Abel J. P. Gomes

Learn More
This paper is concerned with the mathematics and formal specification of " set-like " operations for the mixed dimension cellular objects of the Djinn Application Programming Interface. The relationships between these operations and stratifications of dimensionally heterogeneous semi-analytic point-sets are uncovered and formalised. Semianalytic geometry is(More)
The major purpose of this paper is to introduce a general theory within which previous boundary representations (B-reps) are a special case. Basically, this theory combines sub-analyt,ic geometry and theory of stratifications. The sub-analyt,ic geometry covers almost, all geometric engineering artefacts, and it is a generalisation of the semi-analytic(More)
Computing molecular surfaces is important to measure areas and volumes of molecules, as well as to infer useful information about interactions with other molecules. Over the years many algorithms have been developed to triangulate and to render molecular surfaces. However, triangulation algorithms usually are very expensive in terms of memory storage and(More)
Results from the study of O-minimal structures are used to formalise fundamental objects and operations for geometric modelling kernels. O-minimal structures provide a more general setting than the traditional semialgebraic sets; they allow semianalytic sets such as screw-threads to be modelled accurately. O-minimality constrains the class of sets to ensure(More)
This paper introduces a concise and responsiveness data structure, called AIF (Adjacency and Incidence Framework), for multiresolution meshes, as well as a new simplification algorithm based on the planarity of neighboring faces. It is an optimal data structure for polygonal meshes, manifold and non-manifold, which means that a minimal number of direct and(More)