An n-sided polygonal model to calculate the impact of cyber security events

This paper presents a model to represent graphically the impact of cyber events (e.g., attacks, countermeasures) in a polygonal systems of n-sides. The approach considers information about all entities composing an information system (e.g., users, IP addresses, communication protocols, physical and logical resources, etc.). Every axis is composed of entities that contribute to the execution of the security event. Each entity has an associated weighting factor that measures its contribution using a multi-criteria methodology named CARVER. The graphical representation of cyber events is depicted as straight lines (one dimension) or polygons (two or more dimensions). Geometrical operations are used to compute the size (i.e, length, perimeter, surface area) and thus the impact of each event. As a result, it is possible to identify and compare the magnitude of cyber events. A case study with multiple security events is presented as an illustration on how the model is built and computed.Comment: 16 pages, 5 figures, 2 tables, 11th International Conference on Risks and Security of Internet and Systems, (CRiSIS 2016), Roscoff, France, September 201

Graphs with Plane Outside-Obstacle Representations

An \emph{obstacle representation} of a graph consists of a set of polygonal obstacles and a distinct point for each vertex such that two points see each other if and only if the corresponding vertices are adjacent. Obstacle representations are a recent generalization of classical polygon--vertex visibility graphs, for which the characterization and recognition problems are long-standing open questions. In this paper, we study \emph{plane outside-obstacle representations}, where all obstacles lie in the unbounded face of the representation and no two visibility segments cross. We give a combinatorial characterization of the biconnected graphs that admit such a representation. Based on this characterization, we present a simple linear-time recognition algorithm for these graphs. As a side result, we show that the plane vertex--polygon visibility graphs are exactly the maximal outerplanar graphs and that every chordal outerplanar graph has an outside-obstacle representation.Comment: 12 pages, 7 figure

Simple and Robust Boolean Operations for Triangulated Surfaces

Boolean operations of geometric models is an essential issue in computational geometry. In this paper, we develop a simple and robust approach to perform Boolean operations on closed and open triangulated surfaces. Our method mainly has two stages: (1) We firstly find out candidate intersected-triangles pairs based on Octree and then compute the inter-section lines for all pairs of triangles with parallel algorithm; (2) We form closed or open intersection-loops, sub-surfaces and sub-blocks quite robustly only according to the cleared and updated topology of meshes while without coordinate computations for geometric enti-ties. A novel technique instead of inside/outside classification is also proposed to distinguish the resulting union, subtraction and intersection. Several examples have been given to illus-trate the effectiveness of our approach.Comment: Novel method for determining Union, Subtraction and Intersectio

Morphing of Triangular Meshes in Shape Space

We present a novel approach to morph between two isometric poses of the same non-rigid object given as triangular meshes. We model the morphs as linear interpolations in a suitable shape space $\mathcal{S}$. For triangulated 3D polygons, we prove that interpolating linearly in this shape space corresponds to the most isometric morph in $\mathbb{R}^3$. We then extend this shape space to arbitrary triangulations in 3D using a heuristic approach and show the practical use of the approach using experiments. Furthermore, we discuss a modified shape space that is useful for isometric skeleton morphing. All of the newly presented approaches solve the morphing problem without the need to solve a minimization problem.Comment: Improved experimental result

Periodic boundary conditions on the pseudosphere

We provide a framework to build periodic boundary conditions on the pseudosphere (or hyperbolic plane), the infinite two-dimensional Riemannian space of constant negative curvature. Starting from the common case of periodic boundary conditions in the Euclidean plane, we introduce all the needed mathematical notions and sketch a classification of periodic boundary conditions on the hyperbolic plane. We stress the possible applications in statistical mechanics for studying the bulk behavior of physical systems and we illustrate how to implement such periodic boundary conditions in two examples, the dynamics of particles on the pseudosphere and the study of classical spins on hyperbolic lattices.Comment: 30 pages, minor corrections, accepted to J. Phys.

Connectivity Compression for Irregular Quadrilateral Meshes

Applications that require Internet access to remote 3D datasets are often limited by the storage costs of 3D models. Several compression methods are available to address these limits for objects represented by triangle meshes. Many CAD and VRML models, however, are represented as quadrilateral meshes or mixed triangle/quadrilateral meshes, and these models may also require compression. We present an algorithm for encoding the connectivity of such quadrilateral meshes, and we demonstrate that by preserving and exploiting the original quad structure, our approach achieves encodings 30 - 80% smaller than an approach based on randomly splitting quads into triangles. We present both a code with a proven worst-case cost of 3 bits per vertex (or 2.75 bits per vertex for meshes without valence-two vertices) and entropy-coding results for typical meshes ranging from 0.3 to 0.9 bits per vertex, depending on the regularity of the mesh. Our method may be implemented by a rule for a particular splitting of quads into triangles and by using the compression and decompression algorithms introduced in [Rossignac99] and [Rossignac&Szymczak99]. We also present extensions to the algorithm to compress meshes with holes and handles and meshes containing triangles and other polygons as well as quads