diff --git a/src/sampling/regular.jl b/src/sampling/regular.jl
index fe6d5cbde..afb8b25d4 100644
--- a/src/sampling/regular.jl
+++ b/src/sampling/regular.jl
@@ -40,17 +40,21 @@ end
 floattype(T::Type{<:Quantity}) = floattype(Unitful.numtype(T))
 floattype(T::Type) = float(T)
 
-firstoffset(::Sphere{3}) = (n -> inv(n + 1), n -> zero(n))
-lastoffset(::Sphere{3}) = (n -> inv(n + 1), n -> inv(n))
-extrapoints(s::Sphere{3}) = (s(0, 0), s(1, 0))
+firstoffset(g::Geometry) = ntuple(i -> (n -> zero(n)), paramdim(g))
+lastoffset(g::Geometry) = ntuple(i -> (n -> isperiodic(g)[i] ? inv(n) : zero(n)), paramdim(g))
+extrapoints(::Geometry) = ()
+
+firstoffset(d::Disk) = (n -> inv(n), firstoffset(boundary(d))...)
+lastoffset(d::Disk) = (n -> zero(n), lastoffset(boundary(d))...)
+extrapoints(d::Disk) = (center(d),)
 
-firstoffset(b::Ball) = (n -> inv(n + 1), firstoffset(boundary(b))...)
+firstoffset(b::Ball) = (n -> inv(n), firstoffset(boundary(b))...)
 lastoffset(b::Ball) = (n -> zero(n), lastoffset(boundary(b))...)
 extrapoints(b::Ball) = (center(b),)
 
-firstoffset(d::Disk) = (n -> inv(n + 1), firstoffset(boundary(d))...)
-lastoffset(d::Disk) = (n -> zero(n), lastoffset(boundary(d))...)
-extrapoints(d::Disk) = (center(d),)
+firstoffset(::Sphere{3}) = (n -> inv(n + 1), n -> zero(n))
+lastoffset(::Sphere{3}) = (n -> inv(n + 1), n -> inv(n))
+extrapoints(s::Sphere{3}) = (s(0, 0), s(1, 0))
 
 firstoffset(::CylinderSurface) = (n -> zero(n), n -> zero(n))
 lastoffset(::CylinderSurface) = (n -> inv(n), n -> zero(n))
@@ -60,10 +64,6 @@ firstoffset(::ConeSurface) = (n -> zero(n), n -> inv(n))
 lastoffset(::ConeSurface) = (n -> inv(n), n -> zero(n))
 extrapoints(c::ConeSurface) = (apex(c), base(c)(0, 0))
 
