Combining globally rigid frameworks

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 rigid frameworks and rigid tensegrity graphs in the plane

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...

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...

Rigid Singularity Theorem in Globally Hyperbolic Spacetimes

30 years ago, Penrose-Hawking have shown that spacetimes are geodesically incomplete under some physically reasonable conditions [1] [2] [3] [4]. The generic condition is the key assumption to induce singularities rigidly. Geroch improved these theorems with “no observer horizon” condition in place of the generic condition for the spatially closed universe [5,6]. Here, the “no observer horizon”...