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\page area_page Area \page area_page Area
\n \b Area mesh quality control is based on the algorithm of area \n \b Area mesh quality control is based on the algorithm of area
calculation of meshing elements. It can be applied to meshes calculation of mesh faces.
consisting of 2D meshing elements with 3 and 4 nodes (triangles and
quadrangles).
<em>To apply the Area quality control to your mesh:</em> <em>To apply the Area quality control to your mesh:</em>
<ol> <ol>
@ -17,7 +15,7 @@ quadrangles).
\image html image35.png \image html image35.png
<center><em>"Area" button</em></center> <center><em>"Area" button</em></center>
Your mesh will be displayed in the viewer with its elements colored Your mesh will be displayed in the viewer with its faces colored
according to the applied mesh quality control criterion: according to the applied mesh quality control criterion:
\image html image5.jpg \image html image5.jpg

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\page borders_at_multi_connection_page Borders at multi-connection \page borders_at_multi_connection_page Borders at multi-connection
\n This mesh quality control highlights borders of faces consisting of \n This mesh quality control highlights segments according to number
edges belonging to several faces. The amount of faces is specified by of elements, faces and volumes, the segment belongs to.
user.
\image html image151.gif \image html image151.gif

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\page borders_at_multi_connection_2d_page Borders at multi-connection 2D \page borders_at_multi_connection_2d_page Borders at multi-connection 2D
\n This mesh quality control highlights borders of elements of mesh, \n This mesh quality control highlights borders of faces (links
consisting of edges belonging to several elements of mesh. between nodes) according to number of faces the link belongs to.
\image html image127.gif \image html image127.gif

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@ -14,7 +14,7 @@ quadratic meshes.
<em>To produce a conversion:</em> <em>To produce a conversion:</em>
<ol> <ol>
<li>Select a mesh or a sub-mesh in the Object Browser or in the <li>Select a mesh or a sub-mesh in the Object Browser or in the
Viewer.</li> Viewer.</li>
<li>From the Modification menu or from the contextual menu in the <li>From the Modification menu or from the contextual menu in the
Object Browser choose <b> Convert to/from Quadratic Mesh</b> item, Object Browser choose <b> Convert to/from Quadratic Mesh</b> item,
or click <em>"Convert to/from quadratic"</em> button in the or click <em>"Convert to/from quadratic"</em> button in the

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\page extrusion_along_path_page Extrusion along Path \page extrusion_along_path_page Extrusion along Path
\n In principle, <b>Extrusion along Path</b> works in the same way \n In principle, <b>Extrusion along Path</b> works in the same way
as \ref extrusion_page "Extrusion", the main difference is that we define not a vector, as \ref extrusion_page "Extrusion", the main difference is that we
but a path of extrusion which must be a 1D mesh or 1D sub-mesh. define not a vector, but a path of extrusion which must be an 1D mesh
or 1D sub-mesh.
To get an idea of how this algorithm works, examine several examples, To get an idea of how this algorithm works, examine several examples,
starting from the most simple case of extrusion along a straight edge. starting from the most simple case of extrusion along a straight edge.
In the examples the sample mesh will be extruded along different In the examples the sample mesh will be extruded along different
@ -66,8 +67,8 @@ six coincident nodes and two coincident faces in the resulting
mesh.</center> mesh.</center>
\image html circle_angles_after.png \image html circle_angles_after.png
<center>The same, but using angles {45, -45, 45, -45, 45, -45, 45, <center>The same, but using angles {45, -45, 45, -45, 45, -45, 45, -45}
-45}</center> </center>
<br><em>To use Extrusion along Path:</em> <br><em>To use Extrusion along Path:</em>
<ol> <ol>
@ -93,7 +94,7 @@ The following dialog will appear:
of following means: of following means:
<ul> <ul>
<li><b>Select the whole mesh, sub-mesh or group</b> activating this <li><b>Select the whole mesh, sub-mesh or group</b> activating this
checkbox.</li> check-box.</li>
<li>Choose mesh elements with the mouse in the 3D Viewer. It is <li>Choose mesh elements with the mouse in the 3D Viewer. It is
possible to select a whole area with a mouse frame.</li> possible to select a whole area with a mouse frame.</li>
<li>Input the element IDs directly in <b>Node IDs</b>, <b>Edge <li>Input the element IDs directly in <b>Node IDs</b>, <b>Edge
@ -107,10 +108,10 @@ The following dialog will appear:
<li>Define the \b Path along which the elements will be extruded.<br> <li>Define the \b Path along which the elements will be extruded.<br>
Path definition consists of several elements: Path definition consists of several elements:
<ul> <ul>
<li><b>Mesh or submesh</b> - 1D mesh or sub-mesh, along which <li><b>Mesh or sub-mesh</b> - 1D mesh or sub-mesh, along which
proceeds the extrusion.</li> proceeds the extrusion.</li>
<li><b>Start node</b> - the start node. It is used to define <li><b>Start node</b> - the start node of the Path. It is used
the direction of extrusion. </li> to define the direction of extrusion. </li>
</ul> </ul>
</li> </li>
<li>If you activate <b>Generate Groups</b> check-box, the <em>result elements</em> <li>If you activate <b>Generate Groups</b> check-box, the <em>result elements</em>

