diff --git a/gridlock/base.py b/gridlock/base.py
new file mode 100644
index 0000000..6bd5fb8
--- /dev/null
+++ b/gridlock/base.py
@@ -0,0 +1,198 @@
+from typing import ClassVar, Self, Protocol
+from collections.abc import Callable, Sequence
+
+import numpy
+from numpy.typing import NDArray, ArrayLike
+
+from . import GridError
+
+
+class GridBase(Protocol):
+    exyz: list[NDArray]
+    """Cell edges. Monotonically increasing without duplicates."""
+
+    periodic: list[bool]
+    """For each axis, determines how far the rightmost boundary gets shifted. """
+
+    shifts: NDArray
+    """Offsets `[[x0, y0, z0], [x1, y1, z1], ...]` for grid `0,1,...`"""
+
+    @property
+    def dxyz(self) -> list[NDArray]:
+        """
+        Cell sizes for each axis, no shifts applied
+
+        Returns:
+            List of 3 ndarrays of cell sizes
+        """
+        return [numpy.diff(ee) for ee in self.exyz]
+
+    @property
+    def xyz(self) -> list[NDArray]:
+        """
+        Cell centers for each axis, no shifts applied
+
+        Returns:
+            List of 3 ndarrays of cell edges
+        """
+        return [self.exyz[a][:-1] + self.dxyz[a] / 2.0 for a in range(3)]
+
+    @property
+    def shape(self) -> NDArray[numpy.int_]:
+        """
+        The number of cells in x, y, and z
+
+        Returns:
+            ndarray of [x_centers.size, y_centers.size, z_centers.size]
+        """
+        return numpy.array([coord.size - 1 for coord in self.exyz], dtype=int)
+
+    @property
+    def num_grids(self) -> int:
+        """
+        The number of grids (number of shifts)
+        """
+        return self.shifts.shape[0]
+
+    @property
+    def cell_data_shape(self):
+        """
+        The shape of the cell_data ndarray (num_grids, *self.shape).
+        """
+        return numpy.hstack((self.num_grids, self.shape))
+
+    @property
+    def dxyz_with_ghost(self) -> list[NDArray]:
+        """
+        Gives dxyz with an additional 'ghost' cell at the end, whose value depends
+         on whether or not the axis has periodic boundary conditions. See main description
+         above to learn why this is necessary.
+
+         If periodic, final edge shifts same amount as first
+         Otherwise, final edge shifts same amount as second-to-last
+
+        Returns:
+            list of [dxs, dys, dzs] with each element same length as elements of `self.xyz`
+        """
+        el = [0 if p else -1 for p in self.periodic]
+        return [numpy.hstack((self.dxyz[a], self.dxyz[a][e])) for a, e in zip(range(3), el, strict=True)]
+
+    @property
+    def center(self) -> NDArray[numpy.float64]:
+        """
+        Center position of the entire grid, no shifts applied
+
+        Returns:
+            ndarray of [x_center, y_center, z_center]
+        """
+        # center is just average of first and last xyz, which is just the average of the
+        #  first two and last two exyz
+        centers = [(self.exyz[a][:2] + self.exyz[a][-2:]).sum() / 4.0 for a in range(3)]
+        return numpy.array(centers, dtype=float)
+
+    @property
+    def dxyz_limits(self) -> tuple[NDArray, NDArray]:
+        """
+        Returns the minimum and maximum cell size for each axis, as a tuple of two 3-element
+         ndarrays. No shifts are applied, so these are extreme bounds on these values (as a
+         weighted average is performed when shifting).
+
+        Returns:
+            Tuple of 2 ndarrays, `d_min=[min(dx), min(dy), min(dz)]` and `d_max=[...]`
+        """
+        d_min = numpy.array([min(self.dxyz[a]) for a in range(3)], dtype=float)
+        d_max = numpy.array([max(self.dxyz[a]) for a in range(3)], dtype=float)
