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#396 - Concrete intersection of two hyperrectangles #399

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7 changes: 7 additions & 0 deletions docs/src/lib/binary_functions.md
Original file line number Diff line number Diff line change
@@ -43,3 +43,10 @@ is_intersection_empty(::Hyperplane{Float64}, ::Zonotope{Float64})
is_intersection_empty(::Ball2{Float64}, ::Ball2{Float64})
is_intersection_empty(::LineSegment{Float64}, ::LineSegment{Float64})
```

## Intersection of two sets

```@docs
intersection(::Line{Float64}, ::Line{Float64})
intersection(::Hyperrectangle{Float64}, ::Hyperrectangle{Float64})
```
1 change: 0 additions & 1 deletion docs/src/lib/representations.md
Original file line number Diff line number Diff line change
@@ -154,7 +154,6 @@ vertices_list(::Interval)
Line
dim(::Line{Float64})
σ(::AbstractVector{Float64}, ::Line{Float64})
intersection(::Line{Float64}, ::Line{Float64})
```

## Line segment
49 changes: 48 additions & 1 deletion src/concrete_intersection.jl
Original file line number Diff line number Diff line change
@@ -10,7 +10,6 @@ Return the intersection of two 2D lines.
### Input

- `L1` -- first line

- `L2` -- second line

### Output
@@ -42,3 +41,51 @@ function intersection(L1::Line{N}, L2::Line{N})::Vector{N} where {N<:Real}
return N[]
end
end

"""
intersection(H1::AbstractHyperrectangle{N},
H2::AbstractHyperrectangle{N}
)::Union{<:Hyperrectangle{N}, EmptySet{N}} where {N<:Real}

Return the intersection of two hyperrectangles.

### Input

- `H1` -- first hyperrectangle
- `H2` -- second hyperrectangle

### Output

If the hyperrectangles do not intersect, the result is the empty set.
Otherwise the result is the hyperrectangle that describes the intersection.

### Algorithm

In each isolated direction `i` we compute the rightmost left border and the
leftmost right border of the hyperrectangles.
If these borders contradict, then the intersection is empty.
Otherwise the result uses these borders in each dimension.
"""
function intersection(H1::AbstractHyperrectangle{N},
H2::AbstractHyperrectangle{N}
)::Union{<:Hyperrectangle{N}, EmptySet{N}} where {N<:Real}
n = dim(H1)
c1 = center(H1)
c2 = center(H2)
r1 = radius_hyperrectangle(H1)
r2 = radius_hyperrectangle(H2)
high = Vector{N}(n)
low = Vector{N}(n)
for i in 1:n
high1 = c1[i] + r1[i]
low1 = c1[i] - r1[i]
high2 = c2[i] + r2[i]
low2 = c2[i] - r2[i]
high[i] = min(high1, high2)
low[i] = max(low1, low2)
if high[i] < low[i]
return EmptySet{N}()
end
end
return Hyperrectangle(high=high, low=low)
end
9 changes: 7 additions & 2 deletions test/unit_Hyperrectangle.jl
Original file line number Diff line number Diff line change
@@ -118,13 +118,18 @@ for N in [Float64, Rational{Int}, Float32]
@test ⊆(H2, B1) && ⊆(B1, H2)
@test ⊆(B1, B2) && !⊆(B2, B1)

# intersection emptiness
# intersection & intersection emptiness
H1 = Hyperrectangle(N[1.0, 1.0], N[2.0, 2.0])
H2 = Hyperrectangle(N[3.0, 3.0], N[2.0, 2.0])
B1 = BallInf(N[2.0, 4.0], N(0.5))
intersection_empty, point = is_intersection_empty(H1, H2, true)
cap = intersection(H1, H2)
@test cap isa Hyperrectangle{N} && center(cap) == N[2., 2.] &&
radius_hyperrectangle(cap) == N[1., 1.]
@test !is_intersection_empty(H1, H2) &&
!intersection_empty && point ∈ H1 && point ∈ H2
!intersection_empty && point ∈ H1 && point ∈ H2
cap = intersection(H1, B1)
@test cap isa EmptySet{N}
@test is_intersection_empty(H1, B1) && is_intersection_empty(H1, B1, true)[1]

# linear map (concrete)