From cc02e76bb436a32a8d62ee6fcd21666c81b2c1a8 Mon Sep 17 00:00:00 2001
From: Anshul Singhvi <anshulsinghvi@gmail.com>
Date: Mon, 20 Apr 2026 17:22:10 -0400
Subject: [PATCH] Make `_contains(::SphericalCap, ::SphericalCap)` inclusive
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

Change `<` to `<=` so that an internally-tangent small cap counts as
contained. Matches the convention of the sibling
`_contains(::SphericalCap, ::UnitSphericalPoint)` method one line
below (which uses `<=` for a point exactly on the cap boundary) and
S2's `S2Cap::Contains(const S2Cap&)`.

The pre-existing `@test_broken` in `test/utils/unitspherical.jl`
exercised exactly this boundary case: big_cap = hemisphere centered
at (1,0,0), small_cap centered at (1/√2, 1/√2, 0) with radius π/4.
`dist(centers) = π/4` and `small.radius + dist = π/2 = big.radius`
exactly. Flip the tripwire to `@test`.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
---
 src/utils/UnitSpherical/cap.jl | 6 ++++--
 test/utils/unitspherical.jl    | 2 +-
 2 files changed, 5 insertions(+), 3 deletions(-)

diff --git a/src/utils/UnitSpherical/cap.jl b/src/utils/UnitSpherical/cap.jl
index 82c4e9ad6..483ddebdb 100644
--- a/src/utils/UnitSpherical/cap.jl
+++ b/src/utils/UnitSpherical/cap.jl
@@ -104,8 +104,10 @@ _disjoint(x::SphericalCap, y::SphericalCap) = !_intersects(x, y)
 
 function _contains(big::SphericalCap, small::SphericalCap)
     dist = spherical_distance(big.point, small.point)
-    # small circle fits in big circle
-    return dist + small.radius < big.radius 
+    # small circle fits in big circle; `<=` so internally-tangent small
+    # caps count as contained, matching the point overload below and
+    # S2's `S2Cap::Contains(const S2Cap&)` convention.
+    return dist + small.radius <= big.radius
 end
 function _contains(cap::SphericalCap, point::UnitSphericalPoint)
     spherical_distance(cap.point, point) <= cap.radius
diff --git a/test/utils/unitspherical.jl b/test/utils/unitspherical.jl
index 620fdfcc9..37f84895b 100644
--- a/test/utils/unitspherical.jl
+++ b/test/utils/unitspherical.jl
@@ -117,7 +117,7 @@ end
         # 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_broken UnitSpherical._contains(big_cap, small_cap)
+        @test UnitSpherical._contains(big_cap, small_cap)
         @test !UnitSpherical._contains(small_cap, big_cap)
     end