Add a subset check ⊆(S1, S2) , in particular for speci

Julia's alias is called issubset (see <a href="https:

Possibly helpful: <a href="https://en.wikipedia.org/wiki/Boolean_operations_on_polygon

I would really like to have <a class="issue-link js-issue-link" data-error-text="Faile

Let us continue with the missing cases another time. I created <a class="issue-link js

Subset check about lazysets.jl HOT 7 CLOSED

juliareach commented on May 23, 2024

Subset check

from lazysets.jl.

Comments (7)

schillic commented on May 23, 2024 1

Julia's alias is called issubset (see here). This works out of the box.

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schillic commented on May 23, 2024

Possibly helpful: Boolean operations on polygons

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schillic commented on May 23, 2024

I would really like to have #58 here.
Now we have to provide

Hyperrectangle ⊆ Hyperrectangle
Hyperrectangle ⊆ BallInf
BallInf ⊆ Hyperrectangle
BallInf ⊆ BallInf
and the algorithm is almost exactly the same except that BallInf's radius is a scalar.
If instead we had a common supertype, we could have a function radius(dim) that returns the radius in a given dimension and thus write one function for all four cases (with no performance penalty).

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schillic commented on May 23, 2024

The following table shows straight-forward implementations for most basic set types.
There might be more efficient implementations, but for the moment I am happy with any solution.
"v_i ∈ S" means "check containment of every vertex in set S"; here we need vertices_list and ∈.

↓ ⊆ →	Ball1	Ball2	Ballp	Hyperrectangle/BallInf	Polygon	Singleton
Ball2		simple		interval hull		c = S & r = 0
Ballp				interval hull		c = S & r = 0
Ball1	v_i ∈ S	v_i ∈ S	v_i ∈ S	v_i ∈ S	v_i ∈ S	c = S & r = 0
HR/BI	v_i ∈ S	v_i ∈ S	v_i ∈ S	box containment	v_i ∈ S	c = S & r = 0
Polygon	v_i ∈ S	v_i ∈ S	v_i ∈ S	v_i ∈ S	v_i ∈ S	v_i ∈ S
Singleton	x ∈ S	x ∈ S	x ∈ S	x ∈ S	x ∈ S	x ∈ S