Visualization of a scalar field in a solid

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 [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 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

{{matlab|codigo= % --- Mallado del arco --- theta = linspace(0, pi, 200);  % más denso para curva suave r = linspace(1, 2, 200);  % radio interior 1, exterior 2 [R, TH] = meshgrid(r, theta);

% Convertir a cartesianas X = R .* cos(TH); Y = R .* sin(TH);

% --- Temperatura --- T = (X - Y).^2;

% --- Representación 2D --- figure; pcolor(X, Y, T);  % representación 2D en colores shading interp  % suavizado del color colormap(jet) colorbar;

title('Temperatura T(x,y) = (x - y)^2 sobre el arco') xlabel('x') ylabel('y') axis equal  % mantiene proporciones reales

2 To go further

Mesh of a parametrized 2-D solid

Visualization of vector fields in a solid

Dibujar un sólido 2-D