# Finding the surface normal of an ellipsoid?

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Hi all, I am trying to find the surface normal of an ellipsoid, given a single xyz point on a surface. I am struggling to work out how to find the tangent of an ellipsoid. I couldnt find anything obvious on google, but I may have found a clue, and that is to somehow use a cone to calculate the tangent? If I could work out how to find the tangent of the surface should easily be able to work out the normal vector on my own. Are there any equations I should be aware of for calculating the tangent? Regards James

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I have just had a thought, perhaps I need to take point p, and find the opposite point to work out where the clone intersects the two points? then where the two points meet, will provide me with a vector tangent to the original point?

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Just google 'ellipsoid normal' (many of the links on the first page of hits look promising).

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I am googled out but I think i got there in the end!

n = 2x/a^2 + 2y/b^2 + 2z/c^2

can i do the following to normalize the point

n = x/a^2 + y/b^2 + z/c^2

then normalise n by its length?

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