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m (→Meshing Octave) |
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[[File:octave.png|200px|center]] | [[File:octave.png|200px|center]] | ||
<!-- | <!-- {{SyntaxHighlight| --> | ||
{{Code|Loading the file as polygon compatible with geometry package| | {{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 | 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"> | {{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>}} | </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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