Assume that I have a points $p_1,...,p_n$ scattered arbitrarily in a two-dimensional plane. Assume further that I have three vectors $v_1,v_2,v_3$ of known norms $|v_1|,|v_2|,|v_3|$ in this two-dimensional space. While the relative orientation of the three vectors must be preserved, I am free to choose an origin and a rotation.
My goal is to find an origin and a rotation such that I can construct points $z = mv_1+nv_2+ov_3$ with $m,n,o \in \mathbb{Z}$ from these three vectors which minimize Euclidian distance to the scattered points $p_1,...,p_n$ (on average).
Do you know of a non-iterative way to do so?