-firstoffset(g::Geometry) = ntuple(i -> (n -> zero(n)), paramdim(g))
-lastoffset(g::Geometry) = ntuple(i -> (n -> isperiodic(g)[i] ? inv(n) : zero(n)), paramdim(g))
-extrapoints(::Geometry) = ()
-
 # --------------
 # SPECIAL CASES
 # --------------
diff --git a/test/sampling.jl b/test/sampling.jl
index 8a26e6172..3d90a4a73 100644
--- a/test/sampling.jl
+++ b/test/sampling.jl
@@ -107,18 +107,18 @@
     ps = sample(b, RegularSampling(3, 4))
     @test all(∈(b), ps)
     ts = P2[
-      (0.5, 0.0),
-      (1.25, 0.0),
+      (0.6666666666666666, 0.0),
+      (1.3333333333333333, 0.0),
       (2.0, 0.0),
-      (3.061616997868383e-17, 0.5),
-      (7.654042494670958e-17, 1.25),
-      (1.2246467991473532e-16, 2.0),
-      (-0.5, 6.123233995736766e-17),
-      (-1.25, 1.5308084989341916e-16),
-      (-2.0, 2.4492935982947064e-16),
-      (-9.184850993605148e-17, -0.5),
-      (-2.296212748401287e-16, -1.25),
-      (-3.6739403974420594e-16, -2.0),
+      (0.0, 0.6666666666666666),
+      (0.0, 1.3333333333333333),
+      (0.0, 2.0),
+      (-0.6666666666666666, 0.0),
+      (-1.3333333333333333, 0.0),
+      (-2.0, 0.0),
+      (0.0, -0.6666666666666666),
+      (0.0, -1.3333333333333333),
+      (0.0, -2.0),
       (0.0, 0.0)
     ]
     for (p, t) in zip(ps, ts)
@@ -129,17 +129,17 @@
     ps = sample(b, RegularSampling(4, 3))
     @test all(∈(b), ps)
     ts = P2[
-      (10.4, 10.0),
-      (10.933333333333334, 10.0),
-      (11.466666666666667, 10.0),
+      (10.5, 10.0),
+      (11.0, 10.0),
+      (11.5, 10.0),
       (12.0, 10.0),
-      (9.8, 10.346410161513775),
-      (9.533333333333333, 10.808290376865475),
-      (9.266666666666666, 11.270170592217177),
+      (9.75, 10.433012701892219),
+      (9.5, 10.86602540378444),
+      (9.25, 11.299038105676658),
       (9.0, 11.732050807568877),
-      (9.8, 9.653589838486225),
-      (9.533333333333333, 9.191709623134523),
-      (9.266666666666667, 8.729829407782823),
+      (9.75, 9.566987298107781),
+      (9.5, 9.13397459621556),
+      (9.25, 8.700961894323342),
       (9.0, 8.267949192431121),
       (10.0, 10.0)
     ]
@@ -151,24 +151,24 @@
     ps = sample(b, RegularSampling(3, 2, 3))
     @test all(∈(b), ps)
     ts = P3[
-      (0.4330127018922193, 0.0, 0.25000000000000006),
-      (1.0825317547305482, 0.0, 0.6250000000000001),
-      (1.7320508075688772, 0.0, 1.0000000000000002),
-      (0.4330127018922193, 0.0, -0.2500000000000001),
-      (1.0825317547305482, 0.0, -0.6250000000000002),
-      (1.7320508075688772, 0.0, -1.0000000000000004),
-      (-0.21650635094610973, 0.37499999999999994, 0.25000000000000006),
-      (-0.5412658773652743, 0.9374999999999999, 0.6250000000000001),
-      (-0.8660254037844389, 1.4999999999999998, 1.0000000000000002),
-      (-0.21650635094610973, 0.37499999999999994, -0.2500000000000001),
-      (-0.5412658773652743, 0.9374999999999999, -0.6250000000000002),
-      (-0.8660254037844389, 1.4999999999999998, -1.0000000000000004),
-      (-0.21650635094610948, -0.37500000000000006, 0.25000000000000006),
-      (-0.5412658773652737, -0.9375000000000001, 0.6250000000000001),
-      (-0.8660254037844379, -1.5000000000000002, 1.0000000000000002),
-      (-0.21650635094610948, -0.37500000000000006, -0.2500000000000001),
-      (-0.5412658773652737, -0.9375000000000001, -0.6250000000000002),
-      (-0.8660254037844379, -1.5000000000000002, -1.0000000000000004),
+      (0.5773502691896257, 0.0, 0.3333333333333333),
+      (1.1547005383792515, 0.0, 0.6666666666666666),
+      (1.7320508075688772, 0.0, 1.0),
+      (0.5773502691896256, 0.0, -0.3333333333333335),
+      (1.1547005383792512, 0.0, -0.666666666666667),
+      (1.732050807568877, 0.0, -1.0000000000000004),
+      (-0.288675134594813, 0.4999999999999999, 0.3333333333333333),
+      (-0.577350269189626, 0.9999999999999998, 0.6666666666666666),
+      (-0.8660254037844389, 1.4999999999999996, 1.0),
+      (-0.2886751345948129, 0.4999999999999998, -0.3333333333333335),
+      (-0.5773502691896258, 0.9999999999999996, -0.666666666666667),
+      (-0.8660254037844388, 1.4999999999999993, -1.0000000000000004),
+      (-0.28867513459481264, -0.5000000000000001, 0.3333333333333333),
+      (-0.5773502691896253, -1.0000000000000002, 0.6666666666666666),
+      (-0.8660254037844379, -1.5000000000000004, 1.0),
+      (-0.2886751345948126, -0.5, -0.3333333333333335),
+      (-0.5773502691896252, -1.0, -0.666666666666667),
+      (-0.8660254037844378, -1.5000000000000002, -1.0000000000000004),
       (0.0, 0.0, 0.0)
     ]
     for (p, t) in zip(ps, ts)