+        return d_min, d_max
+
+    def shifted_exyz(self, which_shifts: int | None) -> list[NDArray]:
+        """
+        Returns edges for which_shifts.
+
+        Args:
+            which_shifts: Which grid (which shifts) to use, or `None` for unshifted
+
+        Returns:
+            List of 3 ndarrays of cell edges
+        """
+        if which_shifts is None:
+            return self.exyz
+        dxyz = self.dxyz_with_ghost
+        shifts = self.shifts[which_shifts, :]
+
+        # If shift is negative, use left cell's dx to determine shift
+        for a in range(3):
+            if shifts[a] < 0:
+                dxyz[a] = numpy.roll(dxyz[a], 1)
+
+        return [self.exyz[a] + dxyz[a] * shifts[a] for a in range(3)]
+
+    def shifted_dxyz(self, which_shifts: int | None) -> list[NDArray]:
+        """
+        Returns cell sizes for `which_shifts`.
+
+        Args:
+            which_shifts: Which grid (which shifts) to use, or `None` for unshifted
+
+        Returns:
+            List of 3 ndarrays of cell sizes
+        """
+        if which_shifts is None:
+            return self.dxyz
+        shifts = self.shifts[which_shifts, :]
+        dxyz = self.dxyz_with_ghost
+
+        # If shift is negative, use left cell's dx to determine size
+        sdxyz = []
+        for a in range(3):
+            if shifts[a] < 0:
+                roll_dxyz = numpy.roll(dxyz[a], 1)
+                abs_shift = numpy.abs(shifts[a])
+                sdxyz.append(roll_dxyz[:-1] * abs_shift + roll_dxyz[1:] * (1 - abs_shift))
+            else:
+                sdxyz.append(dxyz[a][:-1] * (1 - shifts[a]) + dxyz[a][1:] * shifts[a])
+
+        return sdxyz
+
+    def shifted_xyz(self, which_shifts: int | None) -> list[NDArray[numpy.float64]]:
+        """
+        Returns cell centers for `which_shifts`.
+
+        Args:
+            which_shifts: Which grid (which shifts) to use, or `None` for unshifted
+
+        Returns:
+            List of 3 ndarrays of cell centers
+        """
+        if which_shifts is None:
+            return self.xyz
+        exyz = self.shifted_exyz(which_shifts)
+        dxyz = self.shifted_dxyz(which_shifts)
+        return [exyz[a][:-1] + dxyz[a] / 2.0 for a in range(3)]
+
+    def autoshifted_dxyz(self) -> list[NDArray[numpy.float64]]:
+        """
+        Return cell widths, with each dimension shifted by the corresponding shifts.
+
+        Returns:
+            `[grid.shifted_dxyz(which_shifts=a)[a] for a in range(3)]`
+        """
+        if self.num_grids != 3:
+            raise GridError('Autoshifting requires exactly 3 grids')
+        return [self.shifted_dxyz(which_shifts=a)[a] for a in range(3)]
+
+    def allocate(self, fill_value: float | None = 1.0, dtype=numpy.float32) -> NDArray:
+        """
+        Allocate an ndarray for storing grid data.
+
+        Args:
+            fill_value: Value to initialize the grid to. If None, an
+                uninitialized array is returned.
+            dtype: Numpy dtype for the array. Default is `numpy.float32`.
+
+        Returns:
+            The allocated array
+        """
+        if fill_value is None:
+            return numpy.empty(self.cell_data_shape, dtype=dtype)
+        else:
+            return numpy.full(self.cell_data_shape, fill_value, dtype=dtype)
diff --git a/gridlock/draw.py b/gridlock/draw.py
index b4b2176..7146e15 100644
--- a/gridlock/draw.py
+++ b/gridlock/draw.py
@@ -1,13 +1,16 @@
 """
 Drawing-related methods for Grid class
 """
-from typing import Union, Sequence, Callable
+from typing import Union
+from collections.abc import Sequence, Callable
 
