contour2dm

Arguments

x, y

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

polygons

is a [Ntr,N+2] matrix. Each line of polygons specifies a convex polygon of the mesh polygons(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 contour2dm function.

func

a vector of size n : func(i) gives the value at node i of the function.

nz

the level values or the number of levels.

If nz is an integer

its value gives the number of level curves equally spaced from zmin to zmax as follows:

z= zmin + (1:nz)*(zmax-zmin)/(nz+1)

If nz is a vector

nz(i) gives the value of the i-th level curve.

xc, yc

vectors of identical sizes containing the contours definitions. See below for details.

Description

contour2dm computes level curves of a surface z = f(x, y) on a 2D plot. The values of f(x,y) are given by the matrix z at the points of the mesh defined by x and y.

xc(1) contains the level associated with first contour path, yc(1) contains the number N1 of points defining this contour path and (xc(1+(1:N1)), yc(1+(1:N1)) ) contain the coordinates of the paths points. The second path begin at xc(2+N1) and yc(2+N1) and so on.

Note that some loops can appear on a level curve when some vertexes of polygons as the same value as the level one. See example #2

Examples

m = [6 5 4; ...
           6 2 5; ...
           6 4 1; ...
           5 2 3];

nodes = [55  20; ...
          85  5; ...
          100 10; ...
          75  30; ...
          80  20; ...
          70  15];
z_fec = [-1 -1 0 0 1 1];

f = scf();
f.color_map = jetcolormap(12);
fec(nodes(:, 1), nodes(:, 2), [(1:size(m, 1))', m, (1:size(m, 1))'], z_fec);
[xc, yc] = contour2dm(nodes(:,1), nodes(:,2), [(1:size(m, 1))', m, (1:size(m, 1))'], z_fec, [-0.5, 0, 0.5]);
k=1;n=yc(k);c=1;
N = size(xc, '*')
while k <= N & k+yc(k)<=N
  n=yc(k);
  plot2d(xc(k+(1:n)),yc(k+(1:n)));
  c=c+1;
  k=k+n+1;
end

f=scf();
f.color_map = jetcolormap(3);
m = [1  2  3; ...
     1  3  4; ...
     3  4  5; ...
     6  2  3; ...
     7  6  3; ...
     7  3  5; ...
     7  5  8; ...
     2  9  6; ...
     9  6  10; ...
     6  7  10; ...
     10 11 7; ...
     7  8  12; ...
     9  10 13; ...
     7  10 11; ...
     7  12 11; ...
     13 10 14; ...
     10 11 14; ...
     11 14 15; ...
     11 12 15];

nodes = [0  50; ... //1
         20 60; ... //2
         15 40; ... //3
         0  30; ... //4
         20 20; ... //5
         30 45; ... //6
         27 25; ... //7
         26 10; ... //8
         35 65; ... //9
         40 42; ... //10
         45 30; ... //11
         42 15; ... //12
         50 62; ... //13
         55 40; ... //14
         53 17]; //15

z = [0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 2, 2, 2];

nb_mesh = [(1:size(m, 1))', m, (1:size(m, 1))'];
fec(nodes(:, 1), nodes(:, 2), nb_mesh, z, mesh=%t);
e=gce();
e.children.foreground = -2;

// Contour2dm
[xc, yc] = contour2dm(nodes(:,1), nodes(:,2), nb_mesh, z, linspace(0,3,4));
k=1;n=yc(k);c=1;
N = size(xc, '*');
while k <= N & k+yc(k)<=N
    n=yc(k);
    plot2d(xc(k+(1:n)),yc(k+(1:n)));
    e=gce();
    e.children.foreground = -1;
    c=c+1;
    k=k+n+1;
end
// Here we have a loop in the green part because each vertex on this level curve is equal to 1.
// To be clearer, let us change the color_map
f.color_map = jetcolormap(1024);

See also

• contour2di — calcule les courbes de niveau d'une surface
• contour2d — level curves of a surface on a 2D plot
• contour — level curves on a 3D surface
• fec — dessin en pseudo-couleurs d'une surface définie sur un maillage constitué de polygones convexes
• plot2d — 2D plot

History