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@lxvm
lxvm committed Jan 31, 2024
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1 change: 0 additions & 1 deletion test/Project.toml
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[deps]
Combinatorics = "861a8166-3701-5b0c-9a16-15d98fcdc6aa"
CDDLib = "3391f64e-dcde-5f30-b752-e11513730f60"
GLPK = "60bf3e95-4087-53dc-ae20-288a0d20c6a6"
GeometryBasics = "5c1252a2-5f33-56bf-86c9-59e7332b4326"
HiGHS = "87dc4568-4c63-4d18-b0c0-bb2238e4078b"
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244 changes: 130 additions & 114 deletions test/volume.jl
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using Test
using Polyhedra
using CDDLib

# simple algorithm for calculating area of polygons
# requires vertices to be sorted (counter)clockwise
Expand All @@ -15,133 +14,150 @@ function shoelace(verts::AbstractMatrix{<:Real})
A = abs(A)
A isa AbstractFloat ? A/2 : A//2
end
isvertsapprox = (verts, points) -> all(any(isapprox(p, v) for v in verts) for p in points)
isvertsapprox(verts, points) = all(any(isapprox(p, v) for v in verts) for p in points)

# issue 285: area of square [-0.5, -0.5] x [0.5, 0.5]

ineq = [
HalfSpace([-2.0, -2.0], 4.0),
HalfSpace([-2.0, -1.0], 2.5),
HalfSpace([-2.0, 0.0], 2.0),
HalfSpace([-2.0, 1.0], 2.5),
HalfSpace([-2.0, 2.0], 4.0),
HalfSpace([-1.0, -2.0], 2.5),
HalfSpace([-1.0, -1.0], 1.0),
HalfSpace([-1.0, 0.0], 0.5),
HalfSpace([-1.0, 1.0], 1.0),
HalfSpace([-1.0, 2.0], 2.5),
HalfSpace([0.0, -2.0], 2.0),
HalfSpace([0.0, -1.0], 0.5),
HalfSpace([0.0, 0.0], 0.0),
HalfSpace([0.0, 1.0], 0.5),
HalfSpace([0.0, 2.0], 2.0),
HalfSpace([1.0, -2.0], 2.5),
HalfSpace([1.0, -1.0], 1.0),
HalfSpace([1.0, 0.0], 0.5),
HalfSpace([1.0, 1.0], 1.0),
HalfSpace([1.0, 2.0], 2.5),
HalfSpace([2.0, -2.0], 4.0),
HalfSpace([2.0, -1.0], 2.5),
HalfSpace([2.0, 0.0], 2.0),
HalfSpace([2.0, 1.0], 2.5),
HalfSpace([2.0, 2.0], 4.0),
]
square = polyhedron(reduce(intersect, ineq))
sqverts = [-1 1 1 -1; -1 -1 1 1]/2
@test isvertsapprox(eachcol(sqverts), points(square))
@test volume(square) ≈ shoelace(sqverts)
function check_vol_issue285(lib)
ineq = [
HalfSpace([-2.0, -2.0], 4.0),
HalfSpace([-2.0, -1.0], 2.5),
HalfSpace([-2.0, 0.0], 2.0),
HalfSpace([-2.0, 1.0], 2.5),
HalfSpace([-2.0, 2.0], 4.0),
HalfSpace([-1.0, -2.0], 2.5),
HalfSpace([-1.0, -1.0], 1.0),
HalfSpace([-1.0, 0.0], 0.5),
HalfSpace([-1.0, 1.0], 1.0),
HalfSpace([-1.0, 2.0], 2.5),
HalfSpace([0.0, -2.0], 2.0),
HalfSpace([0.0, -1.0], 0.5),
HalfSpace([0.0, 0.0], 0.0),
HalfSpace([0.0, 1.0], 0.5),
HalfSpace([0.0, 2.0], 2.0),
HalfSpace([1.0, -2.0], 2.5),
HalfSpace([1.0, -1.0], 1.0),
HalfSpace([1.0, 0.0], 0.5),
HalfSpace([1.0, 1.0], 1.0),
HalfSpace([1.0, 2.0], 2.5),
HalfSpace([2.0, -2.0], 4.0),
HalfSpace([2.0, -1.0], 2.5),
HalfSpace([2.0, 0.0], 2.0),
HalfSpace([2.0, 1.0], 2.5),
HalfSpace([2.0, 2.0], 4.0),
]
square = polyhedron(reduce(intersect, ineq), lib)
sqverts = [-1 1 1 -1; -1 -1 1 1]/2
@assert isvertsapprox(eachcol(sqverts), points(square))
return volume(square) ≈ shoelace(sqverts)
end

