# Visualization#

Results created by the finite element method can be a huge set of data, so it is very important to render them easy to grasp.

There are two ways of visualization in FreeFem++:

• One, the default view, which supports the drawing of meshes, isovalues of real FE-functions, and of vector fields, all by the command plot (see Plot section below). For publishing purpose, FreeFem++ can store these plots as postscript files.

• Another method is to use external tools, for example, gnuplot (see Gnuplot section, medit section, Paraview section) using the command system to launch them and/or to save the data in text files.

## Plot#

With the command plot, meshes, isovalues of scalar functions, and vector fields can be displayed.

The parameters of the plot command can be meshes, real FE functions, arrays of 2 real FE functions, arrays of two double arrays, to plot respectively a mesh, a function, a vector field, or a curve defined by the two double arrays.

Note

The length of an arrow is always bound to be in [5‰, 5%] of the screen size in order to see something.

The plot command parameters are listed in the Reference part.

The keyboard shortcuts are :

• enter tries to show plot
• p previous plot (10 plots saved)
• ? shows this help
• +,- zooms in/out around the cursor 3/2 times
• = resets the view
• r refreshes plot
• up, down, left, right special keys to tanslate
• 3 switches 3d/2d plot keys :

- z,Z focal zoom and zoom out - H,h increases or decreases the Z scale of the plot - mouse motion - left button rotates - right button zooms (ctrl+button on mac) - right button +alt tanslates (alt+ctrl+button on mac)

• a,A increases or decreases the arrow size

• B switches between showing the border meshes or not
• i,I updates or not: the min/max bound of the functions to the window
• n,N decreases or increases the number of iso value arrays
• b switches between black and white or color plotting
• g switches between grey or color plotting
• f switches between filling iso or iso line
• l switches between lighting or not
• v switches between show or not showing the numerical value of colors
• m switches between show or not showing the meshes
• w window dump in file ffglutXXXX.ppm
• * keep/drop viewpoint for next plot
• k complex data / change view type
• ESC closes the graphics process before version 3.22, after no way to close
• otherwise does nothing

For example:

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 real[int] xx(10), yy(10); mesh Th = square(5,5); fespace Vh(Th, P1); //plot scalar and vectorial FE function Vh uh=x*x+y*y, vh=-y^2+x^2; plot(Th, uh, [uh, vh], value=true, ps="three.eps", wait=true); //zoom on box defined by the two corner points [0.1,0.2] and [0.5,0.6] plot(uh, [uh, vh], bb=[[0.1, 0.2], [0.5, 0.6]], wait=true, grey=true, fill=true, value=true, ps="threeg.eps"); //compute a cut for (int i = 0; i < 10; i++){ x = i/10.; y = i/10.; xx[i] = i; yy[i] = uh; //value of uh at point (i/10., i/10.) } plot([xx, yy], ps="likegnu.eps", wait=true); 
Fig. 1: mesh, isovalue, and vector Fig. 2: Enlargement in grey of isovalue, and vector

Fig. 3: Plots a cut of uh. Note that a refinement of the same can be obtained in combination with gnuplot

To change the color table and to choose the value of iso line you can do :

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 // from: \url{http://en.wikipedia.org/wiki/HSV_color_space} // The HSV (Hue, Saturation, Value) model defines a color space // in terms of three constituent components: // HSV color space as a color wheel // Hue, the color type (such as red, blue, or yellow): // Ranges from 0-360 (but normalized to 0-100% in some applications, like here) // Saturation, the "vibrancy" of the color: Ranges from 0-100% // The lower the saturation of a color, the more "grayness" is present // and the more faded the color will appear. // Value, the brightness of the color: Ranges from 0-100% mesh Th = square(10, 10, [2*x-1, 2*y-1]); fespace Vh(Th, P1); Vh uh=2-x*x-y*y; real[int] colorhsv=[ // color hsv model 4./6., 1 , 0.5, // dark blue 4./6., 1 , 1, // blue 5./6., 1 , 1, // magenta 1, 1. , 1, // red 1, 0.5 , 1 // light red ]; real[int] viso(31); for (int i = 0; i < viso.n; i++) viso[i] = i*0.1; plot(uh, viso=viso(0:viso.n-1), value=true, fill=true, wait=true, hsv=colorhsv); 
Fig. 4: hsv color cylinder Fig. 5: isovalue with an other color table

Note

See HSV.edp for the complete script.