 import numpy
 from numpy.typing import NDArray, ArrayLike
 from float_raster import raster
 
 from . import GridError
+from .base import GridBase
+from .position import GridPosMixin
 
 
 # NOTE: Maybe it would make sense to create a GridDrawer class
@@ -20,372 +23,374 @@ foreground_callable_t = Callable[[NDArray, NDArray, NDArray], NDArray]
 foreground_t = Union[float, foreground_callable_t]
 
 
-def draw_polygons(
-        self,
-        cell_data: NDArray,
-        surface_normal: int,
-        center: ArrayLike,
-        polygons: Sequence[NDArray],
-        thickness: float,
-        foreground: Sequence[foreground_t] | foreground_t,
-        ) -> None:
-    """
-    Draw polygons on an axis-aligned plane.
+class GridDrawMixin(GridPosMixin):
+    def draw_polygons(
+            self,
+            cell_data: NDArray,
+            surface_normal: int,
+            center: ArrayLike,
+            polygons: Sequence[ArrayLike],
+            thickness: float,
+            foreground: Sequence[foreground_t] | foreground_t,
+            ) -> None:
+        """
+        Draw polygons on an axis-aligned plane.
 
-    Args:
-        cell_data: Cell data to modify (e.g. created by `Grid.allocate()`)
-        surface_normal: Axis normal to the plane we're drawing on. Integer in `range(3)`.
-        center: 3-element ndarray or list specifying an offset applied to all the polygons
-        polygons: List of Nx2 or Nx3 ndarrays, each specifying the vertices of a polygon
-            (non-closed, clockwise). If Nx3, the `surface_normal` coordinate is ignored. Each
-            polygon must have at least 3 vertices.
-        thickness: Thickness of the layer to draw
-        foreground: Value to draw with ('brush color'). Can be scalar, callable, or a list
-            of any of these (1 per grid). Callable values should take an ndarray the shape of the
-            grid and return an ndarray of equal shape containing the foreground value at the given x, y,
-            and z (natural, not grid coordinates).
+        Args:
+            cell_data: Cell data to modify (e.g. created by `Grid.allocate()`)
+            surface_normal: Axis normal to the plane we're drawing on. Integer in `range(3)`.
+            center: 3-element ndarray or list specifying an offset applied to all the polygons
+            polygons: List of Nx2 or Nx3 ndarrays, each specifying the vertices of a polygon
+                (non-closed, clockwise). If Nx3, the `surface_normal` coordinate is ignored. Each
+                polygon must have at least 3 vertices.
+            thickness: Thickness of the layer to draw
+            foreground: Value to draw with ('brush color'). Can be scalar, callable, or a list
+                of any of these (1 per grid). Callable values should take an ndarray the shape of the
+                grid and return an ndarray of equal shape containing the foreground value at the given x, y,
+                and z (natural, not grid coordinates).
 
