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normal of implicit function

Started by laeuchli Jul 11, 2004 at 4:05 PM 3 replies 2.4k views

Original Post

Jul 11, 2004 at 4:05 PM

Dear all, I have an implict function F(x,y,z)=0 which I'd like to find a normal to. Happily, mathworld has the defintion at http://mathworld.wolfram.com/NormalVector.html <img>http://mathworld.wolfram.com/nimg1936.gif However, I don't fully understand the meaning of the equation. In paticular, how you write each component of the vector. Do they mean: n.x=(Df/dx)/sqrt(...) n.y=(df/dy)/sqrt(...) or something else? Thanks, Jesse

Motorherp

Jul 11, 2004 at 4:13 PM

I think what they mean is, given F(x,y,z) is a function of x y and z, then Fx is the partial derivative of F(x,y,z) with respect to x.

They kind of say it at the top using lower case f's, although I agree its not very clear.

VolkerG

Jul 11, 2004 at 4:25 PM

The normal vector for f(x,y,z)=0 is given by n=grad f(x,y,z). Or in other words:
nx=d/dx f(x,y,z),...
See also Gradient

Atheist

Jul 11, 2004 at 4:31 PM

... because the gradient (d/dx, d/dy, d/dz)F gives you the direction where F raises most and since your surface is defined by "points where F doesn´t change" that´s perpendicular (losely speaking, but maybe helping to understand it).

laeuchli

Author

laeuchli

Jul 11, 2004 at 5:20 PM

Thanks all.
Jesse

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