# Visualization of a scalar field in a solid

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Scalar field in a rectangular solid

We show how to visualize scalar fields on plane regions, representing solids, with Octave UPM. We focus on the example in Dibujar un sólido 2-D, i.e. the rectangle $[-1/2,1/2]\times [0,2]$ and the scalar field $f(x,y)=-\log (0.1+\sqrt{x^2+y^2})$. 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 coordinates of the mesh points
3. Compute the scalar field in the grid points.
4. We use the surf 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 surf(xx,yy,f)          % Draw the mesh
7 axis([-2,2,-1,3])      % select region for drawing
8 view(2)                % See the pisture from the top
9 colorbar               % Include colorbar