simplexgrid.html

Delaunay三角形的网格剖分程序

<TITLE>COG 2.1: SimplexGrid 2.0</TITLE>

<H1>SimplexGrid 2.0</H1>

 <P>For the grid we use a simple output format named <B>SimplexGrid
2.0</B>.  This format describes the nodes, cells, face cells, and
neighbourhood relations between them.  Every cell has a region number,
and every face cell a face number which identified boundary
conditions.  The general scheme is as follows:

<PRE>
<B>SimplexGrid 2.0</B>
<B>#</B> some comment lines
<B>DIMENSION</B>
<I>g: grid dimension</I> 
<B>NODES</B>
<I>n: number of nodes</I>  <I>d: number of coordinates per node</I>
n lines with d real values (coordinates)
<B>CELLS</B>
<I>c: number of cells</I>
c lines with information about cells
<B>FACES</B>
<I>f: number of face cells</I>
f lines with information about face cells
<B>END</B>
</PRE>

 <P>For every inner cell (in 3D tetrahedra, in 2D triangles, in 1D
segments) we have:

 <UL>
 <LI> the nodes: These are integers between 1 and n (four in 3D, three
in 2D, two in 1D);
 <LI> the region number.  This is a positive integer which identifies
the region containing the cell.
 <LI> the neighbour cells: These are nonzero integers between -f and c
(four in 3D, three in 2D, two in 1D); If positive (between 1 and c),
the neighbour is another inner cell, if negative (between -1 and -f),
the neighbour is a face cell; Their order is related with the order of
the nodes: it is the neighbour opposite to the related node;
 </UL>

 <P>For every boundary face element (in 3D triangles, in 2D segments,
in 1D points) we have:

 <UL>
 <LI> the nodes: These are integers between 1 and n (three in 3D, two
in 2D, one in 1D);
 <LI> the identifier of the boundary condition,
 <LI> left and right inner neighbour cells.  Zero indicates an outer
boundary face;
 <LI> the neighbour face cells (three in 3D, two in 2D, none in 1D);
This output is currently not implemented, thus, we have zeros as
placeholders;
 </UL>

<H2>3D example</H2>

 <P>Let's consider the simplest 3D grid created by
 <A HREF="mainstarttest.html">our start example</A>.
It describes the unit cube, with 8 3D points,
6 tetrahedra, and 12 outer boundary triangles:

<PRE>
SimplexGrid 2.0
#created by wzgrid (c) I.Schmelzer
#Wed Sep 16 11:49:30 1998
DIMENSION
3
NODES
8 3
0.000000 0.000000 0.000000 
0.000000 0.000000 1.000000 
0.000000 1.000000 0.000000 
0.000000 1.000000 1.000000 
1.000000 0.000000 0.000000 
1.000000 0.000000 1.000000 
1.000000 1.000000 0.000000 
1.000000 1.000000 1.000000 
CELLS
6
8 7 1 5 1 -1 2 -2 4 
8 1 6 5 1 -3 -4 1 5 
8 1 3 4 1 -5 -6 6 4 
8 1 7 3 1 -7 -8 3 1 
8 2 6 1 1 -9 2 6 -10 
8 2 1 4 1 -11 3 -12 5 
FACES
12
7 1 5 1 -0 1 0 0 0 
8 7 5 1 -0 1 0 0 0 
1 6 5 1 -0 2 0 0 0 
5 6 8 1 -0 2 0 0 0 
1 3 4 1 -0 3 0 0 0 
4 3 8 1 -0 3 0 0 0 
1 7 3 1 -0 4 0 0 0 
3 7 8 1 -0 4 0 0 0 
2 6 1 1 -0 5 0 0 0 
2 8 6 1 -0 5 0 0 0 
2 1 4 1 -0 6 0 0 0 
8 2 4 1 -0 6 0 0 0 
END
</PRE>

<H2>2D example</H2>

 <P>The same scheme is used for 2D grids:

<PRE>
SimplexGrid 2.0
#created by wzgrid (c) I.Schmelzer
#Wed Sep 16 12:09:00 1998
DIMENSION
2
NODES
4 2
0.000000 0.000000 
0.000000 1.000000 
1.000000 0.000000 
1.000000 1.000000 
CELLS
2
4 2 1 1 -1 2 -2 
4 1 3 1 -3 -4 1 
FACES
4
2 1 1 -0 1 0 0 
4 2 1 -0 1 0 0 
1 3 1 -0 2 0 0 
3 4 1 -0 2 0 0 
END
</PRE>

<H2>1D example</H2>

 <P>The same scheme is used for 1D grids too:

<PRE>
SimplexGrid 2.0
#created by wzgrid (c) I.Schmelzer
#Wed Sep 16 12:11:45 1998
DIMENSION
1
NODES
2 1
0.000000 
1.000000 
CELLS
1
1 2 1 -1 -2 
FACES
2
1 1 -0 1 
2 1 -0 1 
END
</PRE>

<H2>0D example</H2>

 <P>Formally even a 0D grid (a point) may be written in this format:

<PRE>
SimplexGrid 2.0
#created by wzgrid (c) I.Schmelzer
#Wed Sep 16 12:14:32 1998
DIMENSION
0
NODES
1 3
0.000000 0.000000 0.000000 
CELLS
1
1 1 
END
</PRE>