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\page prism_3d_algo_page 3D extrusion meshing algorithm

3D extrusion algorithm can be used for meshing prisms, i.e. 3D shapes
defined by two opposing faces having the same number of vertices and
edges. These two faces should be connected by quadrangle "side" faces.

The prism is allowed to have sides composed of several faces. (A prism
side is a row of faces (or one face) connecting the corresponding edges of
the top and base faces). However, a prism 
side can be split only vertically as indicated in the
picture below. 

\image html prism_ok_ko.png "A suitable and an unsuitable prism"
In this picture, the left prism is suitable for meshing with 3D
extrusion algorithm: it has six sides, two of which are split
vertically. The right prism cannot be meshed with this
algorithm because one of the prism sides is split horizontally (the
splitting edge is highlighted).

The algorithm can propagate 2D mesh not only between horizontal
(i.e. base and top) faces of one prism but also between faces of prisms
organized in a stack and between stacks sharing prism sides.

\image html prism_stack.png "Prism stacks"
This picture shows four neighboring prism stacks, each comprising two prisms.
The shown sub-mesh is used by the algorithm to mesh
all eight prisms in the stacks.

To use <em>3D extrusion</em> algorithm you need to assign algorithms
and hypotheses of lower dimensions as follows.
(A sample picture below shows algorithms and hypotheses used to
mesh a cylinder with prismatic volumes).

\image html prism_needs_hyps.png 

The \b Global algorithms and hypotheses to be chosen at 
\ref create_mesh_anchor "Creation of a mesh object" are:
<ul>
<li> 1D algorithm and hypothesis that will be applied for meshing
  (logically) vertical edges of the prism (which connect the top and the
  base faces of the prism). In the sample picture above these are
  "Regular_1D" algorithm and "Nb. Segments" hypothesis named "Vertical
  Nb. Segments".</li>
</ul>

The \b Local algorithms and hypotheses to be chosen at 
\ref constructing_submeshes_page "Construction of sub-meshes" are:
<ul>
  <li> 1D and 2D algorithms and hypotheses that will be applied for
    meshing the top and the base prism
    \ref submesh_shape_section "faces". These faces can be meshed
    with any type of 2D elements: quadrangles, triangles, polygons or
    their mix. It is enough to define a sub-mesh on either the top or
    the base face. In the sample picture above, "NETGEN_1D2D"
    algorithm meshes "bottom disk" face with triangles. (1D algorithm
    is not assigned as "NETGEN_1D2D" does not require divided edges to
    create a 2D mesh.)
  </li>
  <li> Optionally you can define a 1D sub-mesh on some vertical
    \ref submesh_shape_section "edges" of stacked prisms, which will
    override the global 1D hypothesis mentioned above. In the <b>Prism
    stacks</b> picture, the vertical division is not equidistant on
    the whole length because a "Number Of Segments" hypothesis with
    Scale Factor=3 is assigned to the highlighted edge.
</li></ul>

If <em>3D extrusion</em> algorithm is assigned to a sub-mesh in a mesh
with multiple sub-meshes, the described above approach may not work as
expected. For example the bottom face may be meshed by other algorithm
before <em>3D extrusion</em> have a chance to project a mesh from the
base face. This thing can happen with vertical edges as well. All
these can lead to either a meshing failure or to an incorrect meshing.

In such a case, it's necessary to explicitly define algorithms
that <em>3D extrusion</em> implicitly applies in a simple case:
- assign \ref projection_1D2D algorithm to the top face and
- assign a 1D algorithm to a group of all vertical edges.

\image html image157.gif "Prism with 3D extrusion meshing. Vertical division is different on neighbor edges because several local 1D hypotheses are assigned."

\sa a sample TUI Script of
\ref tui_prism_3d_algo "Use 3D extrusion meshing algorithm".

*/