How do I plot this set as 3d region in matlab?

This is the set I need to plot-

.

My main purpose is to see how this set is convex, so I am trying to plot this graph in MATLAB, but don't know how to. I tried using surf but couldn't plot it correctly.

[Bruno Luong]

From the equation, the set Q(x,y) is intersection of paraboloid and 4 half spaces, all are convex so it must be convex.

Answer 1

[Matt J]

This will plot the hull for x=y=0; Looks pretty convex (as we knew it must be).

x=0;y=0;
fcn=@(u,v,z)x.^2+y.^2+u.^2+v.^2-z + 0./(abs(u)<=1) +0./(abs(v)<=1);

ax=[-2 2 -2 2 0 5];
fimplicit3(fcn,ax)
axis(ax); xlabel 'U', ylabel 'V', zlabel 'Z'

Answer 2

[Bruno Luong]

Code that plot ALL the boundaries of the domain

x = 0;
y = 0;
c = 1+x^2+y^2;

f1 = @(u,v,z) z - (u.^2 + v.^2 + c);
f2 = @(u,v,z) 1 - abs(u);
f3 = @(u,v,z) 1 - abs(v);
d = @(u,v,z) min(abs(cat(4,f1(u,v,z),...
    f2(u,v,z),...
    f3(u,v,z))),[],4);
s =  @(u,v,z) f1(u,v,z)>=0 & ...
    f2(u,v,z)>=0 & ...
    f3(u,v,z)>=0;
f =  @(u,v,z) d(u,v,z).*(2*s(u,v,z)-1);

fimplicit3(f,[-2 2 -2 2 0 5])
xlabel('u')
ylabel('v')
zlabel('z');