tutorial.html

Delaunay三角形的网格剖分程序

<TITLE>COG 2.1: Tutorial</TITLE>

<H1>Tutorial</H1>

 <P>I hope, the technical problems of <A HREF="install.html">
installation</A> of COG have been solved.  Now you want to learn how
to use COG.  In my experience, the best way to learn something is by
modification of working code examples.  That's why I have designed the
documentation in this way: as a collection of documented working code
examples.

 <P>In this tutorial, we start with simple geometries and ad, step by
step, new features:

<H2>Rectangular Geometries</H2>

 <P>Let's start with the
 <A HREF="mainstarttest.html">standard cube (six tetrahedra)</A>.
 Then, let's learn how to define
 <A HREF="mainoctreetest.html">2D rectangular</A>
 and <A HREF="mainwedgetest.html">triangular</A> geometries
 and <A HREF="mainfacetest.html">boundary conditions</A>:
  <BR><A HREF="mainstarttest.html"><IMG SRC="starttest.gif"></A>
  <A HREF="mainoctreetest.html"><IMG SRC="octreetest.gif"></A>
  <A HREF="mainfacetest.html"><IMG SRC="facetest.gif"></A>

 <P>Now you already know how to this in
 <A HREF="mainoctree3dtest.html">3D</A> as in the following
 <A HREF="mainfbh1test.html">FBH example Nr.1</A>.

<H2>Local Refinement</H2>

 <P>The next step is <A HREF="mainreftest.html">local refinement</A>.
You can define isotropic and anisotropic refinement
 in a <A HREF="mainreftest.html">region</A>,
 around a <A HREF="mainreftest.html">point</A>,
 in a <A HREF="mainoctreereftest.html">box</A>,
 in a <A HREF="mainwedgetest.html">triangle</A>.
 <P><A HREF="mainreftest.html"><IMG SRC="reftest.gif"></A>
 <A HREF="mainoctreereftest.html"><IMG SRC="octreereftest.gif"></A>
 <A HREF="mainwedgetest.html"><IMG SRC="wedgetest.gif"></A>

<H2>Other coordinates</H2>

 <P>Based on these rectangular techniques we can define curved  Usage of curved coordinates, starting with
 <A HREF="mainpolartest.html">polar coordinates</A> (see also
 <A HREF="mainspheretest.html">spherical coordinates</A>,
 <A HREF="mainwzcomplextest.html">complex analytic coordinates</A>,
 <A HREF="mainshuktest.html">Shukovski transformation</A>).

 <P><A HREF="mainpolartest.html"><IMG SRC="polartest.gif"></A>
 <A HREF="mainspheretest.html"><IMG SRC="spheretest.gif"></A>
 <A HREF="mainwzcomplextest.html"><IMG SRC="wz2dwing.gif"></A>
 <A HREF="mainshuktest.html"><IMG SRC="shuktest.gif"></A>

<H2>Unions, Intersections</H2>

 <P> Combination of different geometries defined in different
coordinates, starting with the
 <A HREF="mainuniontest.html">union</A> (see also
 TEAM example <A HREF="mainteam7test.html"> Nr.7</A>,
 FBH example
 <A HREF="mainfbh2test.html">Nr.2</A>)

 <P><A HREF="mainuniontest.html"><IMG SRC="union1test.gif"></A>
 <A HREF="mainfbh2test.html"><IMG SRC="fbh2test.gif"></A>

<H2>Using Other Cogenerator for a Cogeometry</H2>

 <P>Until now, we have created the geometry description and the grid
generator input together.  But an essential property of the algorithm
is that these two parts are independent.  The geometry description
used in COG - named <B>cogeometry</B> - may be defined independently.

 <P>For example, you can extract the cogeometry from one of the
previous examples and use the grid generator of another example to
create a grid for this cogeometry.  Of course, the resultat will be
less beautiful in comparison with the previous examples.

