Redundantly globally rigid braced triangulations

Braced edges in plane triangulations

A plane triangulation is an embedding of a maximal planar graph in the Euclidean plane. Foulds and Robinson (1979) first studied the problem of transforming one triangulation to another by a sequence of diagonal operations. where a diagonal operation deletes one edge and inserts the other diagonal of the resulting quadrilateral face. An edge which cannot be removed by a single diagonal operatio...

On Minimally Highly Vertex-Redundantly Rigid Graphs

A graph G = (V,E) is called k-rigid in Rd if |V | ≥ k + 1 and after deleting any set of at most k − 1 vertices the resulting graph is rigid in Rd. A k-rigid graph G is called minimally k-rigid if the omission of an arbitrary edge results in a graph that is not k-rigid. B. Setvatius showed that a 2-rigid graph in R2 has at least 2|V |−1 edges and this bound is sharp. We extend this lower bound f...

Combining Globally Rigid Frameworks

Here it is shown how to combine two generically globally rigid bar frameworks in d-space to get another generically globally rigid framework. The construction is to identify d+1 vertices from each of the frameworks and erase one of the edges that they have in common.

Globally consistent rigid registration

In this paper we present a novel approach to register multiple scans from a static object. We formulate the registration problem as an optimization of the maps from all other scans to one reference scan where any map between two scans can be represented by the composition of these maps. In this way, all loop closures can be automatically guaranteed as the maps among all scans are globally consi...

Globally rigid frameworks and rigid tensegrity graphs in the plane