectivity of elements, one line
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for each element. Each line holds indices of nodes forming an element.
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Index n refers to the node described on the n-th line of section 2.
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The first node index is zero. There must be 3 or 4 indices on each
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line for a 2D pattern (only 2d elements are allowed) and 4, 5, 6 or 8
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indices for a 3D pattern (only 3d elements are allowed).
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for each element. Each line holds indices of nodes forming an element.
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Index n refers to the node described on the n-th line of section 2.
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The first node index is zero. There must be 3 or 4 indices on each
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line for a 2D pattern (only liner 2d elements are allowed) and 4, 5, 6 or 8
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indices for a 3D pattern (only linear 3d elements are allowed).
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A 2D pattern must contain at least one element and at least one
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key-point. All key-points must lie on boundaries.
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@ -107,18 +109,21 @@ In this dialog you should specify:
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<ul>
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<li> \b Pattern, which can be loaded from .smp pattern file previously
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created manually or generated automatically from an existing mesh or submesh.</li>
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created manually or generated automatically from an existing mesh or
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sub-mesh.</li>
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<li> \b Face with the number of vertices equal to the number of
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key-points in the pattern; the number of key-points on internal
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boundaries of the pattern must also be equal to the number of vertices
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on internal boundaries of the face;</li>
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<li> \b Vertex to which the first key-point should be mapped;</li>
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</ul>
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Alternatively, it is possible to select <b>Refine selected mesh elements</b>
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check-box and apply the pattern to <ul>
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<li> <b>Mesh Face</b> instead of a geometric Face</li>
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<li> and select \b Node instead of vertex.</li>
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<li> <b>Mesh Face</b> instead of a geometric Face</li>
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<li> and select \b Node instead of vertex.</li>
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</ul>
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Additionally it is possible to: <ul>
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<li> <b>Reverse the order of key-points</b>. By default, the vertices of
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a face are ordered counterclockwise.</li>
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@ -133,17 +138,18 @@ Additionally it is possible to: <ul>
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In this dialog you should specify:
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<ul>
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<li> \b Pattern, which can be loaded from .smp pattern file previously
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created manually or generated automatically from an existing mesh or submesh.</li>
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created manually or generated automatically from an existing mesh or
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sub-mesh.</li>
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<li> A 3D block (Solid) object.</li>
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<li> Two vertices that specify the order of nodes in the resulting
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mesh.</li>
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</ul>
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Alternatively, it is possible to select <b>Refine selected mesh elements</b>
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checkbox and apply the pattern to
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check-box and apply the pattern to
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<ul>
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<li> One or several <b>Mesh volumes</b> instead of a geometric 3D
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object</li>
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<li> and select two /b Nodes instead of vertices.</li>
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<li> One or several <b>Mesh volumes</b> instead of a geometric 3D object</li>
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<li> and select two /b Nodes instead of vertices.</li>
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</ul>
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Additionally it is possible to:
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<ul>
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@ -152,7 +158,7 @@ Additionally it is possible to:
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</ul>
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<br>
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<h3> Automatic Generation </h3>
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<h3> Automatic Pattern Generation</h3>
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To generate a pattern automatically from an existing mesh or sub-mesh,
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click \b New button.
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@ -164,8 +170,8 @@ The following dialog box will appear:
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In this dialog you should specify:
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<ul>
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<li> <b>Mesh or Submesh</b>, which is a meshed geometrical face (for a
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2D pattern) or a meshed solid (for a 3D pattern). Mesh nodes lying on
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<li> <b>Mesh or Sub-mesh</b>, which is a meshed geometrical face (for a
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2D pattern) or a meshed solid block (for a 3D pattern). Mesh nodes lying on
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the face vertices become key-points of the pattern. </li>
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<li> A custom <b>Pattern Name </b> </li>
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<li>Additionally, for a 2D pattern you may choose to
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@ -204,17 +210,17 @@ The mapping algorithm for a 2D case is as follows:
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vertices. The node position on the edge depends on its distance from the
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key-points.
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\image html image96.gif
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- The cordinates of a non-boundary node in the parametric space of the face
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- The coordinates of a non-boundary node in the parametric space of the face
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are defined in the following way. In the parametric space of the
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pattern, the node lies at the intersection of two iso-lines. Both
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of them intersect the pattern boundary at two
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points at least. If the mapped positions of boundary nodes are known, it is
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possible to find, where the points at the intersection of isolines
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possible to find, where the points at the intersection of iso-lines
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and boundaries are mapped. Then it is possible to find
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the direction of mapped isolinesection and, filally, the poitions of
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the direction of mapped iso-line section and, finally, the positions of
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two nodes on two mapped isolines. The eventual mapped
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position of the node is found as an average of the positions on mapped
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isolines.
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iso-lines.
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\image html image97.gif
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The 3D algorithm is similar.
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@ -2,8 +2,9 @@
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\page smoothing_page Smoothing
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\n Smoothing is used to adjust the locations of element corners
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(nodes) to reduce distortions in these elements.
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\n Smoothing is used to improve quality of 2D mesh by adjusting the
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locations of element corners (nodes). \note Depending on smoothing
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method and mesh geometry smoothing can decrease quality of elements.
