The paper presents LGS, a geometric solver by LEDAS for systems requiring solving of geometric problems with constraints. LGS is presently a stable marketable product, and so the paper focuses on the future of LGS, such as possible development paths and applications to real tasks. Apart from the traditional use in large parametric CAD systems, possibilities for integrating the solver in small C...

Combining task and motion planning requires to interleave causal and geometric reasoning, in order to guarantee the plan to be executable in the real world. The resulting search space, which is the cross product of the symbolic search space and the geometric search space, is huge. Systematically calling a geometric reasoner while evaluating symbolic actions is costly. On the other hand, geometr...

This paper describes an intuitive geometric model for coupled twostate quantum systems (qubits), which is formulated using geometric (aka Clifford) algebra. It begins by showing how Euclidean spinors can be interpreted as entities in the geometric algebra of a Euclidean vector space. This algebra is then lifted to Minkowski space-time and its associated geometric algebra, and the insights this ...

Holographic reduced representations (HRR) are based on superpositions of convolution-bound ntuples, but the n-tuples cannot be regarded as vectors since the formalism is basis dependent. This is why HRR cannot be associated with geometric structures. Replacing convolutions by geometric products one arrives at reduced representations analogous to HRR but interpretable in terms of geometry. Varia...

Current feature modelling systems suffer from a number of shortcomings. One is that the meaning of features is often not adequately maintained during modelling, which implies that modelling is in essence only geometric modelling. Another is that it is not possible to support product models with multiple feature views for all product development phases. This paper discusses solutions for these s...

Recent work of Gromov, Epstein, Cannon, Thurston and many others has generated strong interest in the geometric and algorithmic structure of finitely generated infinite groups. (See [16],[17] and [14].) Many of these structures are preserved by taking graph products. The graph product of groups (not to be confused with the fundamental group of a graph of groups) is a product mixing direct and f...

Computer Aided Design (CAD) software libraries rely on the tensor-product NURBS model as standard spline technology. However, in applications of industrial complexity, this mathematical model does not provide sufficient flexibility as an effective geometric modeling option. In particular, the multivariate tensor–product construction precludes the design of adaptive spline representations that s...

The notion of the shell of a Hilbert space operator, which is a useful generalization (proposed by Wielandt) of the numerical range, is extended to operators in spaces with an indefinite inner product. For the most part, finite dimensional spaces are considered. Geometric properties of shells (convexity, boundedness, being a subset of a line, etc.) are described, as well as shells of operators ...