maincogtest.html

Delaunay三角形的网格剖分程序

<TITLE>COG 2.1: Geometries and grids</TITLE>
<PRE>
#include "<A HREF="coglib.hxx">cog/coglib.hxx</A>"
</PRE>

<H1>COG 2.1: Arbitrary Cogeometries</H1>

 <P>Now it's time to explain a remarkable property of the COG package:
the modular independence of the grid generation data and the geometry
description.  Until now, we have created grid generator data (coarse
grid, coordinates, refinement) and the geometry description together.
That's often useful.  For a given geometry there is often an
"appropriate" set of grid generation data.

 <P>Nonetheless, the grid generation algorithm does not know about
this, it is possible to combine any grid generator with any geometry
description.  Here is how to do this.

 <P>First, we need some cogeometry.  There are various methods how to
do this, for example you can use the cogeometry of an arbitrary
cogenerator <B>gen</B> with <B>gen-&gt;cogeometry()</B>.  This part
will be done in the file <A HREF="cogtest.html">cogtest.cxx</A>, which
defines a function <B>test_cogeometry()</B>:

<PRE>
cogeometry test_cogeometry();

#include "<A HREF="cogtest.cxx">cogtest.cxx</A>"

int main()
{
  cogeometry geom = test_cogeometry();
</PRE>

 <P>Now, we define a cogenerator.  This includes the definition of the
domain of computation, which is not part of the geometry description.
Here we define a 3D box using the class
 <B><A HREF="cogenoctree.html">CogenOctree</A></B>.

<PRE>
  cogenOctree gen = new CogenOctree();
  gen-&gt;setBorder(-1.0,1.0, -1.0,1.0, -1.0,1.0);
  gen-&gt;refinementGlobal(0.2,0.2,0.2);
</PRE>

 <P>What remains is almost the same as before.  We only have the
additional argument <B>geom</B> in the grid generator call:

<PRE>
  wzgrid grid = (*gen)(geom);
  grid->write("test.sg");
}
</PRE>

<H2>Modular Separation between Cogeometry and Cogenerator</H2>

 <P>There are some interesting unexpected properties of the
cogeometry:

 <UL>
 <LI> The cogeometry is global - there is no "box" containing the
cogeometry.  The definition of the box is part of the cogenerator.
You can use the same cogeometry and create grids for various parts of
the global cogeometry.

 <LI> Even the dimension of the cogeometry is undefined. You can use
each cogeometry to create 1D, 2D and 3D grids - intersections of the
global cogeometry with various lines, rectangles and cubes.
 </UL>

 <P>To illustrate these properties, we have some other examples using
the same cogeometry.  You can change independently the cogeometry used
here and in the following examples, and the cogenerator.

 <P><B>&gt; use cog xyz</B> extracts the code for the cogeometry
described in the file
 <A HREF="cogtest.html">cogxyztest.html</A> into the file
 <A HREF="cogtest.cxx">cogtest.cxx</A> included here.

 <P>This test cogeometry may be intersected with various computation
domains in different sample programs:

 <p><B>&gt; cog main cog</B> uses this example;

 <p><B>&gt; cog main <A HREF="maincog3dtest.html">cog3d</A></B> uses a
3D box with boundaries [0,1];

 <p><B>&gt; cog main <A HREF="maincog2dtest.html">cog2d</A></B> uses a
2D rectangular box;

 <p><B>&gt; cog main <A HREF="maincog1dtest.html">cog1d</A></B> uses
an 1D box;

 <p><B>&gt; cog main <A HREF="maincogpolartest.html">cogpolar</A></B>
uses a disc with polar coordinates;