Leírás
A two-dimensional direction-length framework (G, p) consists of a
multigraph G = (V ; D, L) whose edge set is partitioned into
direction edges D (which fix the gradient of the line through both
end-vertices), and length edges L (which specify the distance
between their end-vertices); together with a realisation p of this graph
in the plane.
Given a direction-length framework (G, p), we want to know whether there
are other realisations of G which satisfy the same direction and length
constraints. Any such framework (G, q) is said to be equivalent to (G,
p).We can easily obtain frameworks which are equivalent to (G,p) by
either translating (G, p) in the plane or rotating it by 180 degrees, but
are these the only equivalent frameworks? If so we say that (G,p) is
globally rigid.
In this talk, we will characterise the class of direction-length graphs
which are globally rigid for all generic realisations p.