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106 lines
4.8 KiB
Plaintext
106 lines
4.8 KiB
Plaintext
/*!
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\page cartesian_algo_page Body Fitting 3D meshing algorithm
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Body Fitting algorithm generates hexahedrons of a Cartesian grid in
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the internal part of geometry and polyhedrons and other types of
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elements at the intersection of Cartesian cells with the geometrical
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boundary.
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\image html cartesian3D_sphere.png "A shpere meshed by Body Fitting algorithm"
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The meshing algorithm is as follows.
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<ol>
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<li> Lines of a Cartesian structured grid defined by
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\ref cartesian_hyp_anchor "Body Fitting Parameters" hypothesis are
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intersected with the geometry boundary, thus nodes lying on the
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boundary are found. This step also allows finding out for each node of
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the Cartesian grid if it is inside or outside the geometry. </li>
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<li> For each cell of the grid, check how many of its nodes are outside
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of the geometry boundary. Depending on a result of this check
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<ul>
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<li> skip a cell, if all its nodes are outside </li>
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<li> skip a cell, if it is too small according to <b> Size
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Threshold </b> parameter</li>
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<li> add a hexahedron in the mesh, if all nodes are inside </li>
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<li> add a polyhedron or another cell type in the mesh, if some
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nodes are inside and some outside. </li>
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</ul>
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</li>
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</ol>
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To apply this algorithm when you define your mesh, select <b>Body
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Fitting</b> in the list of 3D algorithms and click <em> "Add
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Hypothesis" </em> button and <em>"Body Fitting Parameters"</em>" menu
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item. Dialog of <b>Body Fitting Parameters
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hypothesis</b> will appear.
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<br>
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\anchor cartesian_hyp_anchor
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<h2>Body Fitting Parameters hypothesis</h2>
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\image html cartesian3D_hyp.png "Body Fitting Parameters hypothesis dialog"
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This dialog allows to define
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<ul>
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<li>\b Name of the algorithm. </li>
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<li> Minimal size of a cell truncated by the geometry boundary. If the
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size of a truncated grid cell is \b Threshold times less than a
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initial cell size, then a mesh element is not created. </li>
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<li> <b> Implement Edges </b> check-box activates incorporation of
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geometrical edges in the mesh.
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\image html cartesian_implement_edge.png "'Implement Edges' switched off (left) and on (right)"
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<li> Cartesian structured grid. Location of nodes along each grid axis
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is defined individually. <b> Definition mode </b> chooses a way of
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grid definition:
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<ul>
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<li> You can specify the \b Coordinates of grid nodes. \b Insert button
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inserts a node at distance \b Step (negative or positive) from a
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selected node. \b Delete button removes a selected node. Double
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click on a coordinate in the list enables its edition.
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\b Note that node coordinates are measured along directions of
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axes that can differ from the directions of the Global Coordinate
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System.</li>
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<li> You can define the \b Spacing of a grid as an algebraic formula
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<em>f(t)</em> where \a t is a position along a grid axis
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normalized at [0.0,1.0]. The whole range of geometry can be
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divided into sub-ranges with their own spacing formulas to apply;
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\a t varies between 0.0 and 1.0 within each sub-range. \b Insert button
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divides a selected range into two ones. \b Delete button adds the
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selected sub-range to the previous one. Double click on a range in
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the list enables edition of its right boundary. Double click on a
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function in the list enables its edition.
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</li> </ul>
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</li>
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<li> Coordinates of a <b> Fixed Point</b>. They allow to exactly
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locate a grid node in a direction defined by spacing. If all the three
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directions are defined by spacing, then there will be a mesh node at
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the <b> Fixed Point</b>. If two directions are defined by spacing,
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then there will be at least a link between mesh nodes passing through
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the <b> Fixed Point</b>. If only one direction is defined by spacing,
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then there will be at least an element facet passing through
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the <b> Fixed Point</b>. If no directions are defined by spacing,
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<b> Fixed Point</b> is disabled.</li>
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<li> <b> Directions of Axes</b>. You can set up almost any
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directions of grid axes that can help in generation of as many as
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possible hexahedral elements.
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<ul>
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<li><b> Orthogonal Axes </b> check-box, if activated, keeps the
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axes orthogonal during their modification. </li>
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<li> Selection buttons enable snapping corresponding axes to
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direction of a geometrical edge selected in the Object
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Browser. Edge direction is defined by coordinates of its end
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points.</li>
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<li><b> Optimal Axes</b> button runs an algorithm that tries to
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set the axes so that a number of generated hexahedra to be
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maximal.</li>
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<li><b> Reset </b> button returns the axes in a default position
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parallel to the axes of the Global Coordinate System.</li>
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</ul></li>
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</ul>
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<br>
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<b>See Also</b> a sample TUI Script of a
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\ref tui_cartesian_algo "Usage of Body Fitting algorithm".
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*/
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