-    Raises:
-        GridError
-    """
-    if surface_normal not in range(3):
-        raise GridError('Invalid surface_normal direction')
-
-    center = numpy.squeeze(center)
-
-    # Check polygons, and remove redundant coordinates
-    surface = numpy.delete(range(3), surface_normal)
-
-    for i, polygon in enumerate(polygons):
-        malformed = f'Malformed polygon: ({i})'
-        if polygon.shape[1] not in (2, 3):
-            raise GridError(malformed + 'must be a Nx2 or Nx3 ndarray')
-        if polygon.shape[1] == 3:
-            polygon = polygon[surface, :]
-
-        if not polygon.shape[0] > 2:
-            raise GridError(malformed + 'must consist of more than 2 points')
-        if polygon.ndim > 2 and not numpy.unique(polygon[:, surface_normal]).size == 1:
-            raise GridError(malformed + 'must be in plane with surface normal '
-                            + 'xyz'[surface_normal])
-
-    # Broadcast foreground where necessary
-    foregrounds: Sequence[foreground_callable_t] | Sequence[float]
-    if numpy.size(foreground) == 1:     # type: ignore
-        foregrounds = [foreground] * len(cell_data)  # type: ignore
-    elif isinstance(foreground, numpy.ndarray):
-        raise GridError('ndarray not supported for foreground')
-    else:
-        foregrounds = foreground    # type: ignore
-
-    # ## Compute sub-domain of the grid occupied by polygons
-    # 1) Compute outer bounds (bd) of polygons
-    bd_2d_min = numpy.array([0, 0])
-    bd_2d_max = numpy.array([0, 0])
-    for polygon in polygons:
-        bd_2d_min = numpy.minimum(bd_2d_min, polygon.min(axis=0))
-        bd_2d_max = numpy.maximum(bd_2d_max, polygon.max(axis=0))
-    bd_min = numpy.insert(bd_2d_min, surface_normal, -thickness / 2.0) + center
-    bd_max = numpy.insert(bd_2d_max, surface_normal, +thickness / 2.0) + center
-
-    # 2) Find indices (bdi) just outside bd elements
-    buf = 2  # size of safety buffer
-    # Use s_min and s_max with unshifted pos2ind to get absolute limits on
-    #  the indices the polygons might affect
-    s_min = self.shifts.min(axis=0)
-    s_max = self.shifts.max(axis=0)
-    bdi_min = self.pos2ind(bd_min + s_min, None, round_ind=False, check_bounds=False) - buf
-    bdi_max = self.pos2ind(bd_max + s_max, None, round_ind=False, check_bounds=False) + buf
-    bdi_min = numpy.maximum(numpy.floor(bdi_min), 0).astype(int)
-    bdi_max = numpy.minimum(numpy.ceil(bdi_max), self.shape - 1).astype(int)
-
-    # 3) Adjust polygons for center
-    polygons = [poly + center[surface] for poly in polygons]
-
-    # ## Generate weighing function
-    def to_3d(vector: NDArray, val: float = 0.0) -> NDArray[numpy.float64]:
-        v_2d = numpy.array(vector, dtype=float)
-        return numpy.insert(v_2d, surface_normal, (val,))
-
-    # iterate over grids
-    for i, _ in enumerate(cell_data):
-        # ## Evaluate or expand foregrounds[i]
-        foregrounds_i = foregrounds[i]
-        if callable(foregrounds_i):
-            # meshgrid over the (shifted) domain
-            domain = [self.shifted_xyz(i)[k][bdi_min[k]:bdi_max[k] + 1] for k in range(3)]
-            (x0, y0, z0) = numpy.meshgrid(*domain, indexing='ij')
-
-            # evaluate on the meshgrid
-            foreground_val = foregrounds_i(x0, y0, z0)
-            if not numpy.isfinite(foreground_val).all():
-                raise GridError(f'Non-finite values in foreground[{i}]')
-        elif numpy.size(foregrounds_i) != 1:
-            raise GridError(f'Unsupported foreground[{i}]: {type(foregrounds_i)}')
-        else:
-            # foreground[i] is scalar non-callable
-            foreground_val = foregrounds_i
-
-        w_xy = numpy.zeros((bdi_max - bdi_min + 1)[surface].astype(int))
-
-        # Draw each polygon separately
-        for polygon in polygons:
-
-            # Get the boundaries of the polygon
-            pbd_min = polygon.min(axis=0)
-            pbd_max = polygon.max(axis=0)
-
-            # Find indices in w_xy just outside polygon
-            #  using per-grid xy-weights (self.shifted_xyz())
-            corner_min = self.pos2ind(to_3d(pbd_min), i,
-                                      check_bounds=False)[surface].astype(int)
-            corner_max = self.pos2ind(to_3d(pbd_max), i,
-                                      check_bounds=False)[surface].astype(int)
-
-            # Find indices in w_xy which are modified by polygon
-            # First for the edge coordinates (+1 since we're indexing edges)
-            edge_slices = [numpy.s_[i:f + 2] for i, f in zip(corner_min, corner_max, strict=True)]
-            # Then for the pixel centers (-bdi_min since we're
-            #  calculating weights within a subspace)
-            centers_slice = tuple(numpy.s_[i:f + 1] for i, f in zip(corner_min - bdi_min[surface],
-                                                                    corner_max - bdi_min[surface], strict=True))
-
-            aa_x, aa_y = (self.shifted_exyz(i)[a][s] for a, s in zip(surface, edge_slices, strict=True))
-            w_xy[centers_slice] += raster(polygon.T, aa_x, aa_y)
