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Delaunay三角形的网格剖分程序

<TITLE>COG 2.1: polar coordinates</TITLE>

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<H1>COG 2.1: polar coordinates</H1>

 <P>Now, let's consider how to create curved grids with coordinate
transformations.  As an example, we use polar coordinates.  This
allows to define curved geometries based on the previous method for
rectangular geometries:

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

 <P>First, we create a rectangular grid and geometry with some
 <A HREF="mainoctreetest.html">regions</A>,
 <A HREF="mainfacetest.html">faces</A> and
 <A HREF="mainreftest.html">refinement</A> as before:

<PRE>
#include "<A HREF="coglib.hxx">cog/coglib.hxx</A>"
int main()
{
  cogenOctree base = new CogenOctree();
  wzIndex i1 = base-&gt;addBox(wzRegion(2), 0.0,0.4,-0.3,1.5);
  wzIndex i2 = base-&gt;addBox(wzRegion(3), 0.2,0.3);
  wzIndex i3 = base-&gt;addBox(wzRegion(4), 0.2,0.3, 0.3,1.0);
  base-&gt;setFaceOfBox(wzFace(2),i1);
  base-&gt;setFaceOfBox(wzFace(3),i2);
  base-&gt;setFaceOfBox(wzFace(4),i3);
  base-&gt;refinementGlobal(0.05,0.3);
//  base-&gt;omitEdgeComputation();
</PRE>

 <P>But we should have in mind that we want to use polar
coordinates. Thus, the minimal value which is allowed here for the
first coordinate (the radius) is zero.  Else, the program will fail.
But the extremal values (radius 0, angles -Pi, Pi) are allowed:

<PRE>
  base-&gt;addPlaneY(wzPi);
  base-&gt;addPlaneY(-wzPi);
</PRE>

 <P>Now we apply the polar coordinates to this rectangular geometry:

<PRE>
  wz2dmap polar = new wz2Dpolar;
  cogenChart gen = new CogenChart(base-&gt;generator(),polar);
</PRE>

 <P>We can apply some conform affine transformations:

 <UL>
 <LI> <B>shift</B> defines a translation;
 <LI> <B>stretch</B> defines an isotropic stretch/shrink;
 <LI> <B>rotate</B> rotates in counter-clockwise direction, with angle
given in radian.
 <LI> <B>switchXY</B> switches the X and Y directions (reflection
for the line (y=x).
 </UL>

 <P>Subsequent operations will be composed. Note that the order matters.

<PRE>
  polar-&gt;rotate(0.7*wzPi);
  polar-&gt;switchXY();
  polar-&gt;stretch(2);
  polar-&gt;shift(10,-10);
  polar-&gt;print();
</PRE>

 <P>Then we compute the grid as usual:

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