volume method for AbstractPolygon

JuliaReach · Apr 10, 2023 · 0096118 · 0096118
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Showing 5 changed files with 29 additions and 6 deletions.
diff --git a/docs/src/lib/sets/HPolygon.md b/docs/src/lib/sets/HPolygon.md
@@ -20,10 +20,10 @@ Inherited from [`LazySet`](@ref):
 Inherited from [`AbstractPolytope`](@ref):
 * [`isempty`](@ref isempty(::AbstractPolytope))
 * [`isuniversal`](@ref isuniversal(::AbstractPolytope{N}, ::Bool=false) where {N})
-* [`volume`](@ref volume(::AbstractPolytope))
 
 Inherited from [`AbstractPolygon`](@ref):
 * [`dim`](@ref dim(::AbstractPolygon))
+* [`volume`](@ref volume(::AbstractPolygon))
 
 Inherited from [`AbstractHPolygon`](@ref):
 * [`an_element`](@ref an_element(::AbstractHPolygon))

diff --git a/docs/src/lib/sets/HPolygonOpt.md b/docs/src/lib/sets/HPolygonOpt.md
@@ -19,10 +19,10 @@ Inherited from [`LazySet`](@ref):
 Inherited from [`AbstractPolytope`](@ref):
 * [`isempty`](@ref isempty(::AbstractPolytope))
 * [`isuniversal`](@ref isuniversal(::AbstractPolytope{N}, ::Bool=false) where {N})
-* [`volume`](@ref volume(::AbstractPolytope))
 
 Inherited from [`AbstractPolygon`](@ref):
 * [`dim`](@ref dim(::AbstractPolygon))
+* [`volume`](@ref volume(::AbstractPolygon))
 
 Inherited from [`AbstractHPolygon`](@ref):
 * [`an_element`](@ref an_element(::AbstractHPolygon))

diff --git a/docs/src/lib/sets/VPolygon.md b/docs/src/lib/sets/VPolygon.md
@@ -34,7 +34,7 @@ Inherited from [`AbstractPolytope`](@ref):
 * [`isbounded`](@ref isbounded(::AbstractPolytope))
 * [`isempty`](@ref isempty(::AbstractPolytope))
 * [`isuniversal`](@ref isuniversal(::AbstractPolytope{N}, ::Bool=false) where {N})
-* [`volume`](@ref volume(::AbstractPolytope))
 
 Inherited from [`AbstractPolygon`](@ref):
 * [`dim`](@ref dim(::AbstractPolygon))
+* [`volume`](@ref volume(::AbstractPolygon))
diff --git a/src/Interfaces/AbstractPolygon.jl b/src/Interfaces/AbstractPolygon.jl
@@ -42,7 +42,7 @@ Return the ambient dimension of a convex polygon.
 
 The ambient dimension of the polygon, which is 2.
 """
-@inline function dim(P::AbstractPolygon)
+@inline function dim(::AbstractPolygon)
     return 2
 end
 
@@ -182,3 +182,24 @@ arguments implements the [`atan2` function](https://en.wikipedia.org/wiki/Atan2)
 function _leq_trig(u::AbstractVector{N}, v::AbstractVector{N}) where {N<:AbstractFloat}
     return jump2pi(atan(u[2], u[1])) <= jump2pi(atan(v[2], v[1]))
 end
+
+"""
+    volume(P::AbstractPolygon)
+
+Compute the volume of a convex polygon.
+
+### Input
+
+- `P` -- convex polygon
+
+### Output
+
+A number representing the volume of `P`.
+
+### Notes
+
+In 2D the volume is equivalent to the area.
+"""
+function volume(P::AbstractPolygon)
+    return area(P)
+end
diff --git a/test/Sets/Polygon.jl b/test/Sets/Polygon.jl
@@ -470,13 +470,15 @@ for N in [Float64, Float32, Rational{Int}]
     Z = minkowski_sum(X + Y, Singleton(zeros(N, 2)))
     @test Z isa VPolygon{N} && ispermutation(vertices_list(Z), vlist)
 
-    # area
+    # area & volume
     v1 = N[1, 3]
     v2 = N[2, 1]
     v3 = N[4, 6]
     v4 = N[9, 2]
     P = VPolygon([v1, v2, v3, v4])
-    @test area(P) == N(21)
+    @test area(P) == volume(P) == N(21)
+    Q = tohrep(P)
+    @test area(Q) == volume(Q) == N(21)
 end
 
 for N in [Float64, Float32]