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Geometry package: Difference between revisions
→Meshing Octave
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<!-- <syntaxhighlight lang="matlab"> --> | <!-- <syntaxhighlight lang="matlab"> --> | ||
{{Code|Loading the file as polygon compatible with geometry package| | {{Code|Loading the file as polygon compatible with geometry package|subst:{{SyntaxHighlight| | ||
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)); | ||
}} | |||
}} | |||
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 line="GESHI_FANCY_LINE_NUMBERS" 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 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 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! | ||
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. | 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|< | {{Code|Symplification of a polygon compatible with geometry package|<syntaxhighlight line="GESHI_FANCY_LINE_NUMBERS" lang="matlab" style="font-size:13px"> | ||
Ps = P; | Ps = P; | ||
n = 1e6; | n = 1e6; | ||
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whos P Ps | whos P Ps | ||
P = Ps; | P = Ps; | ||
</ | </syntaxhighlight>}} | ||
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 line="GESHI_FANCY_LINE_NUMBERS" lang="matlab" 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 line="GESHI_FANCY_LINE_NUMBERS" lang="matlab" 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 | ||