Difference between revisions of "Geometry package"
m (→Meshing Octave) 

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[[File:octave.png200pxcenter]]  [[File:octave.png200pxcenter]]  
−  <!  +  <! {{SyntaxHighlight > 
−  {{CodeLoading the file as polygon compatible with geometry package  +  {{CodeLoading the file as polygon compatible with geometry package<syntaxhighlight line="GESHI_FANCY_LINE_NUMBERS" lang="matlab" style="fontsize:13px"> 
octavesvg = svg ("octave.svg").normalize();  octavesvg = svg ("octave.svg").normalize();  
ids = octavesvg.pathid();  ids = octavesvg.pathid();  
P = octavesvg.path2polygon (ids{1}, 12)(1:end1,:);  P = octavesvg.path2polygon (ids{1}, 12)(1:end1,:);  
P = bsxfun (@minus, P, centroid (P));  P = bsxfun (@minus, P, centroid (P));  
−  }}  +  </syntaxhighlight>}} 
−  +  
Now we have our SVG as a polygon compatible with the Geometry package format. You can plot the polygon using the function {{CodelinedrawPolygon}}.  Now we have our SVG as a polygon compatible with the Geometry package format. You can plot the polygon using the function {{CodelinedrawPolygon}}.  
{{CodePlotting a polygon compatible with geometry package<syntaxhighlight line="GESHI_FANCY_LINE_NUMBERS" lang="matlab" style="fontsize:13px">  {{CodePlotting a polygon compatible with geometry package<syntaxhighlight line="GESHI_FANCY_LINE_NUMBERS" lang="matlab" style="fontsize:13px">  
drawPolygon (P, "o");  drawPolygon (P, "o");  
</syntaxhighlight>}}  </syntaxhighlight>}}  
−  As you can see the polygon has lots of points. We need to simplify the polygon in order to obtain a mesh of reasonable size. Otherwise gmsh will have problems meshing and the result could be huge (or a segmentation fault :( ). The package geometry comes with a simplification function  +  As you can see the polygon has lots of points. We need to simplify the polygon in order to obtain a mesh of reasonable size. Otherwise gmsh will have problems meshing and the result could be huge (or a segmentation fault :( ). The package geometry (> 1.5.0) comes with a simplification function that uses the [http://en.wikipedia.org/wiki/Ramer%E2%80%93Douglas%E2%80%93Peucker_algorithm RamerDouglasPeucker algorithm] to reduce thenumber of points in the polygon. 
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{{CodeSymplification of a polygon compatible with geometry package<syntaxhighlight line="GESHI_FANCY_LINE_NUMBERS" lang="matlab" style="fontsize:13px">  {{CodeSymplification of a polygon compatible with geometry package<syntaxhighlight line="GESHI_FANCY_LINE_NUMBERS" lang="matlab" style="fontsize:13px">  
−  +  P = symplifypolygon(Ps, 'tol', 1e3);  
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</syntaxhighlight>}}  </syntaxhighlight>}}  
+  You should play with the tolerance option until you get a nice polygon.  
The next step is to mesh the interior of the polygon. To do this we could just call {{Codelinedelaunay}} on the polygon and be done with it, but in general such mesh wont be so nice (you will need to add interior points). A very effective way of generating a good mesh is to use the package {{Forgemsh}}, which requires [http://geuz.org/gmsh/ Gmsh] installed in your system. The function {{Codelinedata2geo}} in the Geometry package makes our work very easy:  The next step is to mesh the interior of the polygon. To do this we could just call {{Codelinedelaunay}} on the polygon and be done with it, but in general such mesh wont be so nice (you will need to add interior points). A very effective way of generating a good mesh is to use the package {{Forgemsh}}, which requires [http://geuz.org/gmsh/ Gmsh] installed in your system. The function {{Codelinedata2geo}} in the Geometry package makes our work very easy: 
Revision as of 08:34, 15 April 2012
The geometry package is multipackage providing functions to manipulate geometrical entities in 2D and 3D. It is based in matGeom and extends it with several other functionalities, e.g. the package provides interfaces with SVG files and polygon meshing using Gmsh.
Contents
Relation to matGeom
octCLIP
Piecewise 2D polynomial polygons
Tutorials
Loading SVG files
Meshing Octave
Under construction
This tutorial shows the workflow to generate a triangular mesh inside an arbitrary region.
This tutorial requires that you install the package fpl and msh (which requires Gmsh installed in your system). Alternatively, the core function delaunay
could be used but the result aren't so pretty.
This tutorial requires an interesting shape to mesh. If you have Inkscape you can create one, and use the previous tutorial to load it into octave. Here I will be using this SVG.
Code: Loading the file as polygon compatible with geometry package 
1 octavesvg = svg ("octave.svg").normalize();
2 ids = octavesvg.pathid();
3 P = octavesvg.path2polygon (ids{1}, 12)(1:end1,:);
4 P = bsxfun (@minus, P, centroid (P));

Now we have our SVG as a polygon compatible with the Geometry package format. You can plot the polygon using the function drawPolygon
.
Code: Plotting a polygon compatible with geometry package 
1 drawPolygon (P, "o");

As you can see the polygon has lots of points. We need to simplify the polygon in order to obtain a mesh of reasonable size. Otherwise gmsh will have problems meshing and the result could be huge (or a segmentation fault :( ). The package geometry (> 1.5.0) comes with a simplification function that uses the RamerDouglasPeucker algorithm to reduce thenumber of points in the polygon.
Code: Symplification of a polygon compatible with geometry package 
1 P = symplifypolygon(Ps, 'tol', 1e3);

You should play with the tolerance option until you get a nice polygon.
The next step is to mesh the interior of the polygon. To do this we could just call delaunay
on the polygon and be done with it, but in general such mesh wont be so nice (you will need to add interior points). A very effective way of generating a good mesh is to use the package msh, which requires Gmsh installed in your system. The function data2geo
in the Geometry package makes our work very easy:
Code: Generating mesh for plot with msh package 
1 pkg load msh
2 filename = tmpnam ();
3 meshsize = sqrt (mean (sumsq (diff (P, 1, 1), 2)))/2;
4 data2geo (P, meshsize, "output", [filename ".geo"]);
5 T = msh2m_gmsh (filename);

After this code finishes, the structure T contains our mesh. To plot the generated mesh we use the function pdemesh
from the fpl package. In general is a good idea to use the openGL render (called fltk) to plot meshes.
Code: Plotting mesh with fpl package 
1 pkg load fpl
2 graphics_toolkit ('fltk')
3 pdemesh (T.p, T.e, T.t);
4 view (2)
5 axis tight
6 axis equal

The output should look something like this
Questions? Ideas? Join us in the mailing list or in the #octave IRC channel.