Geometry package: Difference between revisions

193 bytes removed ,  15 April 2012
Line 19: Line 19:
[[File:octave.png|200px|center]]
[[File:octave.png|200px|center]]


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{{Code|Loading the file as polygon compatible with geometry package|{{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();
octavesvg = svg ("octave.svg").normalize();
ids      = octavesvg.pathid();
ids      = octavesvg.pathid();
P        = octavesvg.path2polygon (ids{1}, 12)(1:end-1,:);
P        = octavesvg.path2polygon (ids{1}, 12)(1:end-1,:);
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 {{Codeline|drawPolygon}}.  
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">
{{Code|Plotting a polygon compatible with geometry package|<syntaxhighlight line="GESHI_FANCY_LINE_NUMBERS" lang="matlab" style="font-size: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 but as of version 1.4.0, this function is very naïve and wont fix this problem. If you know how to simplify polygons you can contribute!
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.
We are going to reduce the amount of points of 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">
{{Code|Symplification of a polygon compatible with geometry package|<syntaxhighlight line="GESHI_FANCY_LINE_NUMBERS" lang="matlab" style="font-size:13px">
Ps = P;
P  = symplifypolygon(Ps, 'tol', 1e-3);  
n  = 1e6;
thrsd = 0.38;
while n > size (Ps,1)
  n = size (Ps,1);
  ds = sqrt (sumsq (Ps(1:end,:) - Ps([2:end 1],:),2));
  Ps = Ps(ds > mean (ds)*(1-thrsd),:);
end
whos P Ps
P  = Ps;  
</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 {{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:
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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