How to plot a 3D graph

I am attempting to plot a mesh 3D graph that displays how Y_B varies with t and T. I then want to solve this graph to find the coordinates that gives the maximum value of Y_B. This is the code to give a graph that displays how T varies with Y_B for different variables for t

if true
  % code
T=600:10:850;
t = 1;
k1 = 10^7.*exp(-12700./T);
k2 = 5*10^4.*exp(-10800./T);
k3 = 7*10^7.*exp(-15000./T);
t=1:2:20;
hold on;
for i=1:numel(t)
 Y_B = (k1.*t(i).*(k1+k3))./(((k2.*t(i))+1).*(k1+k3).*(1+(t(i).*(k1+k3))));
 plot(T,Y_B);
end

How do I transform this into a 3D plot for t = 0.2:20 and T = 600:850

[Star Strider]

What is ‘T’?

What is its range?

How does it enter into the calculation of ‘Y_B’?

[sophp]

T changes the value of k1, k2 and k3

k1 = 10^7.*exp(-12700./T);
k2 = 5*10^4.*exp(-10800./T);
k3 = 7*10^7.*exp(-15000./T);

Its range is 600 to 850

Y_B is given by

     Y_B = (k1.*t.*(k1+k3))./(((k2.*t+1).*(k1+k3).*(1+(t.*(k1+k3))));

The range of t is 0.2 to 20

Answer 1

[Star Strider]

Use meshgrid to create matrices for ‘t’ and ‘T’, and remove the subscripts from the ‘Y_B’ calculation:

T=600:10:850;
t=1:2:20;
[tm,Tm] = meshgrid(t, T);
k1 = 10^7.*exp(-12700./Tm);
k2 = 5*10^4.*exp(-10800./Tm);
k3 = 7*10^7.*exp(-15000./Tm);
Y_B = (k1.*tm.*(k1+k3))./(((k2.*tm)+1).*(k1+k3).*(1+(tm.*(k1+k3))));

figure(1)
surf(t,T,Y_B)
grid on
xlabel('t')
ylabel('T')
zlabel('Y\_B')

[sophp]

Thanks Star Strider! I found another question you answered regarding finding the maximum point for a 3D plot. Using your code, but changing the variables

Y_Bmax = max(Y_B(:));
[Y_Bmax,Idx] = max(Y_B(:));
[Y_BmaxRow,Y_BmaxCol] = ind2sub(size(Y_B), Idx);

However it is not printing the indices of the maximum plot. It may be the case that the max value of Y_B occurs at a range of values. Is there a function which tells me these values?

[Star Strider]

As always, my pleasure!

There seems to be only one maximum. (I used find here to be sure.) It plots as a solid red upward-pointing triangle with this code:

Y_Bmax = max(Y_B(:));
Idx = find(Y_B(:) == Y_Bmax);
[Y_BmaxRow,Y_BmaxCol] = ind2sub(size(Y_B), Idx);

figure(1)
surf(t,T,Y_B)
hold on
plot3(tm(Y_BmaxRow,Y_BmaxCol), Tm(Y_BmaxRow,Y_BmaxCol), Y_B(Y_BmaxRow,Y_BmaxCol), '^r', 'MarkerFaceColor','r')
hold off
grid on
xlabel('t')
ylabel('T')
zlabel('Y\_B')
view(40, 45)

To use my code to plot the maximum, it is necessary to use the matrix arguments ‘tm’ and ‘Tm’ in the plot3 call, not the vectors that created them.

[sophp]

I see. This works perfectly, how do I display these coordinates??

[Star Strider]

I would do this:

DisplayCoordinates = [tm(Y_BmaxRow,Y_BmaxCol), Tm(Y_BmaxRow,Y_BmaxCol), Y_B(Y_BmaxRow,Y_BmaxCol)]

DisplayCoordinates =
    19.0000   710.0000   0.5114