In this paper we introduce a general descriptor-type LFT representation of rational parametric matrices. This generalized representation allows to represent arbitrary rationally dependent multivariate functions in LFT-form. As applications, we develop explicit LFT realizations of the transfer-function matrix of a linear descriptor system whose state space matrices depend rationally on a set of ...

We take an approach to specify and control implicitly dened n-dimensional free-form solid primitives using parametric functions of n variables. Outside of the domain, the parametric function value increases or decreases rapidly that is not suitable to design geometric objects. In this paper, we introduce a functional clipping operation which allows a free-form primitive to be treated as traditi...

As a straightforward generalization of the well-known Voronoi construction, Laguerre tessellations have long found application in the modelling, analysis and simulation of polycrystalline microstructures. The application of Laguerre tessellations to real (as opposed to computed) microstructures—such as those obtained by modern 3D characterization techniques like x-ray microtomography or focused...

Measurements of structure orientations are afflicted with uncertainties which arise from many sources. Commonly, such uncertainties involve instrument imprecision, external disturbances and human factors. The aggregated uncertainty depends on the uncertainty of each of the sources. The orientation of an object measured in a borehole (e.g. a fracture) is calculated using four parameters: the bea...

The most important concepts for the handling and storage of freeform shapes in geometry processing applications are parametric representations and volumetric representations. Both have their specific advantages and drawbacks. While the algebraic complexity of volumetric representations S = {(x, y, z) | f(x, y, z) = 0} is independent from the shape complexity, the domain Ω of a parametric repres...

In this paper, we address the problem of multi-frame video registration using an appearance-based framework, where linear subspace constraints are applied in terms of the appearance subspace constancy assumption [3]. We frame the multiple-image registration in a two step iterative algorithm. First, a feature space is built through and Singular Value Decomposition (SVD) of a second moment matrix...

The cortical sulci are brain structures resembling thin convoluted ribbons embedded in three dimensions. The importance of the sulci lies primarily in their relation to the cytoarchitectonic and functional organization of the underlying cortex and in their utilization as features in non-rigid registration methods. This paper presents a methodology for extracting parametric representations of th...

Representing large boolean sets has many important application areas, including hardware verification. There are two main approaches: the characteristic and parametric representation. This note describes the approaches and briefly compares them

Let G be the class of simple planar graphs of minimum degree ≥ 4 in which no two vertices of degree 4 are adjacent. A graph H is light in G if there is a constant w such that every graph in G which has a subgraph isomorphic to H also has a subgraph isomorphic to H whose sum of degrees in G is ≤ w. Then we also write w(H) ≤ w. It is proved that the cycle Cs is light if and only if 3 ≤ s ≤ 6, whe...