Make sphere and circle seam vertices bit-exact - #281
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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.
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Sphere and Circle tessellations duplicate the wrap-seam vertices on purpose (so texture coordinates can differ across the seam), but with the
cos/sinoverLinRange(0, 2pi, n)parametrization the two seam columns evaluate at 0 and 2pi and end up differing by float rounding (cos(2pi) == 0.99999994f0in Float32). Renderers that classify mesh edges by exact position matching, like the edge stroking in MakieOrg/Makie.jl#5727, then see the seam as a mesh boundary and stroke it at full width instead of half.This switches the parametrization to
cospi/sinpioverLinRange(0, 2, n), which evaluates the wrap exactly (cospi(2.0) === 1.0,sinpi(2.0) === 0.0), so the seam columns are bit-identical while staying separate vertices. It also makes the sphere's pole rows bit-identical (previously the bottom pole vertices scattered bycos(phi) * sin(pi) ≈ 1.2e-16) and slightly improves the accuracy of all other vertices. Cylinder and Cone already reuse their seam vertices viamod1indexing and are unaffected.