 <P>Now, we have prepared some standard <B>cogenerators</B> which may
be used to create grids for various parts of the same cogeometry:

 <UL>
 <LI> intersection with the
 <A HREF="maincogtest.html">cube [-1,1]<SUP>3</SUP></A>,
 <LI> intersection with the
 <A HREF="maincog3dtest.html">cube [0,1]<SUP>3</SUP></A>,
 <LI> intersection with the
 <A HREF="maincog2dtest.html">rectangle [-1,1]<SUP>2</SUP></A> at z=0.4,
 <LI> intersection with the
 <A HREF="maincog1dtest.html">segment [-1,1]</A> at y=z=0.4,
 <LI> intersection with a
 <A HREF="maincogpolartest.html">unit disc</A> at z=0.2,
 </UL>

<H2>Using Functions</H2>

 <P>In COG, different <A HREF="mainfunctiontest.html">functions</A>
may be used: grid functions as well as internal C++ functions.  They
may be used, for example, to define
 <A HREF="mainrefisotest.html">isotropic</A> and
 <A HREF="mainrefanisotest.html">anisotropic</A> refinement criteria or
 <A HREF="maincharfunctest.html">characteristic functions</A> of regions:

 <P><A HREF="mainrefisotest.html"><IMG SRC="refisotest.gif"></A>
 <A HREF="mainrefanisotest.html"><IMG SRC="refanisotest.gif"></A>
 <A HREF="maincharfunctest.html"><IMG SRC="charfunctest.gif"></A>

<H2>Using Pixmaps</H2>

 <P>Another input possibility are <B>pixmaps</B> - as in
 <A HREF="mainpixmaptest.html">two dimensions</A>, as in .
 <A HREF="mainvoxmaptest.html">three dimensions</A>
 (<A HREF="mainkiefertest.html">CT example</A>):

 <P><A HREF="mainpixmaptest.html"><IMG SRC="pixmaptest.gif"></A>
 <A HREF="mainvoxmaptest.html"><IMG SRC="voxmaptest.gif"></A>


<H2>Creating Cogeometries</H2>

 <P>For the previously considered standard cogenerators we can
 <A HREF="cogcogentest.html">extract the related cogeometry</A>.
 This already defines a large class of geometries: rectangular
domains, their images in curved coordinates, and unions and
intersections of these objects.

 <P>Nonetheless, a cogeometry may be defined also by other
methods. Here we have listed some of them:

 <UL>
 <LI> <A HREF="cogregiontest.html">using a function region(x)</A>;
 <LI> <A HREF="cogfacetest.html">defining boundary conditions with a
function face(x)</A>;
 </UL>


 <P><B><A NAME=warranty>Warning</A>:</B>This distribution contains
also some other direct methods.  They should be considered as
obsolete. The reason is that for cogeometries with a more or less
natural choice of a cogenerator I plan to implement such a
cogenerator. In this case, the direct method will be replaced by the
 <A HREF="cogcogentest.html">extraction of the cogeometry</A> from the
new standard cogenerator.

<H2>Other possibilities</H2>

 <UL>
 <LI> Creating non-Delaunay grids for
 <A HREF="mainprofiletest.html"> geological profiles</A>.
 <LI> Creating a regular <A HREF="maincontinuationtest.html">3D
continuation</A> of a given 2D grid.
 <LI> <A HREF="wztutorial.html">WZ 1.0: the C++ library</A> used in
COG.
 </UL>

<H2>Output</H2>

 <P><A HREF="mainmaterialtest.html">Writing out materials</A> instead
of regions allows you to write out parts of the grid and identify
different regions:

 <P><A HREF="mainmaterialtest.html"><IMG SRC="materialtest.gif"></A>

<H2>Graphics</H2>

<UL>
<LI> <A HREF="maingridviewtest.html">viewing a grid</A>
<LI> <A HREF="maincogviewtest.html">viewing a geometry</A>
<LI> <A HREF="wzwindow.html">general help for the viewer</A>
<LI> <A HREF="wzgridview.html">grid-specific help for the viewer</A>
<LI> <A HREF="cogview.html">geometry-specific help for the viewer</A>
</UL>

<H2>Problems</H2>

<UL>
<LI> <A HREF="noderemoval.html">Removing some nodes</A>
</UL>