Juan Carlos,
The procedure goes as follows,
1) we introduce a set of vertices as points (x_i,y_i), numbered by the
index "i",
2) connect them forming quads/cells and store the numbering as:
cell_nodes [k] = {i1,i2,i3,i4},
3) making sure that i1,i2,i3,i4 follow a lexicographic ordering
explained in .../structGeometryInfo.html.
In 2D it is messy already to satisfy 1), 2), 3) for
non-trivial/primitive meshes, but we always can sketch the situation,
because it is 2D, and by rotating cells (ordering) we hope that
eventually a solution will come out.
Now, the sketch part is not available in 3D and the number of
permutations/rotations has increased dramatically. This leads me to the
following question:
Is there a tool within deal.II to impose 3), when 1) and 2) are given?
In other words, is there any tool available, such that we get an array
new_cell_nodes satisfying a lexicographic ordering, by inputting the
arrays: vertex, cell_nodes?
In 2d, it would in principle be possible to write such code that, given
an unordered set of vertices brings them into an order so that they form
a lexicographic ordering. That's because -- at least for convex
quadrilaterals -- you can find the centroid of the vertices, sort them
in counter-clockwise sense, and then swap the last two.
But that can't work in 3d. Think, for example, of the vertices of a
cube. Number them as you usually would, and you'd get a cube -- a valid
geometry. But then rotate the top surface by 90 degrees: the (unsorted
set of) vertices are in the exact same location, but the geometry you
want to describe (a "twisted" cube) is a different, though equally
valid, one. In other words, you can't infer the geometry someone has in
mind just from knowing where the vertices are. Consequently, it is not
possible to write a code that can always get that right.
The only thing we can do for you is to avoid having to deal with the
tedium of orienting cells relative to each other. This is what the
GridReordering class does for you.
Best
W.
--
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Wolfgang Bangerth email: [email protected]
www: http://www.math.colostate.edu/~bangerth/
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