  This paper is concerned with a formation shaping problem for point agents in
a two-dimensional space, where control avoids the possibility of reflection
ambiguities. One solution for this type of problems was given first for three
or four agents by considering a potential function which consists of both the
distance error and the signed area terms. Then, by exploiting a hierarchical
control strategy with such potential functions, the method was extended to any
number of agents recently. However, a specific gain on the signed area term
must be employed there, and it does not guarantee the global convergence. To
overcome this issue, this paper provides a necessary and sufficient condition
for the global convergence, subject to the constraint that the desired
formation consists of isosceles triangles only. This clarifies the admissible
range of the gain on the signed area for this case. In addition, as for
formations consisting of arbitrary triangles, it is shown when high gain on the
signed area is admissible for global convergence.
