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Add more analytic tests (#110)
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* Add analytic solution for Circle

* Add analytic solution for Ball 2D

* Add analytic tests for Disk

* Add semi-analytic solution for Ball 3D

* Apply suggestions from code review

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>

* fix Ball 3d test

* fix for general center

* Update test/combinations.jl

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>

* make center const

* define offset

* remove comment

* Change usages of hypot to norm

* Remove redundant using LinearAlgebra statements

* Add analytic solution for Sphere 3D

---------

Co-authored-by: github-actions[bot] <41898282+github-actions[bot]@users.noreply.github.com>
Co-authored-by: Joshua Lampert <[email protected]>
Co-authored-by: Joshua Lampert <[email protected]>
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@mikeingold @github-actions @JoshuaLampert
4 people authored Oct 17, 2024
1 parent aa0270a commit ecfdb71
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97 changes: 61 additions & 36 deletions test/combinations.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -4,13 +4,17 @@

@testitem "Meshes.Ball 2D" setup=[Setup] begin
origin = Point(0, 0)
ball = Ball(origin, 2.8)
radius = 2.8
ball = Ball(origin, radius)

f(p) = 1.0
function f(p::P) where {P <: Meshes.Point}
r = ustrip(u"m", norm(to(p)))
exp(-r^2)
end
fv(p) = fill(f(p), 3)

# Scalar integrand
sol = Meshes.measure(ball)
sol = (π - π * exp(-radius^2)) * u"m^2"
@test integral(f, ball, GaussLegendre(100)) ≈ sol
@test integral(f, ball, GaussKronrod()) ≈ sol
@test integral(f, ball, HAdaptiveCubature()) ≈ sol
Expand All @@ -28,14 +32,23 @@
end

@testitem "Meshes.Ball 3D" setup=[Setup] begin
origin = Point(0, 0, 0)
ball = Ball(origin, 2.8)
using SpecialFunctions: erf

f(p) = 1.0
center = Point(1, 2, 3)
radius = 2.8u"m"
ball = Ball(center, radius)

function f(p::P) where {P <: Meshes.Point}
offset = p - center
ur = norm(offset)
r = ustrip(u"m", ur)
exp(-r^2)
end
fv(p) = fill(f(p), 3)

# Scalar integrand
sol = Meshes.measure(ball)
r = ustrip(u"m", radius)
sol = (π^(3 / 2) * erf(r) - 2π * exp(-r^2) * r) * u"m^3"
@test integral(f, ball, GaussLegendre(100)) ≈ sol
@test_throws "not supported" integral(f, ball, GaussKronrod())≈sol
@test integral(f, ball, HAdaptiveCubature()) ≈ sol
Expand Down Expand Up @@ -201,16 +214,21 @@ end
end

@testitem "Meshes.Circle" setup=[Setup] begin
origin = Point(0, 0, 0)
ẑ = Vec(0, 0, 1)
xy_plane = Plane(origin, ẑ)
circle = Circle(xy_plane, 2.5)
center = Point(1, 2, 3)
n̂ = Vec(1 / 2, 1 / 2, sqrt(2) / 2)
plane = Plane(center, n̂)
radius = 4.4
circle = Circle(plane, radius)

f(p) = 1.0
function f(p::P) where {P <: Meshes.Point}
offset = p - center
r = ustrip(u"m", norm(offset))
exp(-r^2)
end
fv(p) = fill(f(p), 3)

# Scalar integrand
sol = Meshes.measure(circle)
sol = 2π * radius * exp(-radius^2) * u"m"
@test integral(f, circle, GaussLegendre(100)) ≈ sol
@test integral(f, circle, GaussKronrod()) ≈ sol
@test integral(f, circle, HAdaptiveCubature()) ≈ sol
Expand Down Expand Up @@ -344,16 +362,21 @@ end
end

@testitem "Meshes.Disk" setup=[Setup] begin
origin = Point(0, 0, 0)
ẑ = Vec(0, 0, 1)
xy_plane = Plane(origin, ẑ)
disk = Disk(xy_plane, 2.5)
center = Point(1, 2, 3)
n̂ = Vec(1 / 2, 1 / 2, sqrt(2) / 2)
plane = Plane(center, n̂)
radius = 2.5
disk = Disk(plane, radius)

f(p) = 1.0
function f(p::P) where {P <: Meshes.Point}
offset = p - center
r = ustrip(u"m", norm(offset))
exp(-r^2)
end
fv(p) = fill(f(p), 3)

