From a356a3ad322d0206584840f135bb21b54ccf78eb Mon Sep 17 00:00:00 2001
From: Julius Krumbiegel <julius.krumbiegel@gmail.com>
Date: Thu, 6 Aug 2026 11:50:59 +0200
Subject: [PATCH] fix(sphere): Make seam and pole vertices bit-exact via
 sinpi/cospi

Sphere and Circle tessellations duplicate the wrap-seam vertices (the
u = 0 and u = 1 columns) on purpose, so that texture coordinates can
differ across the seam. But parametrizing with cos/sin over
LinRange(0, 2pi, n) evaluates the seam columns at 0 and 2pi, whose
results differ by float rounding (e.g. cos(2pi) = 0.99999994f0 in
Float32). Renderers that classify mesh edges by exact position
matching (e.g. Makie's edge stroking in MakieOrg/Makie.jl#5727) then
see the seam as a mesh boundary and draw it differently.

Parametrize with cospi/sinpi over LinRange(0, 2, n) instead, which
evaluates the wrap exactly: cospi(2.0) === 1.0 and sinpi(2.0) === 0.0.
This also makes all pole-row vertices of the sphere bit-identical
(sinpi(1.0) === 0.0, so the bottom pole no longer scatters by
cos(phi) * 1.2e-16) and slightly improves accuracy of all other
vertices. Cylinder and Cone reuse seam vertices via mod1 indexing and
are unaffected.
---
 src/primitives/spheres.jl |  8 ++++----
 test/geometrytypes.jl     | 18 ++++++++++++++++++
 2 files changed, 22 insertions(+), 4 deletions(-)

diff --git a/src/primitives/spheres.jl b/src/primitives/spheres.jl
index f4fff7e4..2de07929 100644
--- a/src/primitives/spheres.jl
+++ b/src/primitives/spheres.jl
@@ -42,7 +42,7 @@ centered(S::Type{<: HyperSphere}) = S(Point3f(0), 0.5f0)
 
 function coordinates(s::Circle, nvertices=64)
     r = radius(s); o = origin(s)
-    ps = [r * Point(cos(phi), sin(phi)) + o for phi in LinRange(0, 2pi, nvertices)]
+    ps = [r * Point(cospi(phi), sinpi(phi)) + o for phi in LinRange(0, 2, nvertices)]
     # ps[end] = o
     return ps
 end
@@ -59,9 +59,9 @@ end
 
 
 function coordinates(s::Sphere, nvertices=24)
-    θ = LinRange(0, pi, nvertices)
-    φ = LinRange(0, 2pi, nvertices)
-    inner(θ, φ) = Point(cos(φ) * sin(θ), sin(φ) * sin(θ), cos(θ)) .* s.r .+ s.center
+    θ = LinRange(0, 1, nvertices)
+    φ = LinRange(0, 2, nvertices)
+    inner(θ, φ) = Point(cospi(φ) * sinpi(θ), sinpi(φ) * sinpi(θ), cospi(θ)) .* s.r .+ s.center
     return [inner(θ, φ) for φ in φ for θ in θ]
 end
 
diff --git a/test/geometrytypes.jl b/test/geometrytypes.jl
index f5534610..a34024c1 100644
--- a/test/geometrytypes.jl
+++ b/test/geometrytypes.jl
@@ -506,6 +506,24 @@ end
     @test Point2f(-0.5) in circle
     @test centered(Circle) == Circle(Point2f(0), 0.5f0)
     @test centered(Circle{Float64}) == Circle(Point2(0.0), 0.5)
+
+    @testset "bit-exact seam and pole vertices" begin
+        for T in (Float32, Float64)
+            n = 24
+            sphere_points = coordinates(Sphere(Point{3,T}(0.2, -0.3, 0.4), T(1.3)), n)
+            first_meridian = sphere_points[1:n]
+            last_meridian = sphere_points[(end - n + 1):end]
+            @test all(map(===, first_meridian, last_meridian))
+
+            top_pole = sphere_points[1:n:end]
+            bottom_pole = sphere_points[n:n:end]
+            @test all(p === top_pole[1] for p in top_pole)
+            @test all(p === bottom_pole[1] for p in bottom_pole)
+
+            circle_points = coordinates(Circle(Point{2,T}(0.2, -0.3), T(1.3)), n)
+            @test circle_points[1] === circle_points[end]
+        end
+    end
 end
 
 @testset "LineStrings" begin