I am attempting to resolve a problem of inferring Cartesian position from distance. I have a set of nodes arbitrarily but statically positioned on a 2-D plane. Every node is aware of its position relative to the other $n-1$ nodes. From this set of $n$ nodes, is it possible to infer each node's position ($x$,$y$) by choosing any node and using it as a basis?
For example, with two nodes, this is not possible, as the distance alone leaves open the possibility of the node not chosen as the basis for being located anywhere in the radial distance from the basis node.
With three nodes, it also seems impossible because the orientation can be flipped and is thus ambiguous based solely on distance. How many nodes are needed to unambiguously infer the position of the elements on a Cartesian plane?