Re: Comments on Norbert's topological extension of relational algebra

On 2015-12-11 17:39:15 +0000, Tegiri Nenashi said:

> Can you please expand on differences of your method with Egenhofer's
> (aside the database angle)?

Norbert may have better arguments, but what I find it intriguing in his approach is that you store
the *whole* topology of the *whole* space potentially in a cheap and simple way. As far as I know,
in DE-9IM (based on Egenhofer's ideas) you may model the relationship between two objects with one
3x3 matrix, but storing a matrix for each possible pair of objects (or for a subset big enough to
reconstruct the whole topology) is most likely impractical. Hence, such matrices are usually used
to infer the topological relationships between objects from geometric data (e.g., see
ST_Relate() in SQL/MM). Besides, Norbert's model provides a way to build new topological spaces
from existing ones using well-founded well-known constructions. This is a feature I have not seen
elsewhere (not that I know all models out there, though). It might still be infeasible in practice,
given that there are transitive closures to compute here and there, but it has some potential.

Btw, I have found that this paper provides a less formal but way more accessible introduction to the
topic:

https://www.academia.edu/364355/Geometrical_and_Topological_Approaches_In_Building_Information_Modelling

Nicola

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