Level sets of a scalar field

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Level sets of a scalar function

We show how to visualize level sets of scalar fields on plane regions with Octave UPM. We focus on the example in Dibujar un sólido 2-D, i.e. the rectangle [math] [-1/2,1/2]\times [0,2][/math] and the scalar field [math] f(x,y)=-\log (0.1+\sqrt{x^2+y^2})[/math]. We follow the steps:

  1. We introduce a sampling of the two segments with a suitable step
  2. With meshgrid command we define two matrixes with the x and y coordenates of the mesh points
  3. Compute the scalar field in the grid points.
  4. We use the contour command to draw the field and adjunst the axis. We see the picture from the top.

1 MATLAB code

 1 x=-0.5:0.1:0.5;       % sampling of the interval [-1/2,1/2]
 2 y=0:0.1:2;            % sampling of the interval [0,2]
 3 [xx,yy]=meshgrid(x,y); % matrixes of x and y coordinates
 4 figure(1)
 5 f=-log(0.1+sqrt(xx.^2+yy.^2)); % The scalar field
 6 contour(xx,yy,f)       % Draw the level sets
 7 hold on                % We draw the boundary below
 8 plot(x,x-x,'k','linewidth',1);
 9 plot(x,2+x-x,'k','linewidth',1);
10 plot(-0.5+y-y,y,'k','linewidth',1);
11 plot(0.5+y-y,y,'k','linewidth',1);
12 axis([-2,2,-1,3])      % select region for drawing
13 view(2)                % See the pisture from the top
14 colorbar               % Include colorbar

2 To go further

Mesh of a parametrized 2-D solid

Visualization of a scalar field in a solid

Visualization of vector fields in a solid

Dibujar un sólido 2-D