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Geometry package

160 bytes removed, 08:55, 15 April 2012
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<!-- {{SyntaxHighlight| -->
{{Code|Loading the file as polygon compatible with geometry package|<syntaxhighlight line="GESHI_FANCY_LINE_NUMBERS" lang="matlab" style="font-size:13px">
octavesvg = svg ("octave.svg").normalize();
ids = octavesvg.pathid();
Now we have our SVG as a polygon compatible with the Geometry package format. You can plot the polygon using the function {{Codeline|drawPolygon}}.
{{Code|Plotting a polygon compatible with geometry package|<syntaxhighlight line="GESHI_FANCY_LINE_NUMBERS" lang="matlab" style="font-size:13px">
drawPolygon (P, "-o");
</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 (> 1.5.0) comes with a simplification function that uses the [http://en.wikipedia.org/wiki/Ramer%E2%80%93Douglas%E2%80%93Peucker_algorithm Ramer-Douglas-Peucker algorithm] to reduce thenumber of points in the polygon.
{{Code|Symplification of a polygon compatible with geometry package|<syntaxhighlight line="GESHI_FANCY_LINE_NUMBERS" lang="matlab" style="font-size:13px">
P = symplifypolygon(Ps, 'tol', 1e-3);
</syntaxhighlight>}}
The next step is to mesh the interior of the polygon. To do this we could just call {{Codeline|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 {{Forge|msh}}, which requires [http://geuz.org/gmsh/ Gmsh] installed in your system. The function {{Codeline|data2geo}} in the Geometry package makes our work very easy:
{{Code|Generating mesh for plot with msh package|<syntaxhighlight line="GESHI_FANCY_LINE_NUMBERS" lang="matlab" style="font-size:13px">
pkg load msh
filename = tmpnam ();
After this code finishes, the structure T contains our mesh. To plot the generated mesh we use the function {{Codeline|pdemesh}} from the {{Forge|fpl}} package. In general is a good idea to use the openGL render (called ''fltk'') to plot meshes.
{{Code|Plotting mesh with fpl package|<syntaxhighlight line="GESHI_FANCY_LINE_NUMBERS" lang="matlab" style="font-size:13px">
pkg load fpl
graphics_toolkit ('fltk')
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