Is there a vectorial structure on $\mathbb{R}^2$ such that the segments $[x,y]$ with boundary points $x, y \in \mathbb{R}^2$ are not graphically straight?
$[x,y]$ is defined as $\{\lambda x +(1-\lambda)y : \lambda \in [0,1] \}$.
I have no idea about that, so I'm not looking for exact answers but hints, possible structures to verify.