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Set difference between intervals #1316

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mforets opened this issue Apr 30, 2019 · 0 comments · Fixed by #1330
Closed

Set difference between intervals #1316

mforets opened this issue Apr 30, 2019 · 0 comments · Fixed by #1330
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mforets commented Apr 30, 2019

In the 1D case, the set difference I1 \ I2 between the intervals I1 and I2 can be either:

a- the empty set
b- one interval (either corresponding to the left side or to the right side)
c- two intervals (one subinterval corresponding to the left side and another one to the right side)

I thought about this and i'm inclined to make the set difference return a UnionSetArray of intervals both in b and c. This may simplify extending to two or higher dimensions.

See also #1305
@mforets mforets self-assigned this Apr 30, 2019
@mforets mforets mentioned this issue May 1, 2019
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mforets added a commit that referenced this issue May 6, 2019
@mforets
#1316 - Set difference between intervals (#1330)
4f5d775 
* add concrete difference

* add tests

* Update test/unit_Interval.jl

Co-Authored-By: mforets <[email protected]>

* Update src/concrete_difference.jl

Co-Authored-By: mforets <[email protected]>

* rename to difference.jl

* update return type

* update tests

* fix docs

* fix subscripts

* add algorithm

* Update src/difference.jl

Co-Authored-By: mforets <[email protected]>

* Update src/difference.jl

Co-Authored-By: mforets <[email protected]>

* add isflat and additional docs
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#1316 - Set difference between intervals JuliaReach/LazySets.jl
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