Compute the cell area for an infinite polygon

src/Delaunator.jl

@@ -5,7 +5,7 @@ export triangulate, basictriangulation, update!, triangles, points, inhull
 
 include("quicksort.jl")
 include("geometry.jl")
-export isinfinite, dualcell, firstpoint, lastpoint, segments
+export isinfinite, dualcell, firstpoint, lastpoint, segments, cellarea
 
 include("clipping.jl")
 export clippedpoly, clippedpoly!, margin_bbox

src/geometry.jl

@@ -244,6 +244,35 @@ function dualcell(t::Triangulation, centers, i::Integer)
             raystart, rayend)
 end 
 
+"""
+    cellarea(p)
+
+Compute the area of a possibly infinite polygon.
+"""
+function cellarea(p::InfinitePolygon)
+    if isinfinite(p)
+        return typemax(eltype(eltype(p)))
+    # Area of a line is zero
+    elseif length(p.points) < 3
+        return zero(eltype(eltype(p)))
+    else
+        # Compute the area of the polygon using the shoelace formula using iterators
+        area = zero(eltype(eltype(p)))
+        previous, ite = iterate(p.points)
+        while true
+            el = iterate(p.points, ite)
+            if isnothing(el)
+                break
+            end
+            current, ite = el
+            area += (previous[1] + current[1]) * (previous[2] - current[2])
+            previous = current
+        end
+        current = first(p.points)
+        return 0.5 * abs(area + (previous[1] + current[1]) * (previous[2] - current[2]))
+    end
+end
+
 # monotonically increases with real angle, but doesn't need expensive trigonometry
 function pseudoAngle(dx, dy)
     p = dx / (abs(dx) + abs(dy))

test/runtests.jl

@@ -52,6 +52,20 @@ end
     end 
 end
 
+@testset "cellarea" begin
+    # Test Infinite case
+    p = Delaunator.InfinitePolygon([(-5.0,0.0)], (0.0,-1.0), (0.0,1.0))
+    @test cellarea(p) == Inf
+    # Test Degenerate (point, segment) case
+    p = Delaunator.InfinitePolygon([(-5.0,0.0)], (0.0, 0.0), (0.0, 0.0))
+    @test cellarea(p) == 0.0
+    p = Delaunator.InfinitePolygon([(-5.0,0.0), (5.0, 0.0)], (0.0, 0.0), (0.0, 0.0))
+    @test cellarea(p) == 0.0
+    # Test normal case
+    p = Delaunator.InfinitePolygon([(-1.0,-1.0),(1.0,-1.0),(1.0,1.0),(-1.0,1.0)], (0.0,0.0), (0.0,0.0))
+    @test cellarea(p) == 4.0
+end
+
 # test('triangulates plain array', (t) => {
 #     const d = new Delaunator([].concat(...points));
 #     t.same(d.triangles, Delaunator.from(points).triangles);