Pseudo-triangulations, and the closely related geodesic
triangulations, have been used in Computational Geometry in ray
shooting, visibility and kinetic data structures.
My interest is
mainly in the special minimum or pointed
pseudo-triangulations, which I have
introduced in my paper
A Combinatorial Approach to Planar Non-Colliding Robot Arm
(see FOCS 2000 extended
) to give an algorithmic solution to the
Carpenter's Rule Problem. They have remarkable
combinatorial and rigidity-theoretic properties, many more
awaiting to be discovered.
Here's some of the ongoing research in this direction.