in addition to exploring constructions and properties of limits and colimits in categories of topologicalalgebras, we study special subcategories of topological algebras and their properties. in particular, undercertain conditions, reflective subcategories when paired with topological structures give rise to reflectivesubcategories and epireflective subcategories give rise to epireflective subc...

To Bob MacPherson on his 60th birthday

We introduce a new class of morphisms for event structures. The category obtained is cartesian closed, and a natural notion of quotient event structure is defined within it. We study in particular the topological space of maximal configurations of quotient event structures. We introduce the compression of event structures as an example of quotient: the compression of an event structure E is a m...

The three-dimensional mesh compression has increasingly been a vital subject matter for years and has had a rich state of the art. Therefore, it is selected to be the cornerstone of this article. As a matter of fact, we began with the mono-resolution compression methods; then, we moved to the progressive methods and, at last, to the methods based on multi-resolution analysis. Now, we can distin...

Vector Quantization (VQ) is an efficient image compression approach. Among the different existing algorithms, Kohonen's Self Organizing Feature Map (SOFM) is one of the wellknown method for VQ. It allows efficient codebooks design with interesting topological properties to be performed. Furthermore, use of VQ for compression delivers basic information on the image content in the same process. H...

Multiresolution Hierarchies (MH) and Directed Acyclic Graphs (DAG) are two recent approaches for the compression of highresolution shadow information. In this paper, we introduce Merged Multiresolution Hierarchies (MMH), a novel data structure that unifies both concepts. An MMH leverages both hierarchical homogeneity exploited in MHs, as well as topological similarities exploited in DAG represe...

This paper proposes a loss-less method for encoding and compressing three-dimensional (3D) geometric models that may contain any combinations of wireframe, surface, and solid forms as well as various non-simple topological structure (e.g. cavities and strut edges) that could exist in 3D CAD models. Given a model, our method transforms it into a simple triangular mesh model by applying a sequenc...

ÐMost systems that support visual interaction with 3D models use shape representations based on triangle meshes. The size of these representations imposes limits on applications for which complex 3D models must be accessed remotely. Techniques for simplifying and compressing 3D models reduce the transmission time. Multiresolution formats provide quick access to a crude model and then refine it ...

Edgebreaker is a simple scheme for compressing the triangle/vertex incidence graphs (sometimes called connectivity or topology) of three-dimensional triangle meshes. Edgebreaker improves upon the storage required by previously reported schemes, most of which can guarantee only an O(tlog(t)) storage cost for the incidence graph of a mesh of t triangles. Edgebreaker requires at most 2t bits for a...