3 \page cartesian_algo_page Body Fitting 3D meshing algorithm
5 Body Fitting algorithm generates hexahedrons of a Cartesian grid in
6 the internal part of geometry and polyhedrons and other types of
7 elements at the intersection of Cartesian cells with the geometrical
10 \image html cartesian3D_sphere.png "A shpere meshed by Body Fitting algorithm"
12 The meshing algorithm is as follows.
14 <li> Lines of a Cartesian structured grid defined by
15 \ref cartesian_hyp_anchor "Body Fitting Parameters" hypothesis are
16 intersected with the geometry boundary, thus nodes lying on the
17 boundary are found. This step also allows finding out for each node of
18 the Cartesian grid if it is inside or outside the geometry. </li>
19 <li> For each cell of the grid, check how many of its nodes are outside
20 of the geometry boundary. Depending on a result of this check
22 <li> skip a cell, if all its nodes are outside </li>
23 <li> skip a cell, if it is too small according to <b> Size
24 Threshold </b> parameter</li>
25 <li> add a hexahedron in the mesh, if all nodes are inside </li>
26 <li> add a polyhedron or another cell type in the mesh, if some
27 nodes are inside and some outside. </li>
31 To apply this algorithm when you define your mesh, select <b>Body
32 Fitting</b> in the list of 3D algorithms and click <em> "Add
33 Hypothesis" </em> button and <em>"Body Fitting Parameters"</em>" menu
34 item. Dialog of <b>Body Fitting Parameters
35 hypothesis</b> will appear.
38 \anchor cartesian_hyp_anchor
39 <h2>Body Fitting Parameters hypothesis</h2>
41 \image html cartesian3D_hyp.png "Body Fitting Parameters hypothesis dialog"
43 This dialog allows to define
45 <li>\b Name of the algorithm. </li>
46 <li> Minimal size of a cell truncated by the geometry boundary. If the
47 size of a truncated grid cell is \b Threshold times less than a
48 initial cell size, then a mesh element is not created. </li>
49 <li> <b> Implement Edges </b> check-box activates incorporation of
50 geometrical edges in the mesh.
51 \image html cartesian_implement_edge.png "'Implement Edges' switched off (left) and on (right)"
52 <li> Cartesian structured grid. Location of nodes along each grid axis
53 is defined individually. <b> Definition mode </b> chooses a way of
56 <li> You can specify the \b Coordinates of grid nodes. \b Insert button
57 inserts a node at distance \b Step (negative or positive) from a
58 selected node. \b Delete button removes a selected node. Double
59 click on a coordinate in the list enables its edition.
60 \b Note that node coordinates are measured along directions of
61 axes that can differ from the directions of the Global Coordinate
63 <li> You can define the \b Spacing of a grid as an algebraic formula
64 <em>f(t)</em> where \a t is a position along a grid axis
65 normalized at [0.0,1.0]. The whole range of geometry can be
66 divided into sub-ranges with their own spacing formulas to apply;
67 \a t varies between 0.0 and 1.0 within each sub-range. \b Insert button
68 divides a selected range into two ones. \b Delete button adds the
69 selected sub-range to the previous one. Double click on a range in
70 the list enables edition of its right boundary. Double click on a
71 function in the list enables its edition.
74 <li> Coordinates of a <b> Fixed Point</b>. They allow to exactly
75 locate a grid node in a direction defined by spacing. If all the three
76 directions are defined by spacing, then there will be a mesh node at
77 the <b> Fixed Point</b>. If two directions are defined by spacing,
78 then there will be at least a link between mesh nodes passing through
79 the <b> Fixed Point</b>. If only one direction is defined by spacing,
80 then there will be at least an element facet passing through
81 the <b> Fixed Point</b>. If no directions are defined by spacing,
82 <b> Fixed Point</b> is disabled.</li>
83 <li> <b> Directions of Axes</b>. You can set up almost any
84 directions of grid axes that can help in generation as many as
85 possible hexahedral elements.
87 <li><b> Orthogonal Axes </b> check-box, if activated, keeps the
88 axes orthogonal during their modification. </li>
89 <li> Selection buttons enable snapping corresponding axes to
90 direction of a geometrical edge selected in the Object
91 Browser. Edge direction is defined by coordinates of its end
93 <li><b> Optimal Axes</b> button runs an algorithm that tries to
94 set the axes so that a number of generated hexahedra to be
96 <li><b> Reset </b> button returns the axes in a default position
97 parallel to the axes of the Global Coordinate System.</li>
102 <b>See Also</b> a sample TUI Script of a
103 \ref tui_cartesian_algo "Usage of Body Fitting algorithm".