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 sphere 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 add <b>Body Fitting Parameters</b> hypothesis. The following dialog will appear:
35 \anchor cartesian_hyp_anchor
36 <h2>Body Fitting Parameters hypothesis</h2>
38 \image html cartesian3D_hyp.png "Body Fitting Parameters hypothesis dialog"
40 This dialog allows to define
42 <li>\b Name of the algorithm. </li>
44 <li> Minimal size of a cell truncated by the geometry boundary. If the
45 size of a truncated grid cell is \b Threshold times less than a
46 initial cell size, then a mesh element is not created. </li>
48 <li> <b> Implement Edges </b> check-box activates incorporation of
49 geometrical edges in the mesh.
51 \image html cartesian_implement_edge.png "Implement Edges switched off to the left and on to the right"
53 <li> <b>Definition mode</b> allows choosing how Cartesian structured grid is defined. Location of nodes along each grid axis is defined individually:
55 <li> You can specify the \b Coordinates of grid nodes. \b Insert button
56 inserts a node at \b Step distance(negative or positive) from the
57 selected node. \b Delete button removes the selected node. Double
58 click on a coordinate in the list enables its edition.
59 \b Note that node coordinates are measured along directions of
60 axes that can differ from the directions of the Global Coordinate
62 <li> You can define the \b Spacing of a grid as an algebraic formula
63 <em>f(t)</em> where \a t is a position along a grid axis
64 normalized at [0.0,1.0]. The whole range of geometry can be
65 divided into sub-ranges with their own spacing formulas to apply;
66 \a t varies between 0.0 and 1.0 within each sub-range. \b Insert button
67 divides a selected range into two. \b Delete button adds the
68 selected sub-range to the previous one. Double click on a range in
69 the list enables edition of its right boundary. Double click on a
70 function in the list enables its edition.
74 <li> <b> Fixed Point</b> group allows defining an exact location of a grid node in the direction defined by spacing. The following cases are possible:
76 <li>If all three directions are defined by spacing, there will be a mesh node at the <b> Fixed Point</b>. </li>
77 <li>If two directions are defined by spacing, there will be at least a link between mesh nodes passing through the <b> Fixed Point</b>.</li>
78 <li> If only one direction is defined by spacing, there will be at least an element facet passing through the <b> Fixed Point</b>.</li>
79 <li>If no directions are defined by spacing, <b> Fixed Point</b> is disabled.</li>
83 <li> <b> Directions of Axes</b> group allows setting the directions of grid axes.
85 <li>If <b> Orthogonal Axes </b> check-box is activated the
86 axes remain orthogonal during their modification. </li>
87 <li> Selection buttons enable snapping corresponding axes to
88 direction of a geometrical edge selected in the Object
89 Browser. Edge direction is defined by coordinates of its end
91 <li><b> Optimal Axes</b> button runs an algorithm that tries to
92 set the axes to maximize the number of generated hexahedra.</li>
93 <li><b> Reset </b> button returns the axes in a default position
94 parallel to the axes of the Global Coordinate System.</li>
100 <b>See Also</b> a sample TUI Script of a
101 \ref tui_cartesian_algo "Usage of Body Fitting algorithm".