Difference between revisions of "Geometry package"

From Octave
Jump to navigation Jump to search
Line 43: Line 43:
=== From piece-wise polynomial shapes to polygons ===
=== From piece-wise polynomial shapes to polygons ===

Revision as of 07:08, 8 March 2012

The geometry package is multipackage providing functions to manipulate geometrical entities in 2D and 3D.

Relation to matGeom


Piece-wise 2D polynomial polygons


Loading SVG files

Meshing Octave

Under construction

This tutorial shows the workflow to generate a triangular mesh inside an arbitrary region. This tutorial requires that you install the package fpl and msh (which requires Gmsh installed in your system). Alternatively, the core function delaunay could be used (the tutorial explains how) but the result aren't so pretty.

The first part of the tutorial requires an interesting shape. If you have Inkscape you can use the previous tutorial to load it into octave. Here I will be using this SVG.

Code: Loading the file as polygon compatible with geometry package
octavesvg = svg ("octave.svg").normalize();
ids       = octavesvg.pathid();
P         = octavesvg.path2polygon (ids{1}, 12)(1:end-1,:);
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 drawPolygon. the next step is to mesh the interior of the polygon. To do this we could just call 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 msh, which requires Gmsh installed in your system. The function data2geo in the Geometry package makes our work very easy:

Code: Generating mesh for plot with msh package
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);

To plot the generated mesh we use the function pdemesh from the fpl package.

Code: Plotting mesh with fpl package
pkg load fpl 
pdemesh (T.p, T.e, T.t)
Octave meshed.png

From piece-wise polynomial shapes to polygons

See also