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\page free_borders_page Free borders \page free_borders_page Free borders
\n This mesh quality control highlights borders of faces consisting of \n This mesh quality control highlights borders of faces consisting of
edges belonging to one face only. 1D elements (segments) belonging to one face only.
\image html free_borders1.png \image html free_borders1.png

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\page free_edges_page Free edges \page free_edges_page Free edges
\n This mesh quality control highlights borders of elements of mesh \n This mesh quality control highlights borders of faces
consisting of edges belonging to one element of mesh only. consisting of node links belonging to one face only.
\image html free_edges.png \image html free_edges.png
<center>In this picture some elements of mesh have been deleted and <center>In this picture some elements of mesh have been deleted and

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\page length_2d_page Length 2D \page length_2d_page Length 2D
\n This quality control criterion consists of calculation of length of \n This quality control criterion consists of calculation of length of
the edges combining the meshing elements (triangles and quadrangles) the links between corner nodes of mesh faces.
of your mesh.
<em>To apply the Length 2D quality criterion to your mesh:</em> <em>To apply the Length 2D quality criterion to your mesh:</em>
<ol> <ol>
@ -16,7 +15,8 @@ of your mesh.
\image html image34.png \image html image34.png
<center><em>"Length 2D" button</em></center> <center><em>"Length 2D" button</em></center>
Your mesh will be displayed in the viewer with its elements colored according to the applied mesh quality control criterion: Your mesh will be displayed in the viewer with links colored according
to the applied mesh quality control criterion:
\image html length2d.png \image html length2d.png
</li> </li>

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@ -28,8 +28,8 @@ the type of operation you would like to perform.</li>
\n "Create boundary elements" dialog allows creation of boundary elements \n "Create boundary elements" dialog allows creation of boundary elements
of two types. of two types.
<ul> <ul>
<li><b>2D from 3D</b> creates mesh faces on free facets of volume elements</li> <li><b>2D from 3D</b> creates missing mesh faces on free facets of volume elements</li>
<li><b>1D from 2D</b> creates mesh edges on free edges of mesh faces</li> <li><b>1D from 2D</b> creates missing mesh edges on free edges of mesh faces</li>
</ul> </ul>
Here a <em>free facet</em> means a facet shared by only one volume, a <em>free edge</em> Here a <em>free facet</em> means a facet shared by only one volume, a <em>free edge</em>
means an edge shared by only one mesh face. means an edge shared by only one mesh face.

