We consider the class F of 2-connected non-planar K3,3-subdivision-free graphs that are embeddable in the projective plane. We show that these graphs admit a unique decomposition as a graph K5 (the core) where the edges are replaced by two-pole networks constructed from 2-connected planar graphs. A method to enumerate these graphs in the labelled case is described. Moreover, we enumerate the ho...

Subdivision surfaces refer to a class of modelling schemes that define an object through recursive subdivision starting from an initial control mesh. Similar to B-splines, the final surface is defined by the vertices of the initial control mesh. These surfaces were initially conceived as an extension of splines in modelling objects with a control mesh of arbitrary topology. They exhibit a numbe...

We consider the class F of 2-connected non-planar K3,3-subdivision-free graphs that are embeddable in the projective plane. We show that these graphs admit a unique decomposition as a graph K5 (the core) where the edges are replaced by two-pole networks constructed from 2-connected planar graphs. A method to enumerate these graphs in the labelled case is described. Moreover, we enumerate the ho...

‎Let $G=(V(G),E(G))$ be a graph‎, ‎$gamma_t(G)$. Let $ooir(G)$ be the total domination and OO-irredundance number of $G$‎, ‎respectively‎. ‎A total dominating set $S$ of $G$ is called a $textit{total perfect code}$ if every vertex in $V(G)$ is adjacent to exactly one vertex of $S$‎. ‎In this paper‎, ‎we show that if $G$ has a total perfect code‎, ‎then $gamma_t(G)=ooir(G)$‎. ‎As a consequence, ...

We present an algorithm for the two-dimensional translational containmentproblem: nd translations for k polygons (with up tom vertices each) which place them inside a polygonal container (with n vertices) without overlapping. The polygons and container may be nonconvex. The containment algorithm consists of new algorithms for restriction, evaluation, and subdivision of two-dimensional con gurat...

The Eternal system is a CORBA 2.0-compliant system that provides, in addition to the location transparency and the interoperability inherent in the CORBA standard, support for replicated objects and thus fault tolerance. Eternal exploits the Internet Inter-ORB Protocol (IIOP) interface to ‘‘attach’’ itself transparently to objects operating over a commercial CORBA Object Request Broker (ORB). T...

A new technique for the reconstruction of a smooth surface from a set of 3D data points is presented. The reconstructed surface is represented by an everywhere Ccontinuous subdivision surface which interpolates all the given data points. The new technique consists of two major steps. First, an ef£cient surface reconstruction method is applied to produce a polyhedral approximation to the given d...

We introduce a new class of subdivision surfaces which generalize uniform tensor product B-spline surfaces of any bi-degree to meshes of arbitrary topology. Surprisingly , this can be done using subdivision rules that involve direct neighbors only. Consequently, our schemes are very easy to implement, regardless of degree. The famous Catmull-Clark scheme is a special case. Similarly we show tha...

A totally odd H-subdivision means a subdivision of a graph H in which each edge of H corresponds to a path of odd length. Thus this concept is a generalization of a subdivision of H. In this paper, we give a structure theorem for graphs without a fixed graph H as a totally odd subdivision. Namely, every graph with no totally odd H-subdivision has a tree-decomposition such that each piece is eit...