# issue 249
function check_vol_issue249_1(lib)
poly = polyhedron(HalfSpace([-1.0, 0.0], 0.0) ∩
HalfSpace([0.0, -1.0], 0.0) ∩
HalfSpace([1.0, 0.0], 1.0) ∩
HalfSpace([0.0, 1.0], 1.0) ∩
HalfSpace([-0.2, -0.8], -0.0) ∩
HalfSpace([0.6, 0.4], 0.6), lib)

poly = polyhedron(HalfSpace([-1.0, 0.0], 0.0) ∩
HalfSpace([0.0, -1.0], 0.0) ∩
HalfSpace([1.0, 0.0], 1.0) ∩
HalfSpace([0.0, 1.0], 1.0) ∩
HalfSpace([-0.2, -0.8], -0.0) ∩
HalfSpace([0.6, 0.4], 0.6))

verts = [1/3 1 0 0; 1 0 0 1]
@test isvertsapprox(eachcol(verts), points(poly))
@test volume(poly) ≈ shoelace(verts)
verts = [1/3 1 0 0; 1 0 0 1]
@assert isvertsapprox(eachcol(verts), points(poly))
return volume(poly) ≈ shoelace(verts)
end

poly2 = polyhedron(# HalfSpace([-1.0, 0.0], 0.0) ∩
function check_vol_issue249_2(lib)
poly2 = polyhedron(# HalfSpace([-1.0, 0.0], 0.0) ∩
HalfSpace([0.0, -1.0], 0.0) ∩ # Comment here to get correct area
HalfSpace([1.0, 0.0], 1.0) ∩
HalfSpace([0.0, 1.0], 1.0) ∩
HalfSpace([-0.6, -0.4], -0.6) ∩
HalfSpace([0.2, 0.8], 0.95))
verts2 = [1/3 3/4 1 1; 1 1 15/16 0]
@test isvertsapprox(eachcol(verts2), points(poly2))
@test volume(poly2) ≈ shoelace(verts2)
HalfSpace([0.2, 0.8], 0.95), lib)
verts2 = [1/3 3/4 1 1; 1 1 15/16 0]
@assert isvertsapprox(eachcol(verts2), points(poly2))
return volume(poly2) ≈ shoelace(verts2)
end

lib=CDDLib.Library(:exact)
L3 = polyhedron(vrep([
0 0 0 0 0 0
0 0 1 0 0 0
0 1 0 0 0 0
0 1 1 0 0 1
1 0 0 0 0 0
1 0 1 0 1 0
1 1 0 1 0 0
1 1 1 1 1 1
function check_vol_issue249_3(lib)
L3 = polyhedron(vrep([
0 0 0 0 0 0
0 0 1 0 0 0
0 1 0 0 0 0
0 1 1 0 0 1
1 0 0 0 0 0
1 0 1 0 1 0
1 1 0 1 0 0
1 1 1 1 1 1
]),lib)
# reportedly solution taken from https://doi.org/10.1016/j.dam.2018.10.038
@test volume(L3) == 1//180

