simplex.html

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<TITLE>The Simplex Grid Data Format - Version 1.1</TITLE>

<H1>The Simplex Grid Data Format - Version 1.1</H1>

 <P>This documentation describes the Simplex grid data format and
conversion routines with the ibGrid type used in the IBG package.

 <P>The Simplex grid data format can be used to describe simplicial
grid, that means grids consisting of segments (1D), triangles (2D) or
tetrahedrons (3D), as the inner grid (codimension 0) as the boundary
grid (codimension 1) in 2D and 3D.

 <p>It seems to be easy to convert external data formats for
simplicial grids into this format. Now let us describe this data
format in detail. In the following %d denotes an integer value.

<H2>Header</H2>

<H3>Version Line</H3>

 <P>The first line contains the name and version number of the data
format:

<pre>
SimplexGrid  1.1
</pre>

<H3>Comment Line</H3>

 <P>The second line is reserved for comments. In general, it is
allowed to append comments after the data on every line.

<H3><A NAME="dim">Dimensions</A></H3>

 <P>The next line defines two dimensions:

<pre>
%d %d grid dimension resp. space dimension
</PRE>

 <P>We distinguish the <B>grid dimension</B> and the <B>space
dimension</B>.  The dimension of the space is the number of
coordinates defined for every point. The dimension of the grid defines
if the grid cells are lines (1), triangles (2) or tetrahedra (3). The
dimension of the space may be greater. This property may be "misused"
to define some functions on the grid.  

 <P>It is allowed to define only one number for the dimension. In this
case grid dimension coinsides with the space dimension.


<H3>Numbers of Elements</H3>

 <P>The next line defines the numbers necessary for the memory allocation:

<PRE>
%d points
%d cells
%d boundary cells
</pre>

 <P>The text after the numbers is not required and only comment. The
order of these lines is relevant and cannot be changed. 

 <P>The lines define the number of points, the number of region cells
and the number of boundary cells (cells of codimension 1).  As the
number of region cells as the number of boundary cells may be zero
(pure boundary grid resp. pure region grid).

 <P>If above numbers are zero, the file simply describes a point list.

<H2>Point Coordinates</H2>

 <P>Now one line follows for every point. It contains the coordinates
of the point. The number of coordinates in the line is the <A
HREF="#dim">space dimension</A>.

<H2>Cell Description</H2>

 <P>Then for every cell (codimension 0) there will be one line
defining the cell data. 

<H3>2D Case</H3>

<pre>
%d %d %d   %d   %d %d %d
</pre>

 <P>The first three numbers define the nodes of the triangle.

 <P>The next number defines the region number of the triangle.

 <P>The next three numbers define the neighbour cells of the
triangle.

 <P>So we have seven integer numbers for every triangle.

<H3>3D Case</H3>

<pre>
%d %d %d %d   %d   %d %d %d %d
</pre>

 <P>The first four numbers define the nodes of the tetrahedron.  

 <P>The next number defines the region number of the tetrahedron.

 <P>The next four numbers define the neighbour cells of the
tetrahedron. 

 <P>So we have nine integer numbers for every tetrahedron.

<H2>Boundary Cell Description</H2>

 <P>Then for every boundary cell there will be one line defining the
following data:

<H3>2D Case</H3>

<pre>
%d %d   %d   %d %d   %d %d
</pre>

 <P>The first two numbers define the nodes of the edge. 

 <P>The next number defines the boundary segment number of the edge. 

 <P>The next two numbers describe the left and right neighbour triangle.

 <P>The next two numbers define the neighbour boundary edges of the
edge.

 <P>So we have seven integer numbers for every boundary triangle.

<H3>3D Case</H3>

<pre>
%d %d %d   %d   %d %d   %d %d %d
</pre>

 <P>The first three numbers define the nodes of the triangle. 

 <P>The next number defines the boundary segment number of the triangle. 

 <P>The next two numbers describe the left and right neighbour tetrahedron.

 <P>The next three numbers define the neighbour boundary triangles of the
triangle.

 <P>So we have nine integer numbers for every boundary triangle.

<H2>Further Conventions</H2>

 <P>The enumeration of the grid nodes, grid cells and boundary cells
begins with one.

 <P>The region number is usually an identifier for the material of the
cell. The region number must be positive. The value 0 is reserved for
the case if no region information is available.

 <P>The boundary segment number is usually an identifier for the
boundary condition at this boundary cell. The boundary segment number
must be positive. The value 0 is reserved for the case if no boundary
segment information is available.

 <P>In the case of a pure boundary grid, there is obviously no left
and right neighbour for a boundary cell. In this case, this place may
be used to define the left and the right region number. This usage has
to be marked with a minus sign before the region number. The value 0
is reserved for the case if no information about the left or right
neighbour is available.

 <P>The order of the neighbour cells of the cell is related with the
order of the points of the cell so that the n-th point is opposite to
the n-th neighbour cell.

 <P>If the neighbour of a region cell is a boundary cell, this will be
marked with a minus sign.  If there is no neighbour, there will be
zero.

 <P>If no neighbour information is available for the whole grid, the 
related values may be omitted.