-
-        # Clamp overlapping polygons to 1
-        w_xy = numpy.minimum(w_xy, 1.0)
-
-        # 2) Generate weights in z-direction
-        w_z = numpy.zeros(((bdi_max - bdi_min + 1)[surface_normal], ))
-
-        def get_zi(offset, i=i, w_z=w_z):
-            edges = self.shifted_exyz(i)[surface_normal]
-            point = center[surface_normal] + offset
-            grid_coord = numpy.digitize(point, edges) - 1
-            w_coord = grid_coord - bdi_min[surface_normal]
-
-            if w_coord < 0:
-                w_coord = 0
-                f = 0
-            elif w_coord >= w_z.size:
-                w_coord = w_z.size - 1
-                f = 1
-            else:
-                dz = self.shifted_dxyz(i)[surface_normal][grid_coord]
-                f = (point - edges[grid_coord]) / dz
-            return f, w_coord
-
-        zi_top_f, zi_top = get_zi(+thickness / 2.0)
-        zi_bot_f, zi_bot = get_zi(-thickness / 2.0)
-
-        w_z[zi_bot + 1:zi_top] = 1
-
-        if zi_bot < zi_top:
-            w_z[zi_top] = zi_top_f
-            w_z[zi_bot] = 1 - zi_bot_f
-        else:
-            w_z[zi_bot] = zi_top_f - zi_bot_f
-
-        # 3) Generate total weight function
-        w = (w_xy[:, :, None] * w_z).transpose(numpy.insert([0, 1], surface_normal, (2,)))
-
-        # ## Modify the grid
-        g_slice = (i,) + tuple(numpy.s_[bdi_min[a]:bdi_max[a] + 1] for a in range(3))
-        cell_data[g_slice] = (1 - w) * cell_data[g_slice] + w * foreground_val
-
-
-def draw_polygon(
-        self,
-        cell_data: NDArray,
-        surface_normal: int,
-        center: ArrayLike,
-        polygon: ArrayLike,
-        thickness: float,
-        foreground: Sequence[foreground_t] | foreground_t,
-        ) -> None:
-    """
-    Draw a polygon on an axis-aligned plane.
-
-    Args:
-        cell_data: Cell data to modify (e.g. created by `Grid.allocate()`)
-        surface_normal: Axis normal to the plane we're drawing on. Integer in `range(3)`.
-        center: 3-element ndarray or list specifying an offset applied to the polygon
-        polygon: Nx2 or Nx3 ndarray specifying the vertices of a polygon (non-closed,
-            clockwise). If Nx3, the `surface_normal` coordinate is ignored. Must have at
-            least 3 vertices.
-        thickness: Thickness of the layer to draw
-        foreground: Value to draw with ('brush color'). See `draw_polygons()` for details.
-    """
-    self.draw_polygons(cell_data, surface_normal, center, [polygon], thickness, foreground)
-
-
-def draw_slab(
-        self,
-        cell_data: NDArray,
-        surface_normal: int,
-        center: ArrayLike,
-        thickness: float,
-        foreground: Sequence[foreground_t] | foreground_t,
-        ) -> None:
-    """
-    Draw an axis-aligned infinite slab.
-
-    Args:
-        cell_data: Cell data to modify (e.g. created by `Grid.allocate()`)
-        surface_normal: Axis normal to the plane we're drawing on. Integer in `range(3)`.
-        center: `surface_normal` coordinate value at the center of the slab
-        thickness: Thickness of the layer to draw
-        foreground: Value to draw with ('brush color'). See `draw_polygons()` for details.
-    """
-    # Turn surface_normal into its integer representation
-    if surface_normal not in range(3):
-        raise GridError('Invalid surface_normal direction')
-
-    if numpy.size(center) != 1:
+        Raises:
+            GridError
+        """
+        if surface_normal not in range(3):
+            raise GridError('Invalid surface_normal direction')
         center = numpy.squeeze(center)
-        if len(center) == 3:
-            center = center[surface_normal]
+        poly_list = [numpy.array(poly, copy=False) for poly in polygons]
+
+        # Check polygons, and remove redundant coordinates
+        surface = numpy.delete(range(3), surface_normal)
+
+        for i, polygon in enumerate(poly_list):
+            malformed = f'Malformed polygon: ({i})'
+            if polygon.shape[1] not in (2, 3):
+                raise GridError(malformed + 'must be a Nx2 or Nx3 ndarray')
+            if polygon.shape[1] == 3:
+                polygon = polygon[surface, :]
+
+            if not polygon.shape[0] > 2:
+                raise GridError(malformed + 'must consist of more than 2 points')
+            if polygon.ndim > 2 and not numpy.unique(polygon[:, surface_normal]).size == 1:
+                raise GridError(malformed + 'must be in plane with surface normal '
+                                + 'xyz'[surface_normal])
+
+        # Broadcast foreground where necessary
+        foregrounds: Sequence[foreground_callable_t] | Sequence[float]
+        if numpy.size(foreground) == 1:     # type: ignore
+            foregrounds = [foreground] * len(cell_data)  # type: ignore
+        elif isinstance(foreground, numpy.ndarray):
+            raise GridError('ndarray not supported for foreground')
         else:
-            raise GridError(f'Bad center: {center}')
+            foregrounds = foreground    # type: ignore
 
