# How to add two different surface curves in a single plot?

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Deepshikha Deo on 15 Mar 2024
Commented: Star Strider on 20 Mar 2024
I have a bell shaped curve in 3D (generated from curve fitter app) as shown in the figures.
Both are the same curve the only difference is one is without point data and the other has point data.
Problem: I want to add another surface to the same plot for the same data which is at z=1 and parallel to x- and y-axis. Also, is it possible to find the values of major and minor axes of the ellipse formed from the intersection of both the surfaces. Or in other words, the values between the intersection of x and z values of both the curves and the y and z values of both the curves.
I hope I am able to express myself clearly.
Thank you

Star Strider on 15 Mar 2024
Try this —
I want to add another surface to the same plot for the same data which is at z=1 and parallel to x- and y-axis.
[X,Y] = ndgrid(-3:0.1:3);
f = @(x,y) exp(-(x.^2+(2*y).^2)*0.5);
Z = f(X,Y)*3;
figure
surf(X, Y, Z)
hold on
surf(X, Y, ones(size(Z)), 'FaceColor','r', 'FaceAlpha',0.5, 'EdgeColor','none')
hold off
colormap(turbo)
Also, is it possible to find the values of major and minor axes of the ellipse formed from the intersection of both the surfaces.
figure
[c,h] = contour(X, Y, Z, [1 1]);
axis('equal')
grid
Ax = gca;
Ax.XAxisLocation = 'origin';
Ax.YAxisLocation = 'origin';
elpsfcn = @(b,xy) xy(1,:).^2/b(1)^2 + xy(2,:).^2/b(2)^2 - b(3);
opts = optimoptions('fminunc', 'MaxFunctionEvaluations', 5E+3, 'MaxIterations',1E+4);
[B, fv] = fminunc(@(b) norm(elpsfcn(b,c(:,2:end))), rand(3,1), opts)
Local minimum possible. fminunc stopped because it cannot decrease the objective function along the current search direction.
B = 3×1
52.8204 26.4510 0.0008
fv = 1.2653e-05
fprintf('Semimajor Axis = %.4f\nSemiminor Axis = %.4f\nConstant = %.4f\n', B)
Semimajor Axis = 52.8204 Semiminor Axis = 26.4510 Constant = 0.0008
text(-2.5, 2.5, sprintf('$\\frac{x^2}{%.2f^2} + \\frac{y^2}{%.2f^2} = %.4f$',B), 'Interpreter','latex', 'FontSize',16)
.
Deepshikha Deo on 20 Mar 2024
Regards
Star Strider on 20 Mar 2024
As always, my pleasure!