mainwedgetest.html

Delaunay三角形的网格剖分程序

<TITLE>COG 2.1: Wedges</TITLE>

<H1>Wedges</H1>

 <P>A <B>wedge</B> is a triangle in 2D and a prism in 3D - one half of
a rectangle.  All except one side of the wedge are coordinate planes.

 <P>Wedges may be used, at least in principle, to implement regions
with arbitrary polygonal boundaries. But if the number of points in
this polygon is large, this does not seem to be a nice job.  This is
intentional: there are other algorithms which are more appropriate for
regions with polygonal boundaries and large numbers of boundary
points.

 <P>The point is that for every corner point of the wedge all
coordinate lines (in 3D planes) containing this point are part of the
grid:

 <P><IMG SRC="wedgetest.gif">

 <P>For a large number of points this leads to a very fine initial
grid.  But the initial grid should be, in the ideal, a coarse grid.
Thus, this algorithm is appropriate only for a few number of
triangles.

<PRE>
#include "<A HREF="coglib.hxx">cog/coglib.hxx</A>"
int main()
{
  cogenOctree gen = new CogenOctree();
  gen-&gt;setBorder(0.0,1.0,0.0,1.0);
</PRE>

 <P>Now, the creation of a wedge is similar to the creation of a box.
There is only one additional parameter - the direction:

<PRE>
  wzIndex i2,i3,i4,i5;
  i2 = gen-&gt;addWedge(wzRegion(2), wzWedgeLeftUp,    0.1,0.9, 0.2,0.8);
  i3 = gen-&gt;addWedge(wzRegion(3), wzWedgeRightDown, 0.5,0.9, 0.1,0.7);
  i4 = gen-&gt;addWedge(wzRegion(4), wzWedgeRightUp,   0.2,0.4, 0.5,0.9);
  i5 = gen-&gt;addWedge(wzRegion(5), wzWedgeLeftDown,  0.6,0.8, 0.3,0.9);
</PRE>

 <P>The boundary faces for the wedges may be defined in a similar way
as for <A HREF="mainfacetest.html">boxes</A>, using
<B>setFaceOfWedge</B>.

<PRE>
  gen-&gt;setFaceOfWedge(wzFace(2),i2);
  gen-&gt;setFaceOfWedge(wzFace(3),i3);
  gen-&gt;setFaceOfWedge(wzFace(4),i4);
  gen-&gt;setFaceOfWedge(wzFace(5),i5);
</PRE>

 <P> The box-dependend refinement works in the same way as for <A
HREF="mainoctreereftest.html">boxes</A> with
<B>refinementIsotropicInBox</B>, <B>refinementInBox</B>:

<PRE>
  gen-&gt;refinementInBox(0.05,0.2,0,     i3);
  gen-&gt;refinementIsotropicInBox(0.05,  i4);
</PRE>

 <P>What remains is as usual:

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

<H2>Known Bugs</H2>

 <P>It is possible to define nonconvex regions as a union of wedges.
In this case, the inner edge is cut off.

 <P>To avoid this, to use different region numbers (artificial
subdivision of regions).  This avoids non-convex regions. For this
possibility it is useful to write out
 <A HREF="mainmaterialtest.html">material numbers</A> instead of
region numbers.

 <P>The other possibility is to define different
 <A HREF="mainfacetest.html">boundary conditions</A> on different
parts of the boundary (artificial subdivision of boundary faces).
This avoids non-convex boundary faces.