The Design of a Graphics Engine for the Development of Virtual Reality Applications

This work presents the design and the features of a flexible realtime 3D graphics engine aimed at the development of multimedia applications and collaborative virtual environments. The engine, called EnCIMA (Engine for Collaborative andImmersive Multimedia Applications), enables a fast development process of applications by providing a high level interface, which has been implemented using the C++object-oriented programming paradigm. The main features of the proposed engine are the support to scene management, ability to load static and animated 3D models, particle system effects, network connection management to support collaboration, and collision detection. In addition, the engine supports several specialized interaction devices such as 3D mice, haptic devices, 3D motion trackers, data-gloves, and joystickswith and without force feedback. The engine also enables the developer to choose the way the scene should be rendered to, i.e. using standard display devices, stereoscopy, or even several simultaneous projection for spatially immersive devices. As part of the evaluation process, we have compared the performance of EnCIMA to a game engine and two scene graph toolkits, through the use of a testbed application. The performanceresults and the wide variety of non-conventional interaction devices supported are evidences that EnCIMA can be considered a real time virtual reality engine

On Algebraic Connectivity Augmentation

Suppose that G is an undirected graph, and that H is a spanning subgraph of G c whose edges induce a subgraph on p vertices. We consider the expression α(G∪H)− α(G), where α denotes the algebraic connectivity. Specifically, we provide upper and lower bounds on α(G ∪ H) − α(G) in terms of p, and characterise the corresponding equality cases. We also discuss the density of the expression α(G ∪ H) − α(G) in the interval [0, p]. A bound on α(G ∪ H) − α(G) is provided in a special case, and several examples are considered. Key words: Graph, Laplacian matrix, Algebraic connectivity