Parametric representation of paraboloid cylinder

[geft]

The equation is z = y^3. I know how to do normal planes and spheres, but I don't know what to set for r(u,v) when it comes to paraboloid cylinders.

 

[Lancelot59]

The equation is z = y^3. I know how to do normal planes and spheres, but I don't know what to set for r(u,v) when it comes to paraboloid cylinders.

Since x can be anything, make it one of your variables (either u, or v).

 

[geft]

x = u
y = v
z = v^3

r(u, v) = [u, v, v^3]?

Is there a formula for the r(u, v)?

 

[Lancelot59]

x = u
y = v
z = v^3

r(u, v) = [u, v, v^3]?

Is there a formula for the r(u, v)?

If you're asking if there is a formulaic method for determining what r(u,v) should be, then the answer is "sorta". In the case of something along the lines of z(x,y) then you let u and v be x and y, and then just have the function as your z parameter. However you don't always get things defined by functions like that, in which case you need to get a little creative. Either re-arranging things, or even jumping coordinate systems to make stuff easier.