# Scalar integrand
sol = Meshes.measure(disk)
sol = (π - π * exp(-radius^2)) * u"m^2"
@test integral(f, disk, GaussLegendre(100)) ≈ sol
@test integral(f, disk, GaussKronrod()) ≈ sol
@test integral(f, disk, HAdaptiveCubature()) ≈ sol
Expand Down Expand Up @@ -467,8 +490,7 @@ end
line = Line(a, b)

function f(p::P) where {P <: Meshes.Point}
ur = hypot(p.coords.x, p.coords.y, p.coords.z)
r = ustrip(u"m", ur)
r = ustrip(u"m", norm(to(p)))
exp(-r^2)
end
fv(p) = fill(f(p), 3)
Expand Down Expand Up @@ -521,7 +543,6 @@ end
# If the version is specified as minimal compat bound in the Project.toml, the downgrade test fails
if pkgversion(Meshes) >= v"0.51.20"
using CoordRefSystems: Polar
using LinearAlgebra: norm

# Parameterize a circle centered on origin with specified radius
radius = 4.4
Expand Down Expand Up @@ -570,8 +591,7 @@ end
plane = Plane(p, v)

function f(p::P) where {P <: Meshes.Point}
ur = hypot(p.coords.x, p.coords.y, p.coords.z)
r = ustrip(u"m", ur)
r = ustrip(u"m", norm(to(p)))
exp(-r^2)
end
fv(p) = fill(f(p), 3)
Expand Down Expand Up @@ -599,8 +619,7 @@ end
quadrangle = Quadrangle((-1.0, 0.0), (-1.0, 1.0), (1.0, 1.0), (1.0, 0.0))

function f(p::P) where {P <: Meshes.Point}
ur = hypot(p.coords.x, p.coords.y)
r = ustrip(u"m", ur)
r = ustrip(u"m", norm(to(p)))
exp(-r^2)
end
fv(p) = fill(f(p), 3)
Expand Down Expand Up @@ -629,8 +648,7 @@ end
ray = Ray(a, v)

function f(p::P) where {P <: Meshes.Point}
ur = hypot(p.coords.x, p.coords.y, p.coords.z)
r = ustrip(u"m", ur)
r = ustrip(u"m", norm(to(p)))
exp(-r^2)
end
fv(p) = fill(f(p), 3)
Expand Down Expand Up @@ -725,8 +743,7 @@ end
a, b = (7.1, 4.6) # arbitrary constants > 0

function f(p::P) where {P <: Meshes.Point}
ur = hypot(p.coords.x, p.coords.y, p.coords.z)
r = ustrip(u"m", ur)
r = ustrip(u"m", norm(to(p)))
exp(r * log(a) + (1 - r) * log(b))
end
fv(p) = fill(f(p), 3)
Expand Down Expand Up @@ -755,8 +772,7 @@ end
sphere = Sphere(origin, radius)

function f(p::P) where {P <: Meshes.Point}
ur = hypot(p.coords.x, p.coords.y)
r = ustrip(u"m", ur)
r = ustrip(u"m", norm(to(p)))
exp(-r^2)
end
fv(p) = fill(f(p), 3)
Expand All @@ -780,14 +796,23 @@ end
end

@testitem "Meshes.Sphere 3D" setup=[Setup] begin
origin = Point(0, 0, 0)
sphere = Sphere(origin, 4.4)
using CoordRefSystems: Cartesian, Spherical

f(p) = 1.0
center = Point(1, 2, 3)
radius = 4.4u"m"
sphere = Sphere(center, radius)

function f(p::P) where {P <: Meshes.Point}
rθφ = convert(Spherical, Cartesian((p - center)...))
r = ustrip(rθφ.r)
θ = ustrip(rθφ.θ)
φ = ustrip(rθφ.ϕ)
sin(φ)^2 + cos(θ)^2
end
fv(p) = fill(f(p), 3)

# Scalar integrand
sol = Meshes.measure(sphere)
sol = (2π * radius^2) + (4π / 3 * radius^2)
@test integral(f, sphere, GaussLegendre(100)) ≈ sol
@test integral(f, sphere, GaussKronrod()) ≈ sol
@test integral(f, sphere, HAdaptiveCubature()) ≈ sol
Expand Down
1 change: 1 addition & 0 deletions test/runtests.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -5,6 +5,7 @@ using TestItems
@run_package_tests filter=ti -> !(:extended in ti.tags) verbose=true

@testsnippet Setup begin
using LinearAlgebra: norm
using Meshes
using Unitful
end

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