-    # Find center of slab
-    center_shift = self.center
-    center_shift[surface_normal] = center
+        # ## Compute sub-domain of the grid occupied by polygons
+        # 1) Compute outer bounds (bd) of polygons
+        bd_2d_min = numpy.array([0, 0])
+        bd_2d_max = numpy.array([0, 0])
+        for polygon in poly_list:
+            bd_2d_min = numpy.minimum(bd_2d_min, polygon.min(axis=0))
+            bd_2d_max = numpy.maximum(bd_2d_max, polygon.max(axis=0))
+        bd_min = numpy.insert(bd_2d_min, surface_normal, -thickness / 2.0) + center
+        bd_max = numpy.insert(bd_2d_max, surface_normal, +thickness / 2.0) + center
 
-    surface = numpy.delete(range(3), surface_normal)
+        # 2) Find indices (bdi) just outside bd elements
+        buf = 2  # size of safety buffer
+        # Use s_min and s_max with unshifted pos2ind to get absolute limits on
+        #  the indices the polygons might affect
+        s_min = self.shifts.min(axis=0)
+        s_max = self.shifts.max(axis=0)
+        bdi_min = self.pos2ind(bd_min + s_min, None, round_ind=False, check_bounds=False) - buf
+        bdi_max = self.pos2ind(bd_max + s_max, None, round_ind=False, check_bounds=False) + buf
+        bdi_min = numpy.maximum(numpy.floor(bdi_min), 0).astype(int)
+        bdi_max = numpy.minimum(numpy.ceil(bdi_max), self.shape - 1).astype(int)
 
-    xyz_min = numpy.array([self.xyz[a][0] for a in range(3)], dtype=float)[surface]
-    xyz_max = numpy.array([self.xyz[a][-1] for a in range(3)], dtype=float)[surface]
+        # 3) Adjust polygons for center
+        poly_list = [poly + center[surface] for poly in poly_list]
 
