new branch for Bentley Ottman

Author: souma4

src/utils/sweepline.jl

@@ -0,0 +1,76 @@
+# Implementation of Bentley-Ottmann algorith
+# https://en.wikipedia.org/wiki/Bentley%E2%80%93Ottmann_algorithm
+
+using BinaryTrees
+
+
+"""
+    bentleyottmann(segments)
+
+Compute pairwise intersections between n `segments`
+in O(n⋅log(n)) time using Bentley-Ottmann sweep line
+algorithm.
+"""
+function bentleyottmann(segments)
+  # adjust vertices of segments
+  segs = map(segments) do s
+    a, b = extrema(s)
+    a > b ? reverse(s) : s
+  end
+
+  # retrieve relevant info
+  s = first(segs)
+  p = minimum(s)
+  P = typeof(p)
+  S = Tuple{P,P}
+
+  # initialization
+  𝒬 = AVLTree{P}()
+  𝒯 = AVLTree{S}()
+  ℒ = Dict{P,Vector{S}}()
+  𝒰 = Dict{P,Vector{S}}()
+  𝒞 = Dict{P,Vector{S}}()
+  for s in segs
+    a, b = extrema(s)
+    BinaryTrees.insert!(𝒬, a)
+    BinaryTrees.insert!(𝒬, b)
+    haskey(ℒ, a) ? push!(ℒ[a], (a, b)) : (ℒ[a] = [(a, b)])
+    haskey(𝒰, b) ? push!(𝒰[b], (a, b)) : (𝒰[b] = [(a, b)])
+    haskey(ℒ, b) || (ℒ[b] = S[])
+    haskey(𝒰, a) || (𝒰[a] = S[])
+    haskey(𝒞, a) || (𝒞[a] = S[])
+    haskey(𝒞, b) || (𝒞[b] = S[])
+  end
+  m = Point(-Inf, -Inf)
+  M = Point(Inf, Inf)
+  BinaryTrees.insert!(𝒯, (m, m))
+  BinaryTrees.insert!(𝒯, (M, M))
+
+  # sweep line
+  I = Dict{P,Vector{S}}()
+  while !isnothing(BinaryTrees.root(𝒬))
+    p = _key(BinaryTrees.root(𝒬))
+    BinaryTrees.delete!(𝒬, p)
+    handle!(I, p, 𝒬, 𝒯, ℒ, 𝒰, 𝒞)
+  end
+  I
+end
+
+function handle!(I, p, 𝒬, 𝒯, ℒ, 𝒰, 𝒞)
+  ss = ℒ[p] ∪ 𝒰[p] ∪ 𝒞[p]
+  if length(ss) > 1
+    I[p] = ss
+  end
+  for s in ℒ[p] ∪ 𝒞[p]
+    BinaryTrees.delete!(𝒯, s)
+  end
+  for s in 𝒰[p] ∪ 𝒞[p]
+    BinaryTrees.insert!(𝒯, s)
+  end
+  if length(𝒰[p] ∪ 𝒞[p]) == 0
+    # n = BinaryTrees.search(𝒯, p)
+  else
+  end
+end
+
+_key(node::BinaryTrees.AVLNode) = node.key