Results 1 to 6 of 6

Math Help - Normal vector at a point on a sphere/ellipsoid

  1. #1
    Senior Member
    Joined
    Jul 2006
    Posts
    364

    Question Normal vector at a point on a sphere/ellipsoid

    Hi,

    Can someone please let me know how I would go about finding a normal vector at any point on a sphere/ellipsoid?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by scorpion007
    Hi,

    Can someone please let me know how I would go about finding a normal vector at any point on a sphere/ellipsoid?
    If the (any) surface is defined implicitly by an equation of the form:

    <br />
F(x,y,z)=0<br />

    then the gradient of F:

    <br />
\nabla F(x,y,z)<br />

    defines the direction of the normal. In general there will be ambigity
    in the sense of the outward and inward directions of the normal (but with
    the usual forms of the equation of the sphere of ellipse you should get
    an outward normal).

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Jul 2006
    Posts
    364
    Quote Originally Posted by CaptainBlack
    If the (any) surface is defined implicitly by an equation of the form:

    <br />
F(x,y,z)=0<br />

    then the gradient of F:

    <br />
\nabla F(x,y,z)<br />

    defines the direction of the normal. In general there will be ambigity
    in the sense of the outward and inward directions of the normal (but with
    the usual forms of the equation of the sphere of ellipse you should get
    an outward normal).

    RonL
    Okay, so for a sphere with equation:

    F(x,y,z) = x^2 + y^2 + z^2 - r^2 = 0

    I just need to take a derivative? How do I do that with 3 variables?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by scorpion007
    Okay, so for a sphere with equation:

    F(x,y,z) = x^2 + y^2 + z^2 - r^2 = 0

    I just need to take a derivative? How do I do that with 3 variables?
    Gradient not derivative. It is the vector:

    \nabla F(x,y,z)=\left[ \frac{\partial F}{\partial x}, \frac{\partial F}{\partial y}, \frac{\partial F}{\partial z} \right]
    <br />
=\left[2x,\ 2y,\ 2z\right]<br />

    RonL
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member Rebesques's Avatar
    Joined
    Jul 2005
    From
    At my house.
    Posts
    538
    Thanks
    11
    Don't forget to divide by its length

    (...u said normal!)
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Rebesques
    Don't forget to divide by its length

    (...u said normal!)
    He actually said "a normal", but the point is well worth making anyway

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: May 14th 2011, 06:05 PM
  2. Replies: 1
    Last Post: April 6th 2011, 06:44 AM
  3. Normal vector at a point on a surface
    Posted in the Geometry Forum
    Replies: 0
    Last Post: October 18th 2010, 06:51 AM
  4. Replies: 4
    Last Post: September 8th 2010, 09:13 AM
  5. Line Intersection Point on Ellipsoid
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 7th 2008, 01:54 AM

Search Tags


/mathhelpforum @mathhelpforum