Plot 3D of coinstraned optimization

Good evening, for my thesis I should make a 3d plot in which I want something similar to this:

I have a function f(x,y)=x^2-2*x+1+y^2 subject to constraints g(x,y)=x^4+y^4-1.

I'm interested only in the plot.

Answer 1

[Matt J]

Use this,

https://www.mathworks.com/matlabcentral/fileexchange/74010-getcontourlinecoordinates?s_tid=srchtitle

[X,Y]=ndgrid(linspace(-2,2,500));

G=X.^4+Y.^4;

cm = contourf(X,Y,G,1); close

[~, cA] = getContourLineCoordinates(cm);

 f=@(x,y)x.^2-2*x+1+y.^2;

 fsurf(f,[-4,4],'FaceColor','b','FaceAlpha',0.3,'EdgeColor','none'); hold on
 
for i=1:numel(cA)
    
    x=cA{i}(:,1);
    y=cA{i}(:,2);
    z=f(x,y);
    
    line(x,y,z,'COlor','r','LineWidth',2)
  
end

hold off
xlabel X; ylabel Y; view(150,-2)

[Michele Guaragno]

it was exactly what I wanted. But I get this error:

Unrecognized function or variable 'getContourLineCoordinates'.

[Matt J]

Because you didn't download it from the link I gave you.

[Michele Guaragno]

Ah ok, I'm new in Matlab, thanks a lot.

Answer 2

[Torsten]

x=-2:0.01:2;
y=-2:0.01:2;
[X,Y] = meshgrid(x,y);
Z = X.^2-2*X+1+Y.^2;

xx=-1:0.01:1;
yy=-1:0.01:1;
y1 = (1-xx.^4).^(0.25);
y2 = -(1-xx.^4).^(0.25);
z1 = xx.^2-2*xx+1+y1.^2;
z2 = xx.^2-2*xx+1+y2.^2;
surf(X,Y,Z)
hold on
plot3(xx,y1,z1,'Linewidth',4,'Color','red')
hold on
plot3(xx,y2,z2,'Linewidth',4,'Color','red')
view([2,2,4])

[Michele Guaragno]

Thanks a lot, I really appreciate your help.