-    dxyz = numpy.array([max(self.dxyz[i]) for i in surface], dtype=float)
+        # ## Generate weighing function
+        def to_3d(vector: NDArray, val: float = 0.0) -> NDArray[numpy.float64]:
+            v_2d = numpy.array(vector, dtype=float)
+            return numpy.insert(v_2d, surface_normal, (val,))
 
-    xyz_min -= 4 * dxyz
-    xyz_max += 4 * dxyz
+        # iterate over grids
+        foreground_val: NDArray | float
+        for i, _ in enumerate(cell_data):
+            # ## Evaluate or expand foregrounds[i]
+            foregrounds_i = foregrounds[i]
+            if callable(foregrounds_i):
+                # meshgrid over the (shifted) domain
+                domain = [self.shifted_xyz(i)[k][bdi_min[k]:bdi_max[k] + 1] for k in range(3)]
+                (x0, y0, z0) = numpy.meshgrid(*domain, indexing='ij')
 
-    p = numpy.array([[xyz_min[0], xyz_max[1]],
-                     [xyz_max[0], xyz_max[1]],
-                     [xyz_max[0], xyz_min[1]],
-                     [xyz_min[0], xyz_min[1]]], dtype=float)
+                # evaluate on the meshgrid
+                foreground_val = foregrounds_i(x0, y0, z0)
+                if not numpy.isfinite(foreground_val).all():
+                    raise GridError(f'Non-finite values in foreground[{i}]')
+            elif numpy.size(foregrounds_i) != 1:
+                raise GridError(f'Unsupported foreground[{i}]: {type(foregrounds_i)}')
+            else:
+                # foreground[i] is scalar non-callable
+                foreground_val = foregrounds_i
 
-    self.draw_polygon(cell_data, surface_normal, center_shift, p, thickness, foreground)
+            w_xy = numpy.zeros((bdi_max - bdi_min + 1)[surface].astype(int))
+
+            # Draw each polygon separately
+            for polygon in poly_list:
+
+                # Get the boundaries of the polygon
+                pbd_min = polygon.min(axis=0)
+                pbd_max = polygon.max(axis=0)
+
+                # Find indices in w_xy just outside polygon
+                #  using per-grid xy-weights (self.shifted_xyz())
+                corner_min = self.pos2ind(to_3d(pbd_min), i,
+                                          check_bounds=False)[surface].astype(int)
+                corner_max = self.pos2ind(to_3d(pbd_max), i,
+                                          check_bounds=False)[surface].astype(int)
+
+                # Find indices in w_xy which are modified by polygon
+                # First for the edge coordinates (+1 since we're indexing edges)
+                edge_slices = [numpy.s_[i:f + 2] for i, f in zip(corner_min, corner_max, strict=True)]
+                # Then for the pixel centers (-bdi_min since we're
+                #  calculating weights within a subspace)
+                centers_slice = tuple(numpy.s_[i:f + 1] for i, f in zip(corner_min - bdi_min[surface],
+                                                                        corner_max - bdi_min[surface], strict=True))
+
+                aa_x, aa_y = (self.shifted_exyz(i)[a][s] for a, s in zip(surface, edge_slices, strict=True))
+                w_xy[centers_slice] += raster(polygon.T, aa_x, aa_y)
+
+            # Clamp overlapping polygons to 1
+            w_xy = numpy.minimum(w_xy, 1.0)
+
+            # 2) Generate weights in z-direction
+            w_z = numpy.zeros(((bdi_max - bdi_min + 1)[surface_normal], ))
+
+            def get_zi(offset, i=i, w_z=w_z):
+                edges = self.shifted_exyz(i)[surface_normal]
+                point = center[surface_normal] + offset
+                grid_coord = numpy.digitize(point, edges) - 1
+                w_coord = grid_coord - bdi_min[surface_normal]
+
+                if w_coord < 0:
+                    w_coord = 0
+                    f = 0
+                elif w_coord >= w_z.size:
+                    w_coord = w_z.size - 1
+                    f = 1
+                else:
+                    dz = self.shifted_dxyz(i)[surface_normal][grid_coord]
+                    f = (point - edges[grid_coord]) / dz
+                return f, w_coord
+
+            zi_top_f, zi_top = get_zi(+thickness / 2.0)
+            zi_bot_f, zi_bot = get_zi(-thickness / 2.0)
+
+            w_z[zi_bot + 1:zi_top] = 1
+
+            if zi_bot < zi_top:
+                w_z[zi_top] = zi_top_f
+                w_z[zi_bot] = 1 - zi_bot_f
+            else:
+                w_z[zi_bot] = zi_top_f - zi_bot_f
+
+            # 3) Generate total weight function
+            w = (w_xy[:, :, None] * w_z).transpose(numpy.insert([0, 1], surface_normal, (2,)))
+
+            # ## Modify the grid
+            g_slice = (i,) + tuple(numpy.s_[bdi_min[a]:bdi_max[a] + 1] for a in range(3))
+            cell_data[g_slice] = (1 - w) * cell_data[g_slice] + w * foreground_val
 