Example Membrane shows how to generate a gnuplot from a FreeFem++ file. Here is another technique which has the advantage of being online, i.e. one doesn't need to quit FreeFem++ to generate a gnuplot.

However, this works only if gnuplot is installed, and only on an Unix-like computer.

Add to the previous example:

 1 2 3 4 5 6 7 8 9 {// file for gnuplot ofstream gnu("plot.gp"); for (int i = 0; i < n; i++) gnu << xx[i] << " " << yy[i] << endl; } // to call gnuplot command and wait 5 second (due to the Unix command) // and make postscript plot exec("echo 'plot \"plot.gp\" w l \n pause 5 \n set term postscript \n set output \"gnuplot.eps\" \n replot \n quit' | gnuplot"); 
Fig. 6: Plots a cut of uh with gnuplot

Note

See Plot.edp for the complete script.

As said above, medit is a freeware display package by Pascal Frey using OpenGL. Then you may run the following example.

Now medit software is included in FreeFem++ under ffmedit name.

The medit command parameters are listed in the Reference part.

Fig. 7: medit plot

With version 3.2 or later

 1 2 3 4 5 6 7 8 load "medit" mesh Th = square(10, 10, [2*x-1, 2*y-1]); fespace Vh(Th, P1); Vh u=2-x*x-y*y; medit("u", Th, u); 

Before:

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 mesh Th = square(10, 10, [2*x-1, 2*y-1]); fespace Vh(Th, P1); Vh u=2-x*x-y*y; savemesh(Th, "u", [x, y, u*.5]); //save u.points and u.faces file // build a u.bb file for medit { ofstream file("u.bb"); file << "2 1 1 " << u[].n << " 2 \n"; for (int j = 0; j < u[].n; j++) file << u[][j] << endl; } //call medit command exec("ffmedit u"); //clean files on unix-like OS exec("rm u.bb u.faces u.points"); 

Note

See Medit.edp for the complete script.

One can also export mesh or results in the .vtk format in order to post-process data using Paraview.

  1 2 3 4 5 6 7 8 9 10 load "iovtk" mesh Th = square(10, 10, [2*x-1, 2*y-1]); fespace Vh(Th, P1); Vh u=2-x*x-y*y; int[int] Order = [1]; string DataName = "u"; savevtk("u.vtu", Th, u, dataname=DataName, order=Order); 
Fig. 8: Paraview plot

Note

See Paraview.edp for the complete script.

In order to create plots from FreeFem++ simulations in Octave and Matlab the FEM mesh and the FE function must be exported to text files:

  1 2 3 4 5 6 7 8 9 10 mesh Th = square(10, 10, [2*x-1, 2*y-1]); fespace Vh(Th, P1); Vh u=2-x*x-y*y; savemesh(Th,"export_mesh.msh"); ofstream file("export_data.txt"); for (int j=0; j

Within Matlab or Octave the files can be processed with the ffmatlib library:

 1 2 3 4 5 addpath('path to ffmatlib'); [p,b,t]=ffreadmesh('export_mesh.msh'); u=ffreaddata('export_data.txt'); ffpdeplot(p,b,t,'XYData',u,'ZStyle','continuous','Mesh','on'); grid; `

Fig. 9: Matlab / Octave plot

Note

For more Matlab / Octave plot examples have a look at the tutorial section Matlab / Octave Examples or visit the ffmatlib library at github.