Represents an abstract edge as a parameterized line segment with two endpoints [v1,v2]. Contains information about the linear interpolation parameter of the new vertices added along the edge and their vertex IDs.  O----x----x----x----O           x  -  New vertices added. We only store their lerp coefficients (t1,t2,t3)v1 a1 a2 a3 v2 with respect to the end points, s.t. a_i = vi + t_i*(v2-v1).