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Geometry package: Difference between revisions
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== Tutorials == | == Tutorials == | ||
=== Loading SVG files === | === Loading SVG files === | ||
'''<span style="color:#FF0000;">Coming soon</span>''' | |||
=== Meshing Octave === | === Meshing Octave === | ||
'''<span style="color:#FF0000;">Under construction</span>''' | <!--'''<span style="color:#FF0000;">Under construction</span>''' --> | ||
This tutorial shows the workflow to generate a triangular mesh inside an arbitrary region. | This tutorial shows the workflow to generate a triangular mesh inside an arbitrary region. | ||
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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 lang="octave" 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|< | {{Code|Plotting a polygon compatible with geometry package|<syntaxhighlight lang="matlab" style="font-size:13px"> | ||
drawPolygon (P, "-o"); | 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 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 lang="octave" style="font-size:13px"> | |||
{{Code|Symplification of a polygon compatible with geometry package|< | P = simplifypolygon(P, 'tol', 1e-3); | ||
</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: | ||
{{Code|Generating mesh for plot with msh package|< | {{Code|Generating mesh for plot with msh package|<syntaxhighlight lang="octave" style="font-size:13px"> | ||
pkg load msh | pkg load msh | ||
filename = tmpnam (); | filename = tmpnam (); | ||
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data2geo (P, meshsize, "output", [filename ".geo"]); | data2geo (P, meshsize, "output", [filename ".geo"]); | ||
T = msh2m_gmsh (filename); | T = msh2m_gmsh (filename); | ||
</ | </syntaxhighlight>}} | ||
<!-- </syntaxhighlight> --> | <!-- </syntaxhighlight> --> | ||
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. | 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|< | {{Code|Plotting mesh with fpl package|<syntaxhighlight lang="octave" style="font-size:13px"> | ||
pkg load fpl | pkg load fpl | ||
graphics_toolkit ('fltk') | graphics_toolkit ('fltk') | ||
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axis tight | axis tight | ||
axis equal | axis equal | ||
</ | </syntaxhighlight>}} | ||
The output should look something like this | The output should look something like this | ||
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* [http://sourceforge.net/apps/mediawiki/matgeom/index.php?title=Main_Page matGeom] | * [http://sourceforge.net/apps/mediawiki/matgeom/index.php?title=Main_Page matGeom] | ||
[[Category: | [[Category:Octave Forge]] | ||