Mesh/Surf plot of function with if statements

I’m trying to plot the following function (cost curve), basically combining two functions in a plot separated by an upper bound:

However, I can’t get the if statements working properly – the functions are not combining correctly in the plot.

It’s my code so far:

[X,Y] = meshgrid(0:1:20); %Evaluates the function between 0 and 20 in both x and y. Interval set at 1.
if 4*X.^2+3*Y.^2<=225
    Z = 2*sqrt(100*X.^2+75*Y.^2); %Conditionally  Function (1)
  else
    Z = 75+4/3*X.^2+Y.^2; %Conditionally  Function (2)
end

figure(1); %Allows working with multiple figures simultaneously
mesh(X,Y,Z) %mesh plot
colorbar %add colorbar in plot
xlabel('Output, q_{2}','FontSize',8,'FontWeight','normal','Color','k') %label x-axis
ylabel('Output, q_{1}','FontSize',8,'FontWeight','normal','Color','k') %label y-axis
zlabel('Cost, C(q;P)','FontSize',8,'FontWeight','normal','Color','k') %label z-axis
 
figure(2); %Next figure
surf(X,Y,Z) %surface plot
colorbar %add colorbar in plot
xlabel('Output, q_{2}','FontSize',8,'FontWeight','normal','Color','k') %label x-axis
ylabel('Output, q_{1}','FontSize',8,'FontWeight','normal','Color','k') %label y-axis
zlabel('Cost, C(q;P)','FontSize',8,'FontWeight','normal','Color','k') %label z-axis

I have also looked at conditionally defined expression or function using piecewise but couldn’t get it to work either.

Please could someone offer corrected code or suggestions for changes?

Many thanks in advance.

Answer 1

[Star Strider]

Try this:

Z1 = (2*sqrt(100*X.^2+75*Y.^2)).*((4*X.^2+3*Y.^2)<=225);
Z2 = (75+4/3*X.^2+Y.^2).*((4*X.^2+3*Y.^2)>225);
Z = Z1 + Z2;

It creates a logical matrix separately with ‘((4*X.^2+3*Y.^2)<=225)’ and ‘((4*X.^2+3*Y.^2)>225)’ that then become numeric matrices with (0,1) elements when used in the calculations of ‘Z1’ and ‘Z2’. These are then added to form ‘Z’. Unfortunately, ‘logical indexing’ will not otherwise work here, because the logical operations will create logical vectors, destroying the matrix structure.

[Morten Hansen]

Thanks Star Strider for the suggusted code and the explanation regarding 'logical indexing'

[Star Strider]

As always, my pleasure.

To see how it works, plot ‘Z1’ and ‘Z2’ separately.