1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Help with parameterization of surface

  1. Apr 25, 2012 #1
    1. The problem statement, all variables and given/known data

    If I have been given a surface x = 12 − y^2 − z^2 between x = 3 and x = 8, oriented by the unit normal which points away from the x–axis.

    I want to find an orientation preserving parameterization.
    2. Relevant equations



    3. The attempt at a solution

    I know orientation preserving means that the normal vector is pointing outward. I'm not sure how to apply this to parameterize this surface however.
     
  2. jcsd
  3. Apr 25, 2012 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Parameterization and orientation are separate issues. Try cylindrical like coordinates only on y and z instead of x and y.
     
  4. Apr 25, 2012 #3
    I figure I can parameterize it no problem but the question literally asks what I said. Find an orientation preserving parameterization. What does that mean?
     
  5. Apr 26, 2012 #4

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    I have seen instances when textbooks say the parameterization itself determines the orientation. For example, if your surface is parameterized as ## \vec R =\vec R(u,v)##, then the direction of ##\vec R_u \times \vec R_v## determines the positive orientation of the surface. So, if you parameterize your surface using ##r## and ##\theta##, one or the other of ##\vec R_r\times \vec R_\theta## or ##\vec R_\theta\times\vec R_r## will point in the direction that was specified by the problem. If it is the first, then write your parameterization as ##\vec R = \vec R(r,\theta)= \ ...## and if it is the second write it as ##\vec R = \vec R(\theta,r)=\ ...##. Personally, I don't care for that notion because, as in your problem, the orientation is given separately. Anyway, that's my best guess what it might mean.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook