A global visibility map is a spherical image built to describe the complete set of global visible view directions for a surface. In this paper, we consider the computation of global visibility maps for regions on the boundary of a polyhedron. Both the self-occlusions introduced by a region and the global occlusions introduced by the rest of the surfaces on the boundary of the polyhedron are con...

In a partially ordered semigroup with the duality (or polarity) transform, it is possible to define a generalisation of continued fractions. General sufficient conditions for convergence of continued fractions are provided. Two particular applications concern the cases of convex sets with the Minkowski addition and the polarity transform and the family of non-negative convex functions with the ...

Given a lattice polytope Q ⊆ IR, we define an affine scheme M̄ that reflects the possibilities of splitting Q into a Minkowski sum. On the other hand, Q induces a toric Gorenstein singularity Y , and we construct a flat family over M̄ with Y as special fiber. In case Y has an isolated singularity only, this family is versal.

This paper discusses the visual algebraic speciication (vas) formalism and its supporting interactive environment (vase). The vas formalism is intended for the deenition of visual syntax and semantics and is aimed at generating language speciic environments. The collection construct of vas is emphasized in that it supports the convenient speciication of language constructs involving arbitrarily...

With the growth of its popularity, VoIP is increasingly popular nowadays. Similarly to other Internet applications, VoIP users may desire to be unlinkable with their participated VoIP session records for privacy issues. In this paper, we explore the Items of Interests (IOIs) from anonymisation aspects based on a simplified VoIP model and analyse the potential links between them. We address poss...

We consider the problem of listing faces of the Minkowski sum of several V-polytopes in R. An algorithm for listing all faces of dimension up to j is presented, for any given 0 ≤ j ≤ d − 1. It runs in time polynomial in the sizes of input and output.

AAA 2 1 Introduction

In this short note we give a characterization of the support map from classical convexity. We show it is the unique additive transformation from the class of closed convex sets in Rn which include 0 to the class of positive 1-homogeneous functions on Rn. This will be a consequence of a theorem about transforms from the class of convex sets to itself which preserve Minkowski addition. © 2009 Els...

Given a disk O in the plane called the objective, we want to find n small disks P1, . . . , Pn called the pupils such that ⋃n i,j=1 Pi ⊖ Pj ⊇ O, where ⊖ denotes the Minkowski difference operator, while minimizing the number of pupils, the sum of the radii or the total area of the pupils. This problem is motivated by the construction of very large telescopes from several smaller ones by so-calle...