Offset curves have diverse engineering applications, which have consequently motivated extensive research concerning various offset techniques. Offset research in the early 1980s focused on approximation techniques to solve immediate application problems in practice. This trend continued until 1988, when Hoschek [1, 2] applied non-linear optimization techniques to the offset approximation probl...

Tutorial topics • A bit of history • Examples of variational methods • A brief intro to graphical models • Variational mean field theory – Accuracy of variational mean field – Structured mean field theory • Variational methods in Bayesian estimation • Convex duality and variational factorization methods – Example: variational inference and the QMR-DT Variational methods • Classical setting: " f...

In this paper we introduce a variant of the three-field formulation where we use only two sets of variables. Considering, to fix the ideas, the homogeneous Dirichlet problem for −∆u = g in Ω, our variables are i) the approximations uh of u in each sub-domain Ωs (each on its own grid), and ii) an approximation ψh of u on the skeleton (the union of the interfaces of the sub-domains) on an indepen...

Techniques are presented to progressively approximate and compress in a lossless manner two-colored (i.e. binary) 3D objects (as well as objects of arbitrary dimensionality). The objects are represented by a region octree implemented using a pointerless representation based on locational codes. Approximation is achieved through the use of a forest. This method labels the internal nodes of the o...

1 Aula UTFSM-CIMNE, Departamento de Ingenierı́a Mecánica, Universidad Técnica Federico Santa Marı́a, Avenida España 1680, 2340000 Valparaı́so, Chile 2 Departamento de Matemática, Universidad Técnica Federico Santa Marı́a, Avenida España 1680, 2340000 Valparaı́so, Chile 3 Escuela de Ingenierı́a Mecánica, Pontificia Universidad Católica de Valparaı́so, Los Carrera 01567, Quilpué, 2430120 Valparaı́so, Chile

Effective boundary conditions (wall laws) are commonly employed to approximate PDEs in domains with rough boundaries, but it is neither easy to design such laws nor to estimate the related approximation error. A two-scale asymptotic expansion based on a domain decomposition result is used here to mitigate such difficulties, and as an application we consider the Poisson equation. The proposed sc...