Finding a closest point in a lattice of Voronoi's first kind

We show that for those lattices of Voronoi's first kind with known obtuse superbasis, a closest lattice point can be computed in $O(n^4)$ operations where $n$ is the dimension of the lattice. To achieve this a series of relevant lattice vectors that converges to a closest lattice point is found. We show that the series converges after at most $n$ terms. Each vector in the series can be efficiently computed in $O(n^3)$ operations using an algorithm to compute a minimum cut in an undirected flow network

VISIO-HAPTIC DEFORMABLE MODEL FOR HAPTIC DOMINANT PALPATION SIMULATOR

Vision and haptic are two most important modalities in a medical simulation. While visual cues assist one to see his actions when performing a medical procedure, haptic cues enable feeling the object being manipulated during the interaction. Despite their importance in a computer simulation, the combination of both modalities has not been adequately assessed, especially that in a haptic dominant environment. Thus, resulting in poor emphasis in resource allocation management in terms of effort spent in rendering the two modalities for simulators with realistic real-time interactions. Addressing this problem requires an investigation on whether a single modality (haptic) or a combination of both visual and haptic could be better for learning skills in a haptic dominant environment such as in a palpation simulator. However, before such an investigation could take place one main technical implementation issue in visio-haptic rendering needs to be addresse

VISIO-HAPTIC DEFORMABLE MODEL FOR HAPTIC DOMINANT PALPATION SIMULATOR

Vision and haptic are two most important modalities in a medical simulation. While visual cues assist one to see his actions when performing a medical procedure, haptic cues enable feeling the object being manipulated during the interaction. Despite their importance in a computer simulation, the combination of both modalities has not been adequately assessed, especially that in a haptic dominant environment. Thus, resulting in poor emphasis in resource allocation management in terms of effort spent in rendering the two modalities for simulators with realistic real-time interactions. Addressing this problem requires an investigation on whether a single modality (haptic) or a combination of both visual and haptic could be better for learning skills in a haptic dominant environment such as in a palpation simulator. However, before such an investigation could take place one main technical implementation issue in visio-haptic rendering needs to be addresse

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described