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@ -14,17 +14,19 @@ The smp file contains 4 sections:
-# The first line indicates the total number of pattern nodes (N). -# The first line indicates the total number of pattern nodes (N).
-# The next N lines describe nodes coordinates. Each line contains 2 -# The next N lines describe nodes coordinates. Each line contains 2
node coordinates for a 2D pattern or 3 node coordinates for a 3D pattern. node coordinates for a 2D pattern or 3 node coordinates for a 3D pattern.
Note, that node coordinates of a 3D pattern can be defined only by relative values in range [0;1]. Note, that node coordinates of a 3D pattern can be defined only by
relative values in range [0;1].
-# The key-points line contains the indices of the nodes to be mapped on geometrical -# The key-points line contains the indices of the nodes to be mapped on geometrical
vertices (for a 2D pattern only). Index n refers to the node described vertices (for a 2D pattern only). Index n refers to the node described
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. on the n-th line of section 2. The index of the first node is
zero. For a 3D pattern the key points are not specified.
-# The remaining lines describe nodal connectivity of elements, one line -# The remaining lines describe nodal connectivity of elements, one line
for each element. Each line holds indices of nodes forming an element. for each element. Each line holds indices of nodes forming an element.
Index n refers to the node described on the n-th line of section 2. Index n refers to the node described on the n-th line of section 2.
The first node index is zero. There must be 3 or 4 indices on each The first node index is zero. There must be 3 or 4 indices on each
line for a 2D pattern (only 2d elements are allowed) and 4, 5, 6 or 8 line for a 2D pattern (only liner 2d elements are allowed) and 4, 5, 6 or 8
indices for a 3D pattern (only 3d elements are allowed). indices for a 3D pattern (only linear 3d elements are allowed).
A 2D pattern must contain at least one element and at least one A 2D pattern must contain at least one element and at least one
key-point. All key-points must lie on boundaries. key-point. All key-points must lie on boundaries.
@ -107,18 +109,21 @@ In this dialog you should specify:
<ul> <ul>
<li> \b Pattern, which can be loaded from .smp pattern file previously <li> \b Pattern, which can be loaded from .smp pattern file previously
created manually or generated automatically from an existing mesh or submesh.</li> created manually or generated automatically from an existing mesh or
sub-mesh.</li>
<li> \b Face with the number of vertices equal to the number of <li> \b Face with the number of vertices equal to the number of
key-points in the pattern; the number of key-points on internal key-points in the pattern; the number of key-points on internal
boundaries of the pattern must also be equal to the number of vertices boundaries of the pattern must also be equal to the number of vertices
on internal boundaries of the face;</li> on internal boundaries of the face;</li>
<li> \b Vertex to which the first key-point should be mapped;</li> <li> \b Vertex to which the first key-point should be mapped;</li>
</ul> </ul>
Alternatively, it is possible to select <b>Refine selected mesh elements</b> Alternatively, it is possible to select <b>Refine selected mesh elements</b>
check-box and apply the pattern to <ul> check-box and apply the pattern to <ul>
<li> <b>Mesh Face</b> instead of a geometric Face</li> <li> <b>Mesh Face</b> instead of a geometric Face</li>
<li> and select \b Node instead of vertex.</li> <li> and select \b Node instead of vertex.</li>
</ul> </ul>
Additionally it is possible to: <ul> Additionally it is possible to: <ul>
<li> <b>Reverse the order of key-points</b>. By default, the vertices of <li> <b>Reverse the order of key-points</b>. By default, the vertices of
a face are ordered counterclockwise.</li> a face are ordered counterclockwise.</li>
