In this paper, we present a framework to simulate biological cellular processes involving a strong topological and geometric structuration. Our framework is based on topology-based geometric modelling. The edge labels of a graph sub-class, the n-dimensional generalized maps, model the neighbouring relations between biological compartments. Thus, membranes become topological objects of the n-dim...

In this work we extend the geometric approach to the theory of evidence in order to study the geometric behavior of the two quantities inherently associated with a belief function. i.e. the plausibility and commonality functions. After introducing the analogous of the basic probability assignment for plausibilities and commonalities, we exploit it to understand the simplicial form of both plaus...

The representation of geometric objects and their transformation are the two key aspects in computer graphics applications. Traditionally, computer-intensive matrix calculations are involved in modeling and rendering three-dimensional (3D) scenery. Geometric algebra (aka Clifford algebra) is attracting attention as a natural way to model geometric facts and as a powerful analytical tool for sym...

Transforming a geometric algorithm into an effective computer program is a difficult task. This transformation is particularly made hard by the basic assumptions of most theoretical geometric algorithms concerning complexity measures and (more crucially) the handling of robustness issues, namely issues related to arithmetic precision and degenerate input. The paper starts with a discussion of t...

Although exposure to bacteria has been assessed in cabin air previously, minimal numbers of samples have been collected in-flight. The purpose of this research was to comprehensively characterize bacterial concentrations in the aircraft cabin. Twelve randomly selected flights were sampled on Boeing-767 aircraft, each with a flight duration between 4.5 and 6.5 h. N-6 impactors were used to colle...

Many graphics systems allow a user to describe three dimensional objects with polygon meshes or surface patches. However to achieve realistic scenes for making animated film some objects are better described with stochastic techniques. Some examples would be clouds. tire and mountains. We describe here a hierarchical graphics system consisting of objects which contain geometrical transformation...

We introduce a novel basis for multivariate hierarchical tensor-product spline spaces. Our construction combines the truncation mechanism (Giannelli et al., 2012) with the idea of decoupling basis functions (Mokrǐs et al., 2014). While the first mechanism ensures the partition of unity property, which is essential for geometric modeling applications, the idea of decoupling allows us to obtain a...

We formulate an approach to the geometry of Riemann–Cartan spaces provided with nonholonomic distributions defined by generic off–diagonal and nonsymmetric metrics inducing effective nonlinear and affine connections. Such geometries can be modelled by moving nonholonomic frames on (pseudo) Riemannian manifolds and describe various types of nonholonomic Einstein, Eisenhart–Moffat and Finsler–Lag...

This work presents a novel method for haptic rendering contact force and surface properties for virtual objects using the Conformal Geometric Algebra orthogonal decomposition approach. The mathematical representation of geometric primitives along with collision algorithms based on its mathematical properties is presented. The orthogonal decomposition of contact and interaction forces is achieve...

In this work we extend the geometric approach to the theory of evidence in order to study the geometric behavior of the two quantities inherently associated with a belief function. i.e. the plausibility and commonality functions. After introducing the analogous of the basic probability assignment for plausibilities and commonalities, we exploit it to understand the simplicial form of both plaus...