Tag Archive for 'surf'

Frequently we will get a function f(x,y) that we will need to plot. The naive way will be to generate an array for x and y and then iterate through all combinations and then use the plot3 function. Here is a sample:

1. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2. % Assume function f(x,y)=-(x^2-2)^2 - (x^2-exp(y))^2
3. % Crude Method
4. x = -5:.1:5;
5. y = 1:.1:4;
6. points=[];
7.  
8. i=1;
9. for xp = x
10. for yp= y
11. f = -(xp^2-2)^2 - (xp^2-exp(yp))^2;
12. points(i,1) = xp;
13. points(i,2) = yp;
14. points(i,3) = f;
15. i=i+1;
16. end
17. end
18.  
19. figure;hold on;grid on;
20. xlabel('x');ylabel('y');zlabel('f');
21.  
22. plot3(points(:,1),points(:,2),points(:,3),'.');
23.  
24. hold off;
25. Download this code: plot3d.m

But this code is inefficient. Looping is to be avoided in MATLAB because operations on matrices are faster. Moreover, the plot3 function does not give shading. We get the following as the output:

Avoiding loops, we can implement the above code in a different way. We avoid loops and use the surf command.

1. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2. % Assume function f(x,y)=-(x^2-2)^2 - (x^2-exp(y))^2
3. % Better Method
4. x = -5:.2:5;
5. y = 1:.2:4;
6.  
7. x_2d = ones(length(y),length(x))*diag(x);
8. y_2d = diag(y)*ones(length(y),length(x));
9.  
10. func = -(x_2d.^2-2).^2 - (x_2d.^2-exp(y_2d)).^2;
11.  
12. figure;hold on;grid on;
13.  
14. xlabel('x');ylabel('y');zlabel('f');
15. surf(x,y,func);
16.  
17. hold off;
18. Download this code: surf.m

We get the following output

The trick in the above code involves creating the x_2d and y_2d array.

References:
(1) plot3
(2) surf