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87 lines
3.9 KiB
Plaintext
87 lines
3.9 KiB
Plaintext
/*!
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\page prism_3d_algo_page 3D extrusion meshing algorithm
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3D extrusion algorithm can be used for meshing prisms, i.e. 3D shapes
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defined by two opposing faces having the same number of vertices and
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edges. These two faces should be connected by quadrangle "side" faces.
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The prism is allowed to have sides composed of several faces. (A prism
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side is a row of faces (or one face) connecting the corresponding edges of
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the top and base faces). However, a prism
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side can be split only vertically as indicated in the
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picture below.
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\image html prism_ok_ko.png "A suitable and an unsuitable prism"
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In this picture, the left prism is suitable for meshing with 3D
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extrusion algorithm: it has six sides, two of which are split
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vertically. The right prism cannot be meshed with this
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algorithm because one of the prism sides is split horizontally (the
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splitting edge is highlighted).
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The algorithm can propagate 2D mesh not only between horizontal
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(i.e. base and top) faces of one prism but also between faces of prisms
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organized in a stack and between stacks sharing prism sides.
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\image html prism_stack.png "Prism stacks"
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This picture shows four neighboring prism stacks, each comprising two prisms.
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The shown sub-mesh is used by the algorithm to mesh
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all eight prisms in the stacks.
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To use <em>3D extrusion</em> algorithm you need to assign algorithms
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and hypotheses of lower dimensions as follows.
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(A sample picture below shows algorithms and hypotheses used to
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mesh a cylinder with prismatic volumes).
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\image html prism_needs_hyps.png
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The \b Global algorithms and hypotheses to be chosen at
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\ref create_mesh_anchor "Creation of a mesh object" are:
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<ul>
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<li> 1D algorithm and hypothesis that will be applied for meshing
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(logically) vertical edges of the prism (which connect the top and the
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base faces of the prism). In the sample picture above these are
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"Regular_1D" algorithm and "Nb. Segments" hypothesis named "Vertical
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Nb. Segments".</li>
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</ul>
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The \b Local algorithms and hypotheses to be chosen at
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\ref constructing_submeshes_page "Construction of sub-meshes" are:
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<ul>
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<li> 1D and 2D algorithms and hypotheses that will be applied for
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meshing the top and the base prism
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\ref submesh_shape_section "faces". These faces can be meshed
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with any type of 2D elements: quadrangles, triangles, polygons or
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their mix. It is enough to define a sub-mesh on either the top or
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the base face. In the sample picture above, "NETGEN_1D2D"
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algorithm meshes "bottom disk" face with triangles. (1D algorithm
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is not assigned as "NETGEN_1D2D" does not require divided edges to
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create a 2D mesh.)
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</li>
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<li> Optionally you can define a 1D sub-mesh on some vertical
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\ref submesh_shape_section "edges" of stacked prisms, which will
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override the global 1D hypothesis mentioned above. In the <b>Prism
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stacks</b> picture, the vertical division is not equidistant on
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the whole length because a "Number Of Segments" hypothesis with
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Scale Factor=3 is assigned to the highlighted edge.
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</li></ul>
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If <em>3D extrusion</em> algorithm is assigned to a sub-mesh in a mesh
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with multiple sub-meshes, the described above approach may not work as
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expected. For example the bottom face may be meshed by other algorithm
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before <em>3D extrusion</em> have a chance to project a mesh from the
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base face. This thing can happen with vertical edges as well. All
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these can lead to either a meshing failure or to an incorrect meshing.
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In such a case, it's necessary to explicitly define algorithms
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that <em>3D extrusion</em> implicitly applies in a simple case:
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- assign \ref projection_1D2D algorithm to the top face and
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- assign a 1D algorithm to a group of all vertical edges.
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\image html image157.gif "Prism with 3D extrusion meshing. Vertical division is different on neighbor edges because several local 1D hypotheses are assigned."
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\sa a sample TUI Script of
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\ref tui_prism_3d_algo "Use 3D extrusion meshing algorithm".
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*/
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