Piecewise constant surface in MATLAB - matlab

Question

I would like to produce a piecewise constant surface which is zero outside of some rectangle. More specifically, for t = (x,y) in R^2, I want
f(t) = 1 when 5<y<10 and 0<x<1;
-1 when 0<y<5 and 0<x<1;
1 when -5<y<0 and 0<x<1;
0 elsewhere
But, the surface I get doesn't look like what I want. I'm somewhat of a Matlab novice, so I suspect the problem is in the logical operators. My code is:
x = -2:.01:2; y = -15:15
[X,Y] = meshgrid(x,y); %Make domain
for i = 1:numel(X) %Piecewise function
for j = 1:numel(Y)
if Y(j) >= 0 && Y(j)<= 5 && X(i)>=0 && X(i)<=1
h2(i,j)= -1;
elseif Y(j)>5 && Y(j) <= 10 &&X(i)>=0 &&X(i)<=1
h2(i,j) = 1;
elseif Y(j)<0 && Y(j)>=-5 &&X(i)>=0 &&X(i)<=1
h2(i,j) = 1;
elseif X(i) <0 || X(i)>1 || Y(j)<-5 || Y(j)>10
h2(i,j) = 0;
end
end
end
%Normalize
C = trapz(abs(h2));
c = trapz(C);
h2 = c^(-1)*h2;
Thank you for your help and please let me know if you'd like me to specify more clearly what function I want.

Answer 1

You can very easily achieve what you want vectorized using a combination of logical operators. Avoid using for loops for something like this. Define your meshgrid like you did before, but allocate a matrix of zeroes, then only set the values within the meshgrid that satisfy the requirements you want to be the output values of f(t). In other words, do this:
%// Your code
x = -2:0.1:2; y = -15:15;
[X,Y] = meshgrid(x,y); %Make domain
%// New code
Z = zeros(size(X));
Z(Y > 5 & Y < 10 & X > 0 & X < 1) = 1;
Z(Y > 0 & Y < 5 & X > 0 & X < 1) = -1;
Z(Y > -5 & Y < 0 & X > 0 & X < 1) = 1;
mesh(X,Y,Z);
view(-60,20); %// Adjust for better angle
The above code allocates a matrix of zeroes, then starts to go through each part of your piecewise definition and searches for those x and y values that satisfy the particular range of interest. It then sets the output of Z to be whatever the output of f(t) is given those constraints. Take note that the otherwise condition is already handled by setting the whole matrix to be zero first. I then use mesh to visualize the surface, then adjust the azimuthal and elevation angle of the plot for a better view. Specifically, I set these to -60 degrees and 20 degrees respectively. Also take note that I decreased the resolution of the x values to have a step size of 0.1 instead of 0.01 for a lesser amount of granularity. This is solely so that you can see the mesh better.
This is the graph I get:

Answer 2

You can just use logical indexing:
x = -2:.01:2; y = -15:15;
[X,Y] = meshgrid(x,y); %// Make domain
h2=zeros(size(X));
h2(5<Y & Y<10 & 0<X & X<1)=1;
h2(0<Y & Y<5 & 0<X & X<1)=-1;
h2(-5<Y & Y<0 & 0<X & X<1)=1;
This statement: 5<Y & Y<10 & 0<X & X<1 returns a matrix of 1's and 0's where a 1 means that all 4 inequalities are satisfied, and a 0 means at least one is not. Where that matrix has a one, h2 will be modified to the value you want.