Set-combinations of the mixed-dimension cellular objects of the Djinn API

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 semianalytic point-sets are uncovered and formalised. Semianalytic geometry is central to the algebraic model discussed in this paper, but multidisciplinary concepts from topology, differential geometry and computer aided geometric design also have been used. In particular, the use of strong relative topological stratifications enables Djinn to satisfy significant industrial requirements. Acknowledgements The Djinn API design decisions that are discussed or implicit in this paper reflect a consensus of the Djinn project team: Cecil Armstrong, Adrian Bowyer, Stephen Cameron, Jonathan Corney, Graham Jared, Ralph Martin, Alan Middleditch, Malcolm Sabin, Jonathan Salmon, and John Woodwark. The Djinn project was funded by the Engineering and Physical Sciences Research Council (EPSRC) of the UK.