Generically Globally Rigid Graphs Have Generic Universally Rigid Frameworks

Globally rigid frameworks and rigid tensegrity graphs in the plane

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.

Generically globally rigid zeolites in the plane

A d-dimensional zeolite is a d-dimensional body-and-pin framework with a (d+1)-regular underlying graph G. That is, each body of the zeolite is incident with d+1 pins and each pin belongs to exactly two bodies. The corresponding d-dimensional combinatorial zeolite is a bar-and-joint framework whose graph is the line graph of G. We show that a two-dimensional combinatorial zeolite is generically...

A Characterization of Generically Rigid Frameworks on Surfaces of Revolution

A foundational theorem of Laman provides a counting characterisation of the finite simple graphs whose generic bar-joint frameworks in two dimensions are infinitesimally rigid. Recently a Laman-type characterisation was obtained for frameworks in three dimensions whose vertices are constrained to concentric spheres or to concentric cylinders. Noting that the plane and the sphere have 3 independ...

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...