 
-def draw_cuboid(
-        self,
-        cell_data: NDArray,
-        center: ArrayLike,
-        dimensions: ArrayLike,
-        foreground: Sequence[foreground_t] | foreground_t,
-        ) -> None:
-    """
-    Draw an axis-aligned cuboid
+    def draw_polygon(
+            self,
+            cell_data: NDArray,
+            surface_normal: int,
+            center: ArrayLike,
+            polygon: ArrayLike,
+            thickness: float,
+            foreground: Sequence[foreground_t] | foreground_t,
+            ) -> None:
+        """
+        Draw a polygon on an axis-aligned plane.
 
-    Args:
-        cell_data: Cell data to modify (e.g. created by `Grid.allocate()`)
-        center: 3-element ndarray or list specifying the cuboid's center
-        dimensions: 3-element list or ndarray containing the x, y, and z edge-to-edge
-             sizes of the cuboid
-        foreground: Value to draw with ('brush color'). See `draw_polygons()` for details.
-    """
-    dimensions = numpy.array(dimensions, copy=False)
-    p = numpy.array([[-dimensions[0], +dimensions[1]],
-                     [+dimensions[0], +dimensions[1]],
-                     [+dimensions[0], -dimensions[1]],
-                     [-dimensions[0], -dimensions[1]]], dtype=float) / 2.0
-    thickness = dimensions[2]
-    self.draw_polygon(cell_data, 2, center, p, thickness, foreground)
+        Args:
+            cell_data: Cell data to modify (e.g. created by `Grid.allocate()`)
+            surface_normal: Axis normal to the plane we're drawing on. Integer in `range(3)`.
+            center: 3-element ndarray or list specifying an offset applied to the polygon
+            polygon: Nx2 or Nx3 ndarray specifying the vertices of a polygon (non-closed,
+                clockwise). If Nx3, the `surface_normal` coordinate is ignored. Must have at
+                least 3 vertices.
+            thickness: Thickness of the layer to draw
+            foreground: Value to draw with ('brush color'). See `draw_polygons()` for details.
+        """
+        self.draw_polygons(cell_data, surface_normal, center, [polygon], thickness, foreground)
 
 
-def draw_cylinder(
-        self,
-        cell_data: NDArray,
-        surface_normal: int,
-        center: ArrayLike,
-        radius: float,
-        thickness: float,
-        num_points: int,
-        foreground: Sequence[foreground_t] | foreground_t,
-        ) -> None:
-    """
-    Draw an axis-aligned cylinder. Approximated by a num_points-gon
+    def draw_slab(
+            self,
+            cell_data: NDArray,
+            surface_normal: int,
+            center: ArrayLike,
+            thickness: float,
+            foreground: Sequence[foreground_t] | foreground_t,
+            ) -> None:