
Calculating unit normal
Hi all,
I am struggling with the below problem:
X(u,v) = (u  u^3 / 3 + uv^2 , v  v^3 /3 + vu^2, u^2  v^2)
So I know the normal is defined as:
N = Xu x Xv / Xu x Xv
And I have calculated Xu x Xv to be: (4uv^2  2u(1v^2+u^2) , (2v(1u^2+v^2)  4vu^2) , (1  u^2 + v^2)^2  4u^2*v^2))
Which looks horrible and is nowhere near as simple as the answer in my solutions
N(u; v) =
(2u; 2v; 1  u2  v2) / (1 + u2 + v2)
Could someone point out if I have gone wrong or how I should go about simplifying?
Many thanks