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| 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. | | The geometry package is multipackage providing functions to manipulate geometrical entities in 2D and 3D. |
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| == Relation to matGeom == | | == Realtion to matGeom == |
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| == octCLIP == | | == Extensions == |
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| == Piece-wise 2D polynomial polygons == | | === octCLIP === |
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| == Tutorials ==
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| === Loading SVG files ===
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| '''<span style="color:#FF0000;">Coming soon</span>'''
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| === Meshing Octave ===
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| <!--'''<span style="color:#FF0000;">Under construction</span>''' -->
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| This tutorial shows the workflow to generate a triangular mesh inside an arbitrary region.
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| 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.
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| 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].
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| [[File:octave.png|200px|center]]
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| <!-- {{SyntaxHighlight| -->
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| {{Code|Loading the file as polygon compatible with geometry package|<syntaxhighlight lang="octave" style="font-size:13px">
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| octavesvg = svg ("octave.svg").normalize();
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| ids = octavesvg.pathid();
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| P = octavesvg.path2polygon (ids{1}, 12)(1:end-1,:);
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| P = bsxfun (@minus, P, centroid (P));
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| </syntaxhighlight>}}
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| Now we have our SVG as a polygon compatible with the Geometry package format. You can plot the polygon using the function {{Codeline|drawPolygon}}.
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| {{Code|Plotting a polygon compatible with geometry package|<syntaxhighlight lang="matlab" style="font-size:13px">
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| drawPolygon (P, "-o");
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| </syntaxhighlight>}}
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| 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.
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| {{Code|Symplification of a polygon compatible with geometry package|<syntaxhighlight lang="octave" style="font-size:13px">
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| P = simplifypolygon(P, 'tol', 1e-3);
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| </syntaxhighlight>}}
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| You should play with the tolerance option until you get a nice polygon.
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| 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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| {{Code|Generating mesh for plot with msh package|<syntaxhighlight lang="octave" style="font-size:13px">
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| pkg load msh
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| filename = tmpnam ();
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| meshsize = sqrt (mean (sumsq (diff (P, 1, 1), 2)))/2;
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| data2geo (P, meshsize, "output", [filename ".geo"]);
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| T = msh2m_gmsh (filename);
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| </syntaxhighlight>}}
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| <!-- </syntaxhighlight> -->
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| 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.
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| {{Code|Plotting mesh with fpl package|<syntaxhighlight lang="octave" style="font-size:13px">
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| pkg load fpl
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| graphics_toolkit ('fltk')
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| pdemesh (T.p, T.e, T.t);
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| view (2)
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| axis tight
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| axis equal
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| </syntaxhighlight>}}
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| The output should look something like this
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| [[File:octave_meshed.png|400px|center]]
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| Questions? Ideas? Join us in the mailing list or in the #octave IRC channel.
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| === From piece-wise polynomial shapes to polygons ===
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| == See also == | | == See also == |
| * {{Forge|geometry}} at [[Octave Forge]]
| | * [http://octave.sourceforge.net/geometry/overview.html function reference] at [[Octave Forge]]. |
| * [http://sourceforge.net/apps/mediawiki/matgeom/index.php?title=Main_Page matGeom] | |
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| [[Category:Octave Forge]] | | [[Category:Packages|Package documentation]] |