cogmaptest.html

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<TITLE>COG 1.0 - CogeometrySimpleMap</TITLE>

<H2>class <A NAME="Map">CogeometrySimpleMap</A></H2>

<PRE>
#include &lt;math.h&gt;
#include "cogfunction.hxx"
</PRE>

 <P>This class allows to define an arbitrary transformation of a
geometry by a map f: X -&gt; Y:

<PRE>
static void Map(cogPoint&amp; y, const cogPoint&amp; x)
{
 y[0] = x[0]  + 0.15*sin(5*x[1]);
 y[1] = x[1]  + 0.15*sin(5*x[2]);
 y[2] = x[2]  + 0.15*sin(5*x[0]);
}
</PRE>

The function Map has to define the coordinates y[0], y[1], y[2] of y
dependent on x.  The mapping is assumed to be continuous, it will work
better if it is smooth. But it has not to be reversible, may be a
projection or an embedding.

<PRE>

cogeometry	test_cogeometry()
{
  cogeometry original = test_cogeometry_1();
  return new CogeometrySimpleMap(<A HREF="#Map">Map</A>,original);
}
</PRE>

<H2>Modification for Local Parameter Dependence</H2>

 <P>Of course, global parameters are not a problem. But you may want
to define a general scheme of a cogeometry by a parameter-dependent
function, and to define a cogeometry which depends on these parameters
locally, in the sense that a change of these parameters for on
geometry does not change the parameters for another. A function
depending on global parameters doesn't help. In this case, I recommend
to define an own class. Name it
<B>Cogeometry<I>WhateverYouWant</I></B>, and simply use the scheme of
definition of the class <B>CogeometrySimpleMap</B> which is defined in
<A HREF="cogfunction.hxx">cogfunction.hxx</A>.  Examples you can find
in <A HREF="cogmap.hxx">cogmap.hxx</A>

<PRE>
#ifdef test_cogeometry
this code can be used only in cogtest.cxx !!!!!  see test.html#parameters for more;
#endif
</PRE>