mainwzrectangulartest.html

Delaunay三角形的网格剖分程序

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

<H1>Rectangular Coordinates</H1>

 <P>Rectangular coordinates are compositions of
 <A HREF="mainwz1dmaps.html">1D coordinates</A>.  The 1D coordinates
themself are rectangular coordinates in this sense too. But the more
interesting case are compositions of 1D coordinates into
 <A HREF="mainwz2dmaps.html">2D coordinates</A> defined by the class
<B>wz2Drectangular</B> and into
 <A HREF="mainwz3dmaps.html">3D coordinates</A> by
<B>wz3Drectangular</B>:

<PRE>
#include "coglib.hxx"
int main()
{
  wz1dmap cx = new wz1Dexp();
  wz1dmap cy = new wz1Dsinh();
  wz1dmap cz = new wz1Datan();
  wz2dmap c2 = new wz2Drectangular(cx,cy);
  wz3dmap c3 = new wz3Drectangular(cx,cy,cz);
</PRE>

 <P>There is also a similar way to compose 2D coordinates with 1D
coordinates to 3D cylindrical coordinates:

<PRE>
  wz3dmap c4 = new wz3Dcylindrical(c2,cz);
</PRE>

 <P>defines the same system of coordinates as c3 (in a slightly slower
implementation).

<H2>Values, affine transformations</H2>

 <P>Value computation and affine transformations are as usual for
 <A HREF="mainwz2dmaps.html">2D</A> resp.
 <A HREF="mainwz3dmaps.html">3D</A> coordinates.



 <P>The usual print method can be used:

<PRE>
  c2-&gt;print();
  c3-&gt;print();
  c4-&gt;print();

</PRE>

<H2>Compositions</H2>

 <P>An essential difference to usual coordinates is that there are
other composition operations - the natural composition operations.
Once they are not defined for the proxy classes <I>wz2dmap</I>
resp. <I>wz3dmap</I>, we have to define them for the classes
themself:

<PRE>
  wz2Drectangular *d2 = new wz2Drectangular();
  wz3Drectangular *d3 = new wz3Drectangular();
  wz3Dcylindrical *d4 = new wz3Dcylindrical();
  d2-&gt;composeX(cx);
  d2-&gt;composeY(cy);
  d3-&gt;composeX(cx);
  d3-&gt;composeY(cy);
  d3-&gt;composeZ(cz);
  d4-&gt;composeXY(c2);
  d4-&gt;composeZ(cz);
</PRE>

 <P>Note that, while we have named these coordinates rectangular, they
are no longer rectangular after rotating them.  So, don't wonder if
the coordinates are named rectangular and, below, it is written that
they are not - that's correct:

<PRE>
  d3-&gt;rotateZ(0.1);
  d3-&gt;print();
  fine();
}
</PRE>