@ -133,17 +138,18 @@ Additionally it is possible to: <ul>
In this dialog you should specify: In this dialog you should specify:
<ul> <ul>
<li> \b Pattern, which can be loaded from .smp pattern file previously <li> \b Pattern, which can be loaded from .smp pattern file previously
created manually or generated automatically from an existing mesh or submesh.</li> created manually or generated automatically from an existing mesh or
sub-mesh.</li>
<li> A 3D block (Solid) object.</li> <li> A 3D block (Solid) object.</li>
<li> Two vertices that specify the order of nodes in the resulting <li> Two vertices that specify the order of nodes in the resulting
mesh.</li> mesh.</li>
</ul> </ul>
Alternatively, it is possible to select <b>Refine selected mesh elements</b> Alternatively, it is possible to select <b>Refine selected mesh elements</b>
checkbox and apply the pattern to check-box and apply the pattern to
<ul> <ul>
<li> One or several <b>Mesh volumes</b> instead of a geometric 3D <li> One or several <b>Mesh volumes</b> instead of a geometric 3D object</li>
object</li> <li> and select two /b Nodes instead of vertices.</li>
<li> and select two /b Nodes instead of vertices.</li>
</ul> </ul>
Additionally it is possible to: Additionally it is possible to:
<ul> <ul>
@ -152,7 +158,7 @@ Additionally it is possible to:
</ul> </ul>
<br> <br>
<h3> Automatic Generation </h3> <h3> Automatic Pattern Generation</h3>
To generate a pattern automatically from an existing mesh or sub-mesh, To generate a pattern automatically from an existing mesh or sub-mesh,
click \b New button. click \b New button.
@ -164,8 +170,8 @@ The following dialog box will appear:
In this dialog you should specify: In this dialog you should specify:
<ul> <ul>
<li> <b>Mesh or Submesh</b>, which is a meshed geometrical face (for a <li> <b>Mesh or Sub-mesh</b>, which is a meshed geometrical face (for a
2D pattern) or a meshed solid (for a 3D pattern). Mesh nodes lying on 2D pattern) or a meshed solid block (for a 3D pattern). Mesh nodes lying on
the face vertices become key-points of the pattern. </li> the face vertices become key-points of the pattern. </li>
<li> A custom <b>Pattern Name </b> </li> <li> A custom <b>Pattern Name </b> </li>
<li>Additionally, for a 2D pattern you may choose to <li>Additionally, for a 2D pattern you may choose to
@ -204,17 +210,17 @@ The mapping algorithm for a 2D case is as follows:
vertices. The node position on the edge depends on its distance from the vertices. The node position on the edge depends on its distance from the
key-points. key-points.
\image html image96.gif \image html image96.gif
- The cordinates of a non-boundary node in the parametric space of the face - The coordinates of a non-boundary node in the parametric space of the face
are defined in the following way. In the parametric space of the are defined in the following way. In the parametric space of the
pattern, the node lies at the intersection of two iso-lines. Both pattern, the node lies at the intersection of two iso-lines. Both
of them intersect the pattern boundary at two of them intersect the pattern boundary at two
points at least. If the mapped positions of boundary nodes are known, it is points at least. If the mapped positions of boundary nodes are known, it is
possible to find, where the points at the intersection of isolines possible to find, where the points at the intersection of iso-lines
and boundaries are mapped. Then it is possible to find and boundaries are mapped. Then it is possible to find
the direction of mapped isolinesection and, filally, the poitions of the direction of mapped iso-line section and, finally, the positions of
two nodes on two mapped isolines. The eventual mapped two nodes on two mapped isolines. The eventual mapped
position of the node is found as an average of the positions on mapped position of the node is found as an average of the positions on mapped
isolines. iso-lines.
\image html image97.gif \image html image97.gif
The 3D algorithm is similar. The 3D algorithm is similar.

