Search for spatial predicate proof

[Gabriel De Luca]

Hello everyone,

 I am working with a group of researchers on developing an algorithm to
decompose 2D polygons into meaningful parts, without using triangulations.

 Our algorithm relies on spatial set operations.
 Due to finite-precision floating point arithmetic, as clarified in the
Robustness section of the GEOS FAQs, as well as in section D.7 of the JTS
FAQs, some predicates do not necessarily agree in theory and practice.

 However, I am interested in finding out if there is any proof for the
following predicate, for which I do not find in practice that differ from
the theory:

Given two polygons P and Q, which overlaps:

 - *((P difference Q) touches (P difference(P difference Q)))* seems to be
always True and the intersection between their boundaries has dimension 1
(their interiors do not intersect and their boundaries have at least one
segment in common).

  If you know of any academic article in which this case has been
investigated, applied to finite-precision floating point computations, even
if you knew a counterexample, it would be of great help in our research.


Regards, and thank you very much for your great work,
Gabriel
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