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Parametric representation of paraboloid cylinder

  1. Sep 26, 2011 #1
    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.
     
  2. jcsd
  3. Sep 26, 2011 #2
    Since x can be anything, make it one of your variables (either u, or v).
     
  4. Sep 26, 2011 #3
    x = u
    y = v
    z = v^3

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

    Is there a formula for the r(u, v)?
     
  5. Sep 26, 2011 #4
    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.
     
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