function parabola
%parabola.m produces two images of a paraboloid.  

n=40;
X=ones(n,1)*linspace(-sqrt(2),sqrt(2),n);
Y=flipud(X');
for r=1:n
    for c=1:n
        if X(r,c)==0 & Y(r,c)==0
        elseif abs(X(r,c))<=abs(Y(r,c))
            x=X(r,c);
            y=Y(r,c);
            X(r,c)=x*abs(y)/sqrt(x^2+y^2)/sqrt(2);
            Y(r,c)=y*abs(y)/sqrt(x^2+y^2)/sqrt(2);
        else
            x=X(r,c);
            y=Y(r,c);
            X(r,c)=abs(x)*x/sqrt(x^2+y^2)/sqrt(2);
            Y(r,c)=abs(x)*y/sqrt(x^2+y^2)/sqrt(2);
        end
    end
end

Z=-X.^2-Y.^2;
%create a first image of the parabola
fig=figure;
set(fig,'color',[1 1 1])
colormap([0 0 0])
mesh(X,Y,Z)
grid off
axis equal off

%create a second image
fig=figure;
set(fig,'color',[1 1 1])
colormap([0.7 0.7 0.7])
a=surf(X,Y,Z);
light
lighting gouraud 
grid off
axis equal off
set(a,'linestyle','none','facealpha',0.7)
hold on
%now add red and green lines to the second image.
r=linspace(-1,1,n);
th1=linspace(0,2*pi,10);
for k=1:length(th1)
    plot3(cos(th1(k))*r,sin(th1(k))*r,-r.^2,'r')
end
th=linspace(0,2*pi,200);
r1=linspace(0.1,1,10);
for k=1:length(r1)
    plot3(r1(k)*cos(th),r1(k)*sin(th),-r1(k)^2*ones(size(th)),'g')
end