Solution (source code)

= Solution
{c}

At a regular point of the <parametrized surface>, the <partial derivatives> $\mathbf r_s$ and $\mathbf r_t$ are <linearly independent> <tangent vectors>. Their <cross product> gives a nonzero <normal vector>:
$$
\boxed{\mathbf n=\mathbf r_s\times\mathbf r_t.}
$$
Dividing by its <Euclidean norm> gives a <unit normal>; changing the sign chooses the opposite orientation. If the <cross product> vanishes, this <parametrization> is singular there and cannot determine a <normal vector> by this formula.