add AI generated tests

it's cruft but it's something..

Author: asinghvi17

test/utils/unitspherical.jl

@@ -77,4 +77,121 @@ import GeoInterface as GI
         @test_throws AssertionError GeographicFromUnitSphere()([1.0, 0.0])
         @test_throws AssertionError GeographicFromUnitSphere()([1.0, 0.0, 0.0, 0.0])
     end
+end
+
+@testset "Spherical caps" begin
+    @testset "Construction" begin
+        # Test construction from UnitSphericalPoint
+        point = UnitSphericalPoint(1.0, 0.0, 0.0)
+        cap = SphericalCap(point, π/4)
+        @test cap.point == point
+        @test cap.radius == π/4
+
+        # Test construction from geographic point
+        geo_point = GI.Point(45, 45)
+        cap = SphericalCap(geo_point, π/4)
+        @test cap.point isa UnitSphericalPoint{Float64}
+        @test cap.radius == π/4
+
+        # Test construction from tuple
+        cap = SphericalCap((45, 45), π/4)
+        @test cap.point isa UnitSphericalPoint{Float64}
+        @test cap.radius == π/4
+    end
+
+    @testset "Intersection and containment" begin
+        # Create two caps that intersect
+        cap1 = SphericalCap(UnitSphericalPoint(1.0, 0.0, 0.0), π/4)
+        cap2 = SphericalCap(UnitSphericalPoint(1/√2, 1/√2, 0.0), π/4)
+        @test UnitSpherical._intersects(cap1, cap2)
+        @test UnitSpherical._intersects(cap2, cap1)
+        @test !UnitSpherical._disjoint(cap1, cap2)
+
+        # Create two caps that don't intersect
+        cap3 = SphericalCap(UnitSphericalPoint(1.0, 0.0, 0.0), π/8)
+        cap4 = SphericalCap(UnitSphericalPoint(0.0, 0.0, 1.0), π/8)
+        @test !UnitSpherical._intersects(cap3, cap4)
+        @test UnitSpherical._disjoint(cap3, cap4)
+
+        # Test containment
+        big_cap = SphericalCap(UnitSphericalPoint(1.0, 0.0, 0.0), π/2)
+        small_cap = SphericalCap(UnitSphericalPoint(1/√2, 1/√2, 0.0), π/4)
+        @test UnitSpherical._contains(big_cap, small_cap)
+        @test !UnitSpherical._contains(small_cap, big_cap)
+    end
+
+    @testset "Circumcenter and circumradius" begin
+        # Test with an equilateral triangle on the equator
+        a = UnitSphericalPoint(1.0, 0.0, 0.0)
+        b = UnitSphericalPoint(-0.5, √3/2, 0.0)
+        c = UnitSphericalPoint(-0.5, -√3/2, 0.0)
+        cap = SphericalCap(a, b, c)
+        
+        # The circumcenter should be at the north pole
+        @test isapprox(cap.point[1], 0.0, atol=1e-10)
+        @test isapprox(cap.point[2], 0.0, atol=1e-10)
+        @test isapprox(cap.point[3], 1.0, atol=1e-10)
+        # The radius should be π/2 (90 degrees)
+        @test isapprox(cap.radius, π/2, atol=1e-10)
+
+        # Test with a triangle in the northern hemisphere
+        a = UnitSphericalPoint(1.0, 0.0, 0.0)
+        b = UnitSphericalPoint(0.0, 1.0, 0.0)
+        c = UnitSphericalPoint(0.0, 0.0, 1.0)
+        cap = SphericalCap(a, b, c)
+        
+        # The circumcenter should be at (1/√3, 1/√3, 1/√3)
+        @test isapprox(cap.point[1], 1/√3, atol=1e-10)
+        @test isapprox(cap.point[2], 1/√3, atol=1e-10)
+        @test isapprox(cap.point[3], 1/√3, atol=1e-10)
+        # The radius should be the angle between the center and any vertex
+        expected_radius = acos(1/√3)
+        @test isapprox(cap.radius, expected_radius, atol=1e-10)
+
+        # Test with nearly colinear points (small angle between them)
+        # Points near the equator with very small angular separation
+        ϵ = 1e-6  # Very small angle in radians
+        a = UnitSphericalPoint(1.0, 0.0, 0.0)
+        b = UnitSphericalPoint(cos(ϵ), sin(ϵ), 0.0)
+        c = UnitSphericalPoint(cos(2ϵ), sin(2ϵ), 0.0)
+        cap = SphericalCap(a, b, c)
+        
+        # The circumcenter should be near the north pole
+        @test isapprox(cap.point[1], 0.0, atol=1e-6)
+        @test isapprox(cap.point[2], 0.0, atol=1e-6)
+        @test isapprox(cap.point[3], 1.0, atol=1e-6)
+        # The radius should be approximately π/2
+        @test isapprox(cap.radius, π/2, atol=1e-6)
+
+        # # Test with nearly identical points
+        # # Points very close to each other in the northern hemisphere
+        # ϵ = 1e-8  # Extremely small angle
+        # base = UnitSphericalPoint(1/√3, 1/√3, 1/√3)
+        # a = base
+        # b = UnitSphericalPoint(cos(ϵ), sin(ϵ), 0.0) * (1/√3)  # Small perturbation
+        # c = UnitSphericalPoint(cos(2ϵ), sin(2ϵ), 0.0) * (1/√3)  # Another small perturbation
+        # cap = SphericalCap(a, b, c)
+        
+        # # The circumcenter should be very close to the base point
+        # @test isapprox(cap.point[1], 1/√3, atol=1e-6)
+        # @test isapprox(cap.point[2], 1/√3, atol=1e-6)
+        # @test isapprox(cap.point[3], 1/√3, atol=1e-6)
+        # # The radius should be very small
+        # @test isapprox(cap.radius, ϵ, atol=1e-6)
+
+        # Test with points forming a very thin triangle
+        # Points near the north pole with small angular separation
+        ϵ = 1e-6
+        a = UnitSphericalPoint(0.0, 0.0, 1.0)  # North pole
+        b = UnitSphericalPoint(sin(ϵ), 0.0, cos(ϵ))
+        c = UnitSphericalPoint(0.0, sin(ϵ), cos(ϵ))
+        cap = SphericalCap(a, b, c)
+        
+        # The circumcenter should be very close to the north pole
+        @test isapprox(cap.point[1], 0.0, atol=1e-6)
+        @test isapprox(cap.point[2], 0.0, atol=1e-6)
+        @test isapprox(cap.point[3], 1.0, atol=1e-6)
+        # The radius should be approximately ϵ
+        @test isapprox(cap.radius, ϵ, atol=1e-6)
+    end
 end