fec

Arguments

x,y

two vectors of size n, (x(i),y(i)) gives the coordinates of node i

func

a vector of size n : func(i) gives the value at node i of the function for which we want the pseudo-color plot.

triangles

is a [Ntr,N+2] matrix. Each line of triangles specifies a convex polygon of the mesh triangles(j) = [number,node1,node2,node3, ..., nodeN, flag]. node1,node2,node3, ..., nodeN are the number of the nodes which constitutes the polygon. number is the number of the polygons and flag is an integer not used in the fec function.

<opt_args>

This represents a sequence of statements key1=value1, key2=value2,... where key1, key2,... can be one of the following: strf, leg, rect, nax, zminmax, colminmax, colout, mesh (see plot2d for the 4 first ones).

strf,leg,rect,nax

see plot2d

zminmax

vector with 2 components [zmin zmax] (useful in particular for animation)

colminmax

vector of 2 positives integers [colmin colmax]

colout

vector of 2 integers [under_min_col upper_max_col]

mesh

boolean scalar, default value %f (must be true if you want also display the mesh)

Description

This function is the good one to draw linear finite element solutions, based on polygons or simply to display a function defined on a polygon mapping. The color interpolation is done through software computation and so it is not too fast.

The function colorbar may be used to see the color scale (see the example section).

The zminmax argument gives the z values associated with the first and the last color (of the current colormap). More exactly if the colormap have nc colors and if we note dz = (zmax-zmin)/nc, then the part of the polygon mapping where zmin + (i-1)dz <= z < zmin + i dz is filled with the color i). By default zmin = min(func) and zmax = max(func). If you want to do an animation with func values that varies in time, take for zmin and zmax the global minimum and maximum or something close.

The colout argument lets the user choosing the colors for the 2 extremes regions {func < zmin} and {func > zmax}, under_min_col and upper_max_col may be equal (independently) to:

-1

in this case the same color than in the neighbouring zone is used (CAUTION: you do not see that the corresponding limit is crossed), this is the default case.

0

in this case the extreme region is not painting at all.

k

(k being a valid index to a color of the current colormap) the extreme region is painting in color k.

If you do not want to use the complete colormap you may use the colminmax argument with 1 <= colmin < colmax <= nc (nc being the number of colors of the current colormap) so as to use only the [colmin,colmax] sub-part of the colormap. (by default all the colors of the colormap are used).

Note that for historical reasons, the third input argument is called triangles, but fec accepts all types of convex polygons.

See the demo files demos/fec:

fec.ex1 is a simple demo file in which a mesh and a function on that mesh is completely built in Scilab syntax

fec.ex2 is an example for which the mesh and the function value where computed by an external mesh builder (amdba type mesh) and an external program. A set of macros ( provided in file macros.sci) can be used to read the data files in Scilab and plot the results.

Examples

// define a mini triangulation (4 vertices, 2 triangles)
x = [0 1 0 -1];
y = [0 0 1  1];
T = [1 1 2 3 1;
     2 3 4 1 1];
z = [0 1 0 -1];  // values of the func at each vertices
clf()
gcf().color_map = jet(64);
subplot(1,2,1)
  colorbar(-1,1)
  fec(x,y,T,z,strf="040",mesh=%t)
  xtitle("fec example (with the mesh)")
subplot(1,2,2)
  colorbar(-1,1)
  fec(x,y,T,z,strf="040")  // rmq: mesh=%f by default
  xtitle("fec example (without the mesh)")
show_window()

// define a mini triangulation (4 vertices, 2 triangles)
x = [0 1 0 -1];
y = [0 0 1  1];
T = [1 1 2 3 1;
     2 3 4 1 1];
z = [0 1 0 -1];  // values of the func at each vertices
// this example shows the effect of zminmax and uses the
// previous example data (you have to execute the it before)
clf()
gcf().color_map = jet(64);
colorbar(-0.5,0.5)  // be careful colorbar must be set by hands !
fec(x,y,T,z,strf="040", zminmax=[-0.5 0.5], mesh=%t)
xtitle("fec example : using zminmax argument")
show_window()

// define a mini triangulation (4 vertices, 2 triangles)
x = [0 1 0 -1];
y = [0 0 1  1];
T = [1 1 2 3 1;
     2 3 4 1 1];
z = [0 1 0 -1];  // values of the func at each vertices
// this example shows the effect of zminmax and colout. It uses
// also the data of the first example (you have to execute the it before)
clf()
gcf().color_map = jet(64);
subplot(2,2,1)
  colorbar(-0.5,0.5)
  fec(x,y,T,z,strf="040", zminmax=[-0.5 0.5], colout=[0 0], mesh=%t)
  xtitle("fec : using zminmax and colout =[0 0]")
subplot(2,2,2)
  colorbar(-0.5,0.5)
  fec(x,y,T,z,strf="040", zminmax=[-0.5 0.5], colout=[32 32], mesh=%t)
  xtitle("fec : using zminmax and colout =[32 32]")
subplot(2,2,3)
  colorbar(-0.5,0.5)
  fec(x,y,T,z,strf="040", zminmax=[-0.5 0.5], colout=[-1 0], mesh=%t)
  xtitle("fec : using zminmax and colout =[-1 0]")
subplot(2,2,4)
  colorbar(-0.5,0.5)
  fec(x,y,T,z,strf="040", zminmax=[-0.5 0.5], colout=[0 -1], mesh=%t)
  xtitle("fec : using zminmax and colout =[0 -1]")
show_window()

// define a mini triangulation (4 vertices, 2 triangles)
x = [0 1 0 -1];
y = [0 0 1  1];
T = [1 1 2 3 1;
     2 3 4 1 1];
z = [0 1 0 -1];  // values of the func at each vertices

// this example shows a feature from colminmax:
// playing with 2 colormaps for 2 subplots. It
// uses also the data of the first example.
clf()
gcf().color_map = [hot(64); jet(64)];
subplot(1,2,1)
  colorbar(-1,1,[1 64])
  fec(x,y,T,z,strf="040", colminmax=[1 64], mesh=%t)
  xtitle("fec using the hot colormap")
subplot(1,2,2)
  colorbar(-1,1,[65 128])
  fec(x,y,T,z,strf="040", colminmax=[65 128], mesh=%t)
  xtitle("fec using the jet colormap")
show_window()

// define a mapping with one quadrangle (4 vertices, 1 quadrangle)
x = [1 2 2 1];
y = [1 1 2 2];
T = [1 1 2 3 4 0];
z = [-1; -1; 1; 1];  // values of the func at each vertices

clf()
f = gcf();
f.color_map = jet(12);
colorbar(-1,1);
fec(x,y,T,z,mesh=%t)
xtitle("fec using the hot colormap, composed by one quadrangle")

See also

• colorbar — draws a vertical color bar
• Sfgrayplot — smooth 2D plot of a surface defined by a function using colors
• Sgrayplot — smooth 2D plot of a surface using colors

History