[Insight-users] itk::Mesh - boundary assignments?

[Luis Ibanez]

Hi Thomas,


The Boundary assigment is intended to stablish a relationship
between neighbor cells.

Every cell in the mesh has a unique identifier, regardless of
its dimension.

The SetBoundaryAssignment() method has parameters

    Dimension
    cellId
    featureId
    cellId 2


The call to

  SetBoundaryAssignment( Dimension, cellId, featureId, cellId2 );

is defining that the cell identified with "cellId" has a neighbor
of dimension "Dimension", whose cell identifier is cellId2.
Because "cellId" may have many neighbors of that dimension, each
one has to be identified with a number (that is local to cellId).
This number is provided by "featureId".


For the case you mention, the numbers 7,9,10 are not of your
free choice. They are the cellID's of the cells that you are
setting as boundaries of dimension "Dimension" of "cellId".




Let's consider the example below

(please make sure that you use a fixed spacing
  font for reading this email).



   [9]-----------------------------[23]
     \            [14]              /
      \                            /
       \                          /
        \                        /
         \                      /
          \        [267]       /
      [24] \                  / [59]
            \                /
             \              /
              \            /
               \          /
                \        /
                 \      /
                  \    /
                   \  /
                   [37]



This is a triangular cell with cellId = 267,
that has three line cells as boundaries of
dimension 1, with cellId' = 14, 24 and 59.
and three point cells as boundaries of dimension 0
with cellId's = 9, 23, 37.

Note that the concept of  PointCell is different
from the concept of being a "Point" of the mesh.
A CellPoint is a cell of dimension zero.

If we do full connectivity here, like a K-Simplex,

the mesh will have the following calls (among others)

A) For the boundaries of the triangular cell

the Dimension=1 boundaries are the line cells

mesh->SetBoundaryAssignment( 1, 267, 0, 14 );
mesh->SetBoundaryAssignment( 1, 267, 1, 24 );
mesh->SetBoundaryAssignment( 1, 267, 2, 59 );

the Dimension=0 boundaries are the point cells

mesh->SetBoundaryAssignment( 0, 267, 0,  9 );
mesh->SetBoundaryAssignment( 0, 267, 1, 23 );
mesh->SetBoundaryAssignment( 0, 267, 2, 37 );


B) For the line cell with cellID= 24, its neighbors
    are two Point cells and one triangle cell

mesh->SetBoundaryAssignment( 0, 24, 0,  9 );
mesh->SetBoundaryAssignment( 0, 24, 1, 37 );

mesh->SetBoundaryAssignment( 2, 24, 0, 267 );


C) For the point cells with cellID = 37
    there are two boundaries of dimension 1,
    the line cells wiht cellId's = 24 and 59,
    and one boundary of dimension=2, the triangle
    cell with cellId = 267


mesh->SetBoundaryAssignment( 1, 37, 0, 24 );
mesh->SetBoundaryAssignment( 1, 37, 1, 59 );

mesh->SetBoundaryAssignment( 2, 37, 0, 267 );



-----------------------------------------------



In order to traverse the neighbor relationships,
take into account that the boundary relationships
are organized by its dimension. There is a separate
container per dimension.

The call

BoundaryAssignmentsContainerPointer cnt =
                mesh->GetBoundaryAssignments( 0 );

will put in "cnt" the container of boundaries
of dimension 0;

The container is a MapContainer<>, and the boundary
information is stored in the class BoundaryAssignementIdentifier
that simply holds the pair of cellIds

   cellId and boundary cellId.

So, in order to get all the lines that are boundaries
of the triangle cell with cellId = 267,
you call

BoundaryAssignmentsContainerPointer cntlines =
                     mesh->GetBoundaryAssignments( 1 );

BoundaryAssignementIdentifier key0( 267, 0 );

   lineCellId0 = cntlines[ key0 ];

BoundaryAssignementIdentifier key1( 267, 1 );

   lineCellId1 = cntlines[ key1 ];

BoundaryAssignementIdentifier key2( 267, 2 );

   lineCellId2 = cntlines[ key2 ];



that should result in

           lineCellId0 ==  14
           lineCellId1 ==  24
           lineCellId2 ==  59


Note that this mesh structure has been designed
for facilitating the access from a specific cell
rather than massive access to all the relationships.

The reason is that the Mesh has been designed for
supporting deformable models and cellular aggregates
where cells are born, cells die and reconfigure under
local circumstances.



Please let us know if you have further questions.



Regards,


   Luis




-----------------------
Thomas Boettger wrote:
> Hello everybody!
> 
> I have some questions about the itk:Mesh class.
> 
> I want to store additional information for my meshes, i.e. an edge list, 
> a face list ( = cell list?), edge neighbour list and a vertex neighbour 
> list. Furthermore I'd like the face list (cell list) in counter 
> clockwise order with respect to the outward unit face (vertex) normal.
> 
> In the software guide I read about the boundary assignements, so I 
> understand how to set my edges for one cell. But still don't know how to 
> traverse all edges or even save a neighbour list. Which meaning has the 
> BoundaryIdentifier? In the guide there was an example for a tri cell:
> 
> 
> mesh->SetBoundaryAssignment( dimension, cellId, featureId++, 7 );
> mesh->SetBoundaryAssignment( dimension, cellId, featureId++, 9 );
> mesh->SetBoundaryAssignment( dimension, cellId, featureId++, 10 );
> 
> 
> Is the user free to choose those numbers? (7,9,10)
> 
> Should I use the boundary assignements method for my necessary 
> attributes or would you suggest to create an extended class containing 
> those new attributes?
> 
> Is there more example code for the mesh class?
> 
> Thanks,
> Thomas
> 
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