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<em>To apply smoothing to the elements of your mesh:</em>
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<ol>
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@ -23,23 +24,25 @@ The following dialog will appear:
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<ul>
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<li>specify the IDs of the elements which will be smoothed:
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<ul>
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<li><b>Select the whole mesh, submesh or group</b> activating this
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checkbox; or</li>
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<li><b>Select the whole mesh, sub-mesh or group</b> activating this
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check-box; or</li>
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<li>choose mesh elements with the mouse in the 3D Viewer. It is
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possible to select a whole area with a mouse frame; or</li>
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<li>input the element IDs directly in <b>ID Elements</b> field. The selected elements will be highlighted in the
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viewer; or</li>
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<li>apply Filters. <b>Set filter</b> button allows to apply a filter to the selection of elements. See more
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about filters in the \ref selection_filter_library_page "Selection filter library" page.</li>
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possible to select a whole area with a mouse frame; or</li>
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<li>input the element IDs directly in <b>ID Elements</b> field. The
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selected elements will be highlighted in the viewer; or</li>
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<li>apply Filters. <b>Set filters</b> button allows to apply a filter
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to the selection of elements. See more about filters in the
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\ref filtering_elements "Selection filter library" page.</li>
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</ul>
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</li>
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<li>define the <b>Fixed nodes ids</b> that should remain at their location during
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smoothing. If a mesh is built on a shape, the nodes built on its
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geometric edges are always fixed. If the smoothing is applied to a part
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of the mesh, the nodes of boundary elements are also
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fixed. It is possible to additionally fix any other nodes. The fixed nodes can be
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selected manually or by filters, just as the smoothed elements.</li>
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<li>define the <b>Fixed nodes ids</b> that should remain at their
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location during smoothing. If a mesh is built on a shape, the nodes
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built on its geometric edges are always fixed. If the smoothing is
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applied to a part of the mesh (a set of element), the nodes on
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boundary of the element set are also fixed. It is possible to
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additionally fix any other nodes. The fixed nodes can be selected
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manually or by filters, just as the smoothed elements.</li>
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<li>choose the <b>Smoothing Method:</b>
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<ul>
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<li>\b Laplacian smoothing pulls a node toward the center of
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@ -48,27 +51,26 @@ edge.
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<li>\b Centroidal smoothing pulls a node toward the
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element-area-weighted centroid of the surrounding elements. </li>
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Typically, the Laplacian method will produce the mesh with the least element
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distortion. It is also the fastest method. Centroidal smoothing usually
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produces a mesh with more uniform element sizes. Both methods
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produce good results with "free" meshes.</li>
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Laplacian method will produce the mesh with the least element
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edge length. It is also the fastest method. Centroidal smoothing
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produces a mesh with more uniform element sizes.</li>
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</ul>
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\image html image83.gif
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</li>
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<li>specify the <b>Iteration limit</b>. Both smoothing methods
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iterate through a number of steps to produce the resulting smoothed
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mesh. At each new step the smoothing is reevaluated with the updated nodal locations. This
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process continues till the limit of iterations has been
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exceeded, or till the aspect ratio of all element is less than or equal to the
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specified one.</li>
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<li>specify the <b>Max. aspect ratio</b> - the target mesh quality at which the
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smoothing algorithm should stop the iterations.</li>
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<li>activate <b>in parametric space</b> checkbox if it is necessary to
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to improve the shape of faces in the parametric space
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of geometrical surfaces on which they are generated, else the shape of
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faces in the 3D space is improved. </li>
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<li>specify the <b>Iteration limit</b>. Both smoothing methods iterate
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through a number of steps to produce the resulting smoothed mesh. At
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each new step the smoothing is reevaluated with the updated nodal
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locations. This process continues till the limit of iterations has
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been exceeded, or till the aspect ratio of all element is less than
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or equal to the specified one.</li>
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<li>specify the <b>Max. aspect ratio</b> - the target mesh quality at
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which the smoothing algorithm should stop the iterations.</li>
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<li>activate <b>in parametric space</b> check-box if it is necessary to
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improve the shape of faces in the parametric space of geometrical
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surfaces on which they are generated, else the shape of faces in the
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3D space is improved that is suitable for <b>planar meshes only</b>. </li>
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</ul>
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</li>
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<li>Click \b Apply or <b> Apply and Close</b> button to confirm the operation.</li>
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@ -3,11 +3,10 @@
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\page taper_page Taper
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\n \b Taper mesh quality criterion represents the ratio of the areas
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of two triangles separated by a diagonal. So it can be calculated only
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for elements consisting of 4 nodes.
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of two triangles separated by a diagonal within a quadrilateral face.
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<b><center>JA=0.25 * (A1 + A2 + A3 + A4)
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<br> TAPER= MAX(|A1/JA - 1|, |A2/JA - 1|, |A3/JA - 1|, |A4/JA - 1|)</center></b>
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<b><center>JA = 0.25 * (A1 + A2 + A3 + A4)
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<br> TAPER = MAX(|A1/JA - 1|, |A2/JA - 1|, |A3/JA - 1|, |A4/JA - 1|)</center></b>
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<br><em>To apply the Taper quality criterion to your mesh:</em>
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