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dc.contributor.advisorMiddleditch, A-
dc.contributor.advisorReade, C-
dc.contributor.authorGomes, Abel Joao Padrao-
dc.descriptionThis thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.en_US
dc.description.abstractThis dissertation focuses on the mathematical design of a unified shape kernel for geometric computing, with possible applications to computer aided design (CAM) and manufacturing (CAM), solid geometric modelling, free-form modelling of curves and surfaces, feature-based modelling, finite element meshing, computer animation, etc. The generality of such a unified shape kernel grounds on a shape theory for objects in some Euclidean space. Shape does not mean herein only geometry as usual in geometric modelling, but has been extended to other contexts, e. g. topology, homotopy, convexity theory, etc. This shape theory has enabled to make a shape analysis of the current geometric kernels. Significant deficiencies have been then identified in how these geometric kernels represent shapes from different applications. This thesis concludes that it is possible to construct a general shape kernel capable of representing and manipulating general specifications of shape for objects even in higher-dimensional Euclidean spaces, regardless whether such objects are implicitly or parametrically defined, they have ‘incomplete boundaries’ or not, they are structured with more or less detail or subcomplexes, which design sequence has been followed in a modelling session, etc. For this end, the basic constituents of such a general geometric kernel, say a combinatorial data structure and respective Euler operators for n-dimensional regular stratified objects, have been introduced and discussed.en_US
dc.publisherBrunel University, School of Information Systems, Computing and Mathematics-
dc.relation.ispartofSchool of Information Systems, Computing and Mathematics-
dc.subjectUnified shape kernelen_US
dc.subjectFree-form modellingen_US
dc.subjectFeature-based modellingen_US
dc.subjectShape theoryen_US
dc.subjectShape analysisen_US
dc.titleShape theory and mathematical design of a general geometric kernel through regular stratified objectsen_US
Appears in Collections:Computer Science
Dept of Computer Science Theses

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