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| + | [[Archivo:levelsets.jpg|400px|thumb|right|Level sets of a scalar function]] | ||
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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: | 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: | ||
| Línea 14: | Línea 16: | ||
f=-log(0.1+sqrt(xx.^2+yy.^2)); % The scalar field | f=-log(0.1+sqrt(xx.^2+yy.^2)); % The scalar field | ||
contour(xx,yy,f) % Draw the level sets | contour(xx,yy,f) % Draw the level sets | ||
| + | hold on % We draw the boundary below | ||
| + | plot(x,x-x,'k','linewidth',1); | ||
| + | plot(x,2+x-x,'k','linewidth',1); | ||
| + | plot(-0.5+y-y,y,'k','linewidth',1); | ||
| + | plot(0.5+y-y,y,'k','linewidth',1); | ||
axis([-2,2,-1,3]) % select region for drawing | axis([-2,2,-1,3]) % select region for drawing | ||
view(2) % See the pisture from the top | view(2) % See the pisture from the top | ||
| + | colorbar % Include colorbar | ||
}} | }} | ||
| − | == | + | == 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]] | ||
[[Categoría:Curso ICE]] | [[Categoría:Curso ICE]] | ||
[[Categoría:Teoría de Campos]] | [[Categoría:Teoría de Campos]] | ||
| + | [[Categoría:Articles in English]] | ||
| + | [[Categoría:TC14/15]] | ||
| + | [[Categoría:TC15/16]] | ||
| + | [[Categoría:TC16/17]] | ||
| + | [[Categoría:TC17/18]] | ||
| + | [[Categoría:TC18/19]] | ||
| + | [[Categoría:TC19/20]] | ||
| + | [[Categoría:TC20/21]] | ||
| + | [[Categoría:TC21/22]] | ||
| + | [[Categoría:TC25/26]] | ||
| + | [[Categoría:Informática]] | ||
Revisión actual del 20:13 25 nov 2025
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:
- We introduce a sampling of the two segments with a suitable step
- With meshgrid command we define two matrixes with the x and y coordenates of the mesh points
- Compute the scalar field in the grid points.
- We use the contour command to draw the field and adjunst the axis. We see the picture from the top.
1 MATLAB code
x=-0.5:0.1:0.5; % sampling of the interval [-1/2,1/2]
y=0:0.1:2; % sampling of the interval [0,2]
[xx,yy]=meshgrid(x,y); % matrixes of x and y coordinates
figure(1)
f=-log(0.1+sqrt(xx.^2+yy.^2)); % The scalar field
contour(xx,yy,f) % Draw the level sets
hold on % We draw the boundary below
plot(x,x-x,'k','linewidth',1);
plot(x,2+x-x,'k','linewidth',1);
plot(-0.5+y-y,y,'k','linewidth',1);
plot(0.5+y-y,y,'k','linewidth',1);
axis([-2,2,-1,3]) % select region for drawing
view(2) % See the pisture from the top
colorbar % Include colorbar
2 To go further
Mesh of a parametrized 2-D solid
Visualization of a scalar field in a solid
