cog.html

Delaunay三角形的网格剖分程序

<TITLE>COG 2.1: Cogeometry in COG</TITLE>

<H1>Cogeometry</H1>

 <P>Part of COG 2.1 is a modular C++ interface for geometry
description.  The key is the definition of the class <B>Cogeometry</B>
in
 <A HREF="cog.hxx"> cog.hxx</A>.

 <P>The class <B>Cogeometry</B> is an abstract class which defines the
interface between geometry description and their applications (for
example a grid generator).  A special case of such applications are
operations on geometry descriptions which define new geometry
descriptions depending on other geometry descriptions.

 <P>The notion <B><A HREF="cogeometry.html">cogeometry</A></B> for
this type of geometry description was created similar to the notion
<B>cohomology</B> in algebraic topology. 

<H3>Advantages</H3>

 <P>The main advantage of a cogeometry is that it is easy to create
and to modify.  As far, with "easy" we do not have in mind a very
beautiful user interface, but a more fundamental level.  That means,
it is easy to implement a new type of cogeometry or a new operation on
cogeometries. 

 <P>It is also possible to implement very wicked, strange
cogeometries. For example, even geometries with infinite complexity
like Julia sets may be described with our interface.

<H3>Problems</H3>

 <P>The easiness of implementation of a cogeometry is not for nothing.
Every application has to be able to handle - at least in the form of
appropriate error messages - all these wicked cogeometries. 

 <P>Moreover, some information which is usually available for almost
any classical geometry description is not available for a cogeometry.
This is a simple consequence of the fact that these data simply do not
exist for some wicked cogeometries, thus, they do not exist in the
general case.