diff --git a/gridlock/read.py b/gridlock/read.py
index 998e79d..9df3e08 100644
--- a/gridlock/read.py
+++ b/gridlock/read.py
@@ -20,6 +20,26 @@ if TYPE_CHECKING:
 
 
 class GridReadMixin(GridPosMixin):
+    @staticmethod
+    def _preview_exyz_from_centers(centers: NDArray, fallback_edges: NDArray) -> NDArray[numpy.float64]:
+        if centers.size > 1:
+            midpoints = 0.5 * (centers[:-1] + centers[1:])
+            first = centers[0] - 0.5 * (centers[1] - centers[0])
+            last = centers[-1] + 0.5 * (centers[-1] - centers[-2])
+            return numpy.hstack(([first], midpoints, [last]))
+        return numpy.array([fallback_edges[0], fallback_edges[-1]], dtype=float)
+
+    def _sampled_exyz(self, which_shifts: int, sample_period: int) -> list[NDArray[numpy.float64]]:
+        if sample_period <= 1:
+            return self.shifted_exyz(which_shifts)
+
+        shifted_xyz = self.shifted_xyz(which_shifts)
+        shifted_exyz = self.shifted_exyz(which_shifts)
+        return [
+            self._preview_exyz_from_centers(shifted_xyz[a][::sample_period], shifted_exyz[a])
+            for a in range(3)
+        ]
+
     def get_slice(
             self,
             cell_data: NDArray,
@@ -262,8 +282,14 @@ class GridReadMixin(GridPosMixin):
         verts, faces, _normals, _values = skimage.measure.marching_cubes(grid, level)
 
         # Convert vertices from index to position
-        pos_verts = numpy.array([self.ind2pos(verts[i, :], which_shifts, round_ind=False)
-                                 for i in range(verts.shape[0])], dtype=float)
+        preview_exyz = self._sampled_exyz(which_shifts, sample_period)
+        pos_verts = numpy.array([
+            [
+                numpy.interp(verts[i, a], numpy.arange(preview_exyz[a].size) - 0.5, preview_exyz[a])
+                for a in range(3)
+            ]
+            for i in range(verts.shape[0])
+        ], dtype=float)
         xs, ys, zs = (pos_verts[:, a] for a in range(3))
 
         # Draw the plot
diff --git a/gridlock/test/test_grid.py b/gridlock/test/test_grid.py
index 60929e8..9f2e4f3 100644
--- a/gridlock/test/test_grid.py
+++ b/gridlock/test/test_grid.py
@@ -226,3 +226,49 @@ def test_extent_accepts_scalar_like_inputs() -> None:
     assert_allclose([extent.center, extent.span, extent.min, extent.max], [3.0, 4.0, 1.0, 5.0])
 
 
+
+
+def test_visualize_isosurface_sampling_uses_preview_lattice(monkeypatch: pytest.MonkeyPatch) -> None:
+    matplotlib = pytest.importorskip('matplotlib')
+    matplotlib.use('Agg')
+    skimage_measure = pytest.importorskip('skimage.measure')
+    from matplotlib import pyplot
+    from mpl_toolkits.mplot3d.axes3d import Axes3D
+
+    captured: dict[str, numpy.ndarray] = {}
+
+    def fake_marching_cubes(_grid: numpy.ndarray, _level: float) -> tuple[numpy.ndarray, numpy.ndarray, None, None]:
+        verts = numpy.array([[0.5, 0.5, 0.5],
+                             [0.5, 1.5, 0.5],
+                             [1.5, 0.5, 0.5]], dtype=float)
+        faces = numpy.array([[0, 1, 2]], dtype=int)
+        return verts, faces, None, None
+
+    def fake_plot_trisurf(     # noqa: ANN202
+            _self: object,
+            xs: numpy.ndarray,
+            ys: numpy.ndarray,
+            faces: numpy.ndarray,
+            zs: numpy.ndarray,
+            *_args: object,
+            **_kwargs: object,
+            ) -> object:
+        captured['xs'] = numpy.asarray(xs)
+        captured['ys'] = numpy.asarray(ys)
+        captured['faces'] = numpy.asarray(faces)
+        captured['zs'] = numpy.asarray(zs)
+        return object()
+
+    monkeypatch.setattr(skimage_measure, 'marching_cubes', fake_marching_cubes)
+    monkeypatch.setattr(Axes3D, 'plot_trisurf', fake_plot_trisurf)
+
+    grid = Grid([numpy.arange(7, dtype=float), numpy.arange(7, dtype=float), numpy.arange(7, dtype=float)], shifts=[[0, 0, 0]])
+    cell_data = numpy.zeros(grid.cell_data_shape)
+
+    fig, _ax = grid.visualize_isosurface(cell_data, level=0.5, sample_period=2, finalize=False)
+
+    assert_allclose(captured['xs'], [1.5, 1.5, 3.5])
+    assert_allclose(captured['ys'], [1.5, 3.5, 1.5])
+    assert_allclose(captured['zs'], [1.5, 1.5, 1.5])
+
+    pyplot.close(fig)