Given a set of $n$ points $P$, a point $p_i\in{P}$, $1\leq i\leq n$ and a number $k
Using $N_k(p_i)$, I want to approximate the surface. One way is to try and find circles centered on all the points in $P$. The radius for each point is defined by the following equation:
$r_i=max_j||(p_j-p_i)-n_i^T(p_j-p_i)n_i||$
This equation is given in a book without further explanations, and I am unable to decipher what type of vector product is being used (I have written the equation exactly as it is written in the book), and why $r_i$ is supposedly best for approximating the surface.
Any ideas would be greatly appreciated.
Edit: The question was solved by a friend of mine. The product above is a dot product. This way, $r_i$ is smaller the more the normals of $p_i$ and $p_j$ differ.