How to Ensure an Elliptic Cylinder Lies Above a Plane?

[Somefantastik]

I know that the equation for an elliptic cylinder is

$$\frac{{\left( {x - x_0 } \right)^2 }}{{a^2 }} + \frac{{\left( {y - y_0 } \right)^2 }}{{b^2 }} = 1$$

How do I add a constraint on that to make sure that it lies above the plane z = -1? I'm confused about it b/c its equation does not involve z (a degenerate quadric?)

 

[mathman]

You just have to specify the z domain for which the equation applies. If you insist on having one equation, define a function of z where f(z)=1 where the cylinder is supposed to exist and f(z)=-1 otherwise. Then in the ellipse equation, replace = 1 by = f(z).

 

[Somefantastik]

Ok, that helps, thank you.