We propose a novel method for determining geometric parameters of general cameras to generate augmented reality images. Visual surveillance systems are usually evaluated by using datasets from different camera configurations. Then, the system is often fixed and one cannot ensure that the same methods can work in all configurations. Our approach deals with the autodetermination of geometric para...

Two methods are proposed for correct and verifiable geometric reasoning using finite precision arithmetic. The first method, data normalization, transforms the geometric structure into a configuration for which all finite precision calculations yield correct answers. The second method, called the hidden variable method, constructs configurations that belong to objects in an infinite precision d...

Configuration Spaces: To begin, let us consider the problem of planning the motion of a single agent among a collection of obstacles. Since the techniques that we will be discussing originated in the field of robotics, henceforth we will usually refer to a moving agent as a “robot”. The environment in which the agent operates is called its workspace, which consists of a collection of geometric ...

In this paper we explicitly construct a triangulation of a 6-dimensional point configuration of 324 points which admits no geometric bistellar operations (or flips, for short). This triangulation is an isolated element in the graph of triangulations of the point configuration. It has been a central open question in polytope combinatorics in the last decade whether point configurations exist for...

Any configuration of lattice vectors gives rise to a hierarchy of higher-dimensional configurations which generalize the Lawrence construction in geometric combinatorics. We prove finiteness results for the Markov bases, Graver bases and facet posets of these configurations, and we discuss applications to the statistical theory of log-linear models.

The aim of this paper is to make progress towards a geometric model theory for non first order theories. The main difficulty is to work in an environment where the compactness theorem fails. This paper continues the work started in [GrLel]. The main result is an axiomatic approach to the Hrushovski-Zilber group configuration theorem.

In this paper, we present a control algorithm to control underactuated mechanical systems that evolve in the configuration space with the fiber bundle structure. We show that by using the geometric tools such as symmetric product, and small amplitude periodic forcing, we can develop unique techniques to control the underactuated dynamic system, such as an unmanned blimp.

In this paper circuits with impasse points, i.e. with jumps in their configuration space will be analyzed. These non-regularized circuits exhibit a fold in their configuration space, which can lead to difficulties during the simulation with standard circuit simulators like SPICE. The former developed geometric approach to simulate these circuits without regularization will be extended by a deta...

We show that the well known homotopy complementation formula of Björner andWalker admits several closely related generalizations on different classes of topological posets (lattices). The utility of this technique is demonstrated on some classes of topological posets including the Grassmannian and configuration posets, G̃n(R) and expn(X) which were introduced and studied by V. Vassiliev. Among o...

This article proposes modeling, simulation and kinematic and workspace analysis of a spatial cable suspended robot as incompletely Restrained Positioning Mechanism (IRPM). These types of robots have six cables equal to the number of degrees of freedom. After modeling, the kinds of workspace are defined then an statically reachable combined workspace for different geometric structures of fixed a...