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The geometry package is | The geometry package is multipackage providing functions to manipulate geometrical entities in 2D and 3D. It is based in [http://sourceforge.net/apps/mediawiki/matgeom/index.php?title=Main_Page matGeom] and extends it with several other functionalities, e.g. the package provides interfaces with SVG files and polygon meshing using Gmsh. | ||
== | == Relation to matGeom == | ||
== | == octCLIP == | ||
=== | == Piece-wise 2D polynomial polygons == | ||
== Tutorials == | |||
=== Loading SVG files === | |||
'''<span style="color:#FF0000;">Coming soon</span>''' | |||
=== Meshing Octave === | |||
<!--'''<span style="color:#FF0000;">Under construction</span>''' --> | |||
This tutorial shows the workflow to generate a triangular mesh inside an arbitrary region. | |||
This tutorial requires that you install the package {{Forge|fpl}} and {{Forge|msh}} (which requires [http://geuz.org/gmsh/ Gmsh] installed in your system). Alternatively, the core function {{Codeline|delaunay}} could be used but the result aren't so pretty. | |||
This tutorial requires an interesting shape to mesh. If you have [http://inkscape.org/index.php?lang=en Inkscape] you can create one, and use the previous tutorial to load it into octave. Here I will be using [http://ubuntuone.com/5pNS12ZChUXeGNBniWNa3J this SVG]. | |||
[[File:octave.png|200px|center]] | |||
<!-- {{SyntaxHighlight| --> | |||
{{Code|Loading the file as polygon compatible with geometry package|<syntaxhighlight lang="octave" 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 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 lang="octave" style="font-size:13px"> | |||
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: | |||
{{Code|Generating mesh for plot with msh package|<syntaxhighlight lang="octave" style="font-size:13px"> | |||
pkg load msh | |||
filename = tmpnam (); | |||
meshsize = sqrt (mean (sumsq (diff (P, 1, 1), 2)))/2; | |||
data2geo (P, meshsize, "output", [filename ".geo"]); | |||
T = msh2m_gmsh (filename); | |||
</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. | |||
{{Code|Plotting mesh with fpl package|<syntaxhighlight lang="octave" style="font-size:13px"> | |||
pkg load fpl | |||
graphics_toolkit ('fltk') | |||
pdemesh (T.p, T.e, T.t); | |||
view (2) | |||
axis tight | |||
axis equal | |||
</syntaxhighlight>}} | |||
The output should look something like this | |||
[[File:octave_meshed.png|400px|center]] | |||
Questions? Ideas? Join us in the mailing list or in the #octave IRC channel. | |||
=== From piece-wise polynomial shapes to polygons === | |||
== See also == | == See also == | ||
* [http:// | * {{Forge|geometry}} at [[Octave Forge]] | ||
* [http://sourceforge.net/apps/mediawiki/matgeom/index.php?title=Main_Page matGeom] | |||
[[Category: | [[Category:Octave Forge]] | ||