# reportedly solution taken from https://doi.org/10.1016/j.dam.2018.10.038
return volume(L3) == 1//180
end
# examples similar to Cohen-Hickey paper, table 1
# https://doi.org/10.1145/322139.322141
s5 = polyhedron(vrep([
0 0 0 0 0
0 0 0 0 1
0 0 0 1 0
0 0 1 0 0
0 1 0 0 0
1 0 0 0 0
]), lib)
@test volume(s5) == 1//120
function check_vol_simplex(n, lib)
s = polyhedron(vrep([i==j for i in 0:n, j in 1:n]), lib)
return volume(s) == 1//factorial(n)
end

flib = CDDLib.Library()

ϕ = (1 + √5)/2
isoc = polyhedron(vrep([
0 1 ϕ
0 1 -ϕ
0 -1 ϕ
0 -1 -ϕ
1 ϕ 0
1 -ϕ 0
-1 ϕ 0
-1 -ϕ 0
ϕ 0 1
ϕ 0 -1
-ϕ 0 1
-ϕ 0 -1
]), flib)
# https://en.wikipedia.org/wiki/Regular_icosahedron
@test volume(isoc) ≈ (5/12)*(3+√5)*2^3
function check_vol_isocahedron(lib)
ϕ = (1 + √5)/2
isoc = polyhedron(vrep([
0 1 ϕ
0 1 -ϕ
0 -1 ϕ
0 -1 -ϕ
1 ϕ 0
1 -ϕ 0
-1 ϕ 0
-1 -ϕ 0
ϕ 0 1
ϕ 0 -1
-ϕ 0 1
-ϕ 0 -1
]), lib)
# https://en.wikipedia.org/wiki/Regular_icosahedron
return volume(isoc) ≈ (5/12)*(3+√5)*2^3
end

function check_vol_dodecahedron(lib)
ϕ = (1 + √5)/2
ϕ² = ϕ^2
dodec = polyhedron(vrep([
ϕ ϕ ϕ
ϕ ϕ -ϕ
ϕ -ϕ ϕ
ϕ -ϕ -ϕ
-ϕ ϕ ϕ
-ϕ ϕ -ϕ
-ϕ -ϕ ϕ
-ϕ -ϕ -ϕ
0 1 ϕ²
0 1 -ϕ²
0 -1 ϕ²
0 -1 -ϕ²
1 ϕ² 0
1 -ϕ² 0
-1 ϕ² 0
-1 -ϕ² 0
ϕ² 0 1
ϕ² 0 -1
-ϕ² 0 1
-ϕ² 0 -1
]), lib)
# https://en.wikipedia.org/wiki/Regular_dodecahedron
return volume(dodec) ≈ (1/4)*(15+7*√5)*2^3
end

ϕ² = ϕ^2
dodec = polyhedron(vrep([
ϕ ϕ ϕ
ϕ ϕ -ϕ
ϕ -ϕ ϕ
ϕ -ϕ -ϕ
-ϕ ϕ ϕ
-ϕ ϕ -ϕ
-ϕ -ϕ ϕ
-ϕ -ϕ -ϕ
0 1 ϕ²
0 1 -ϕ²
0 -1 ϕ²
0 -1 -ϕ²
1 ϕ² 0
1 -ϕ² 0
-1 ϕ² 0
-1 -ϕ² 0
ϕ² 0 1
ϕ² 0 -1
-ϕ² 0 1
-ϕ² 0 -1
]), flib)
# https://en.wikipedia.org/wiki/Regular_dodecahedron
@test volume(dodec) ≈ (1/4)*(15+7*√5)*2^3
@testset "volumes" begin
lib_float = DefaultLibrary{Float64}()
lib_exact = DefaultLibrary{Int}()
@testset "simplex" for n in 1:5
@test check_vol_simplex(n, lib_exact)
end
@test check_vol_issue285(lib_float)
@test check_vol_issue249_1(lib_float)
@test check_vol_issue249_2(lib_float)
@test check_vol_issue249_3(lib_exact)
@test check_vol_isocahedron(lib_float)
@test check_vol_dodecahedron(lib_float)
end

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