This mail is publicly posted to a distribution list as part of a process
of public discussion, any automatically generated statements to the
contrary non-withstanding. It is the opinion of the author, and does not
represent an official company view. (01)
Sean Barker
BAE SYSTEMS - Advanced Technology Centre
Bristol, UK
+44(0) 117 302 8184 (02)
BAE Systems (Operations) Limited
Registered Office: Warwick House, PO Box 87, Farnborough Aerospace
Centre, Farnborough, Hants, GU14 6YU, UK
Registered in England & Wales No: 1996687 (03)
<snip/> (04)
> >The problem I was looking at was not how to represent points
> >accurately, but in the presence of (unquantified)
> inaccuracy, to ensure
> >that topological validity was preserved.
>
> Ah, that is hard. Arbitrarily small 'errors' can completely
> change the topology, is the problem. (05)
But exactly my problem (06)
>
> >In practice, the geometrical errors
> >were too small to worry about, but the topological errors were
> >intractable, at least with the tools we had at the time.
> >
> >In the resulting system, intervals did not have end-points,
> though you
> >could separate two intervals by a point. Alternatively, you
> could say
> >that all intervals were open sets, AS WERE THEIR COMPLIMENTS.
>
> There is a classical way to do this, which is to restrict
> oneself to open regular subsets of points, and use as an
> addition operation the interior of the unions of the
> closures. This 'fills up' any single-point 'cracks' or breaks
> in the solids. Or use the dual:
> closed sets and the addition is the closure of the union of
> the interiors. This eliminates 'foils' one point thick.
> Sounds like one of these might have been what you needed (?) (07)
These regularized set operators were already in use as theoretical tools
in CSG (Computational Solid Geometry). While they solve the theoretical
problem, they did not solve the computational problem. (08)
>
> >Or rather,
> >a point could be classified against an interval as being IN,
> OUT or ON,
> >with ON corresponding to the indeterminate value of the Logic of
> >Partial Functions.
>
> Which logic of PFs? Do you mean 3-valued logic? (Blech) (09)
Definitely one of the three valued ones - though with the sort of
reasoning we were doing, it technical distinctions between the various
LPF's were not important (at least for the LPF's I came across). One
reason for using LPF is that it corresponds nicely to the three way
distinction in CAD between IN, ON, and OUT, and simplifies reasoning
about some classes of intersections. (010)
> > (011)
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