Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  develop a representation for the topological structure of subdivided manifolds (with and without boundary) of dimension  d  ≥ 1 which allows straightforward access of the available order information. It is shown that there exists a large amount of ordering information in subdivided manifolds: given a ( k -2)-cell in the boundary of a ( k +1)-cell, 1 ≤  k  ≤  d , all of the  k - and ( k -1)-cells 'beten them' can be ordered 'around' the ( k -2)-cell. This includes the usual orderings in 2- and 3-dimensional objects.  introduce the 'cell-tuple structure', a simple, uniform representation of the incidence and ordering information in a subdivided manifold. It includes the quad-edge data structure of Guibas and Stolfi [GS 85] and the facet-edge data structure of Dobkin and Laszlo [DL 87] as special cases in dimensions 2 and 3, respectively.
['Erik Brisson']
I am writing a research paper on a idea Representing geometric structures in d dimensions: topology and order
[{"from": "human", "value": "I am writing a research paper on a idea Representing geometric structures in d dimensions: topology and order"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  develop a representation for the topological structure of subdivided manifolds (with and without boundary) of dimension  d  \u2265 1 which allows straightforward access of the available order information. It is shown that there exists a large amount of ordering information in subdivided manifolds: given a ( k -2)-cell in the boundary of a ( k +1)-cell, 1 \u2264  k  \u2264  d , all of the  k - and ( k -1)-cells 'beten them' can be ordered 'around' the ( k -2)-cell. This includes the usual orderings in 2- and 3-dimensional objects.  introduce the 'cell-tuple structure', a simple, uniform representation of the incidence and ordering information in a subdivided manifold. It includes the quad-edge data structure of Guibas and Stolfi [GS 85] and the facet-edge data structure of Dobkin and Laszlo [DL 87] as special cases in dimensions 2 and 3, respectively."}]