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\page smoothing_page Smoothing \page smoothing_page Smoothing
\n Smoothing is used to adjust the locations of element corners \n Smoothing is used to improve quality of 2D mesh by adjusting the
(nodes) to reduce distortions in these elements. locations of element corners (nodes). \note Depending on smoothing
method and mesh geometry smoothing can decrease quality of elements.
<em>To apply smoothing to the elements of your mesh:</em> <em>To apply smoothing to the elements of your mesh:</em>
<ol> <ol>
@ -23,23 +24,25 @@ The following dialog will appear:
<ul> <ul>
<li>specify the IDs of the elements which will be smoothed: <li>specify the IDs of the elements which will be smoothed:
<ul> <ul>
<li><b>Select the whole mesh, submesh or group</b> activating this <li><b>Select the whole mesh, sub-mesh or group</b> activating this
checkbox; or</li> check-box; or</li>
<li>choose mesh elements with the mouse in the 3D Viewer. It is <li>choose mesh elements with the mouse in the 3D Viewer. It is
possible to select a whole area with a mouse frame; or</li> possible to select a whole area with a mouse frame; or</li>
<li>input the element IDs directly in <b>ID Elements</b> field. The selected elements will be highlighted in the <li>input the element IDs directly in <b>ID Elements</b> field. The
viewer; or</li> selected elements will be highlighted in the viewer; or</li>
<li>apply Filters. <b>Set filter</b> button allows to apply a filter to the selection of elements. See more <li>apply Filters. <b>Set filters</b> button allows to apply a filter
about filters in the \ref selection_filter_library_page "Selection filter library" page.</li> to the selection of elements. See more about filters in the
\ref filtering_elements "Selection filter library" page.</li>
</ul> </ul>
</li> </li>
<li>define the <b>Fixed nodes ids</b> that should remain at their location during <li>define the <b>Fixed nodes ids</b> that should remain at their
smoothing. If a mesh is built on a shape, the nodes built on its location during smoothing. If a mesh is built on a shape, the nodes
geometric edges are always fixed. If the smoothing is applied to a part built on its geometric edges are always fixed. If the smoothing is
of the mesh, the nodes of boundary elements are also applied to a part of the mesh (a set of element), the nodes on
fixed. It is possible to additionally fix any other nodes. The fixed nodes can be boundary of the element set are also fixed. It is possible to
selected manually or by filters, just as the smoothed elements.</li> additionally fix any other nodes. The fixed nodes can be selected
manually or by filters, just as the smoothed elements.</li>
<li>choose the <b>Smoothing Method:</b> <li>choose the <b>Smoothing Method:</b>
<ul> <ul>
<li>\b Laplacian smoothing pulls a node toward the center of <li>\b Laplacian smoothing pulls a node toward the center of
@ -48,27 +51,26 @@ edge.
<li>\b Centroidal smoothing pulls a node toward the <li>\b Centroidal smoothing pulls a node toward the
element-area-weighted centroid of the surrounding elements. </li> element-area-weighted centroid of the surrounding elements. </li>
Typically, the Laplacian method will produce the mesh with the least element Laplacian method will produce the mesh with the least element
distortion. It is also the fastest method. Centroidal smoothing usually edge length. It is also the fastest method. Centroidal smoothing
produces a mesh with more uniform element sizes. Both methods produces a mesh with more uniform element sizes.</li>
produce good results with "free" meshes.</li>
</ul> </ul>
\image html image83.gif \image html image83.gif
</li> </li>
<li>specify the <b>Iteration limit</b>. Both smoothing methods <li>specify the <b>Iteration limit</b>. Both smoothing methods iterate
iterate through a number of steps to produce the resulting smoothed through a number of steps to produce the resulting smoothed mesh. At
mesh. At each new step the smoothing is reevaluated with the updated nodal locations. This each new step the smoothing is reevaluated with the updated nodal
process continues till the limit of iterations has been locations. This process continues till the limit of iterations has
exceeded, or till the aspect ratio of all element is less than or equal to the been exceeded, or till the aspect ratio of all element is less than
specified one.</li> or equal to the specified one.</li>
<li>specify the <b>Max. aspect ratio</b> - the target mesh quality at which the <li>specify the <b>Max. aspect ratio</b> - the target mesh quality at
smoothing algorithm should stop the iterations.</li> which the smoothing algorithm should stop the iterations.</li>
<li>activate <b>in parametric space</b> checkbox if it is necessary to <li>activate <b>in parametric space</b> check-box if it is necessary to
to improve the shape of faces in the parametric space improve the shape of faces in the parametric space of geometrical
of geometrical surfaces on which they are generated, else the shape of surfaces on which they are generated, else the shape of faces in the
faces in the 3D space is improved. </li> 3D space is improved that is suitable for <b>planar meshes only</b>. </li>
</ul> </ul>
</li> </li>
<li>Click \b Apply or <b> Apply and Close</b> button to confirm the operation.</li> <li>Click \b Apply or <b> Apply and Close</b> button to confirm the operation.</li>

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\page taper_page Taper \page taper_page Taper
\n \b Taper mesh quality criterion represents the ratio of the areas \n \b Taper mesh quality criterion represents the ratio of the areas
of two triangles separated by a diagonal. So it can be calculated only of two triangles separated by a diagonal within a quadrilateral face.
for elements consisting of 4 nodes.
<b><center>JA=0.25 * (A1 + A2 + A3 + A4) <b><center>JA = 0.25 * (A1 + A2 + A3 + A4)
<br> TAPER= MAX(|A1/JA - 1|, |A2/JA - 1|, |A3/JA - 1|, |A4/JA - 1|)</center></b> <br> TAPER = MAX(|A1/JA - 1|, |A2/JA - 1|, |A3/JA - 1|, |A4/JA - 1|)</center></b>
<br><em>To apply the Taper quality criterion to your mesh:</em> <br><em>To apply the Taper quality criterion to your mesh:</em>