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:Originally Posted by scorpion007
$\displaystyle
F(x,y,z)=0
$
then the gradient of $\displaystyle F$:
$\displaystyle
\nabla F(x,y,z)
$
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
Gradient not derivative. It is the vector:Originally Posted by scorpion007
$\displaystyle \nabla F(x,y,z)=\left[ \frac{\partial F}{\partial x}, \frac{\partial F}{\partial y}, \frac{\partial F}{\partial z} \right] $
$\displaystyle
=\left[2x,\ 2y,\ 2z\right]
$
RonL