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#3629 - Fix intersection of LineSegments #3630

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merged 6 commits into from
Aug 25, 2024
Merged

#3629 - Fix intersection of LineSegments #3630

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cf42b45
fix intersection of LineSegments
schillic Jul 30, 2024
e86ea77
add/update tests
schillic Jul 30, 2024
d1f37b0
better implementation
schillic Jul 30, 2024
9ad333c
fix case for empty intersection
schillic Jul 30, 2024
2714da3
improve tests
schillic Jul 30, 2024
15c2658
Update src/Sets/LineSegment/intersection.jl
schillic Jul 31, 2024
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34 changes: 22 additions & 12 deletions src/Sets/LineSegment/intersection.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -34,24 +34,34 @@ function intersection(LS1::LineSegment, LS2::LineSegment)
m = intersection(L1, L2)
N = promote_type(eltype(LS1), eltype(LS2))
if m == L1
# determine which segment is in both
p1 = max(min(LS1.p[1], LS1.q[1]), min(LS2.p[1], LS2.q[1]))
p2 = max(min(LS1.p[2], LS1.q[2]), min(LS2.p[2], LS2.q[2]))
q1 = min(max(LS1.p[1], LS1.q[1]), max(LS2.p[1], LS2.q[1]))
q2 = min(max(LS1.p[2], LS1.q[2]), max(LS2.p[2], LS2.q[2]))
if _isapprox(p1, q1) && _isapprox(p2, q2)
return Singleton([p1, p2]) # edges have a point in common
# line segments are on the same line

elseif _leq(p1, q1) && _leq(p2, q2)
return LineSegment([p1, p2], [q1, q2])
# check that the line segments intersect
@inbounds begin
# box approximation
l, r = LS1.p[1] < LS1.q[1] ? (LS1.p[1], LS1.q[1]) : (LS1.q[1], LS1.p[1])
b, t = LS1.p[2] < LS1.q[2] ? (LS1.p[2], LS1.q[2]) : (LS1.q[2], LS1.p[2])
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# check that the other line segment has at least one point inside the box
if !(l <= LS2.p[1] <= r && b <= LS2.p[2] <= t) &&
!(l <= LS2.q[1] <= r && b <= LS2.q[2] <= t)
return EmptySet{N}(2)
end
end

# find the middle two points of the four end points
points = [LS1.p, LS1.q, LS2.p, LS2.q]
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sorted_points = sort(points; by=p -> (p[1], p[2]))
@inbounds begin
mid_point1 = sorted_points[2]
mid_point2 = sorted_points[3]
end
if _isapprox(mid_point1, mid_point2)
return Singleton(mid_point1) # only one point in common
else
return EmptySet{N}(2) # no intersection
return LineSegment(mid_point1, mid_point2)
end

elseif m isa Singleton && m.element ∈ LS1 && m.element ∈ LS2
return m # the intersection point between the lines is in the segments

else
return EmptySet{N}(2) # no intersection
end
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40 changes: 22 additions & 18 deletions test/Sets/LineSegment.jl
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Expand Up @@ -123,34 +123,38 @@ for N in [Float64, Rational{Int}, Float32]
@test !is_intersection_empty(l1, l1_copy) && !intersection_empty && point ∈ l1

# intersection
s1 = LineSegment(N[-5.0, -5.0], N[5.0, 5.0])
s1 = LineSegment(N[-5, -5], N[5, 5])
# collinear shifted down
s2 = LineSegment(N[-6.0, -6.0], N[4.0, 4.0])
@test intersection(s1, s2) isa LineSegment
@test isapprox(intersection(s1, s2).p, N[-5, -5])
@test isapprox(intersection(s1, s2).q, N[4, 4])
s2 = LineSegment(N[-6, -6], N[4, 4])
cap = intersection(s1, s2)
@test cap isa LineSegment
@test ispermutation([cap.p, cap.q], [N[-5, -5], N[4, 4]])
# parallel, not intersect
s3 = LineSegment(N[-5.0, -4.0], N[4.0, 5.0])
@test intersection(s1, s3) isa EmptySet
s3 = LineSegment(N[-5, -4], N[4, 5])
@test intersection(s1, s3) == EmptySet{N}(2)
# intersect outside of segment
s4 = LineSegment(N[0.0, 10.0], N[6.0, 5.0])
@test intersection(s1, s4) isa EmptySet
s4 = LineSegment(N[0, 10], N[6, 5])
@test intersection(s1, s4) == EmptySet{N}(2)
# intersect in segment
s5 = LineSegment(N[5.0, -5.0], N[-5.0, 5.0])
s5 = LineSegment(N[5, -5], N[-5, 5])
@test intersection(s1, s5) isa Singleton
@test isapprox(intersection(s1, s5).element, N[0, 0])
# parallel, no points in common
s6 = LineSegment(N[10.0, 10.0], N[11.0, 11.0])
@test intersection(s1, s6) isa EmptySet
s6 = LineSegment(N[10, 10], N[11, 11])
@test intersection(s1, s6) == EmptySet{N}(2)
# parallel one point in common
s7 = LineSegment(N[5.0, 5.0], N[6.0, 6.0])
s7 = LineSegment(N[5, 5], N[6, 6])
@test intersection(s1, s7) isa Singleton
@test isapprox(intersection(s1, s7).element, N[5, 5])
s8 = LineSegment(N[0.0, 0.0], N[1.0, 0.0])
s9 = LineSegment(N[0.0, 0.0], N[2.0, 0.0])
@test intersection(s9, s8) isa LineSegment
@test isapprox(intersection(s9, s8).p, N[0, 0])
@test isapprox(intersection(s9, s8).q, N[1, 0])
s8 = LineSegment(N[0, 0], N[1, 0])
s9 = LineSegment(N[0, 0], N[2, 0])
cap = intersection(s8, s9)
@test cap isa LineSegment
@test ispermutation([cap.p, cap.q], [N[0, 0], N[1, 0]])
# intersect in segment, different orientation
s10 = LineSegment(N[-1, 2], N[2, -1])
s11 = LineSegment(N[0, 1], N[1, 0])
@test intersection(s10, s11) == s11

# subset
l = LineSegment(N[1, 1], N[2, 2])
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