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Geometry package

193 bytes removed, 08:34, 15 April 2012
[[File:octave.png|200px|center]]
<!-- <syntaxhighlight lang="matlab"> {{SyntaxHighlight| -->{{Code|Loading the file as polygon compatible with geometry package|{{SyntaxHighlight|<syntaxhighlight line="GESHI_FANCY_LINE_NUMBERS" lang="matlab" style="font-size:13px">
octavesvg = svg ("octave.svg").normalize();
ids = octavesvg.pathid();
P = octavesvg.path2polygon (ids{1}, 12)(1:end-1,:);
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 {{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 but as of version 1that uses the [http://en.4wikipedia.0, this function is very naïve and wont fix this problem. If you know how to simplify polygons you can contribute!We are going org/wiki/Ramer%E2%80%93Douglas%E2%80%93Peucker_algorithm Ramer-Douglas-Peucker algorithm] to reduce the amount thenumber of points of in the polygon in a drastic and destructive way (i.e. the shape may be considerably damaged). The codes to do so follows, in the future a better procedure will be published here.
{{Code|Symplification of a polygon compatible with geometry package|<syntaxhighlight line="GESHI_FANCY_LINE_NUMBERS" lang="matlab" style="font-size:13px">
Ps = P; n = 1e6;thrsd = 0.38; while n > size (Ps,1) n = size symplifypolygon(Ps,1); ds = sqrt (sumsq (Ps(1:end'tol',:) 1e- Ps([2:end 1],:3),2)); Ps = Ps(ds > mean (ds)*(1-thrsd),:); endwhos P PsP = Ps;
</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 {{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:
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