How I use a parabola in the xy-plane as base curve for the cylinder?

Hi to everyone, I'm really new how to this site so to MatLab, too.

So here is my problem: Here is the code to create a cylinder where my base in the xy-plane one ellipse is:

m = 20; n = 50; u = linspace(0, 1, m); v = linspace(0, 2*pi, n); [U, V] = meshgrid(u,v);

a = 3; b = 5;

X = cos(V)*a + U*0; Y = sin(V)*b + U*0; Z = V*0 + U*10;

s = surf(X, Y, Z);

How can I now edit/modify my code to use parabola or hyperbola as base curve?

Thanks.

Answer 1

[Roger Stafford]

For a hyperbola, x^2/a^2-y^2/b^2 = 1, replace the two lines for X and Y by:

   X = a*cosh(V);
   Y = b*sinh(V);

For a parabola, y = a*x^2, use:

   X = V-pi;
   Y = a*X.^2;

[Besim Helic]

Thank you very much, this works perfect for parabola (!), but not for hyperbola too. The result is than only one line in xy-plane.

[Roger Stafford]

To get a better hyperbola also change v:

   v = linspace(-1,1,n);

This shows only one of its two branches. To get the other branch write

   X = -a*cosh(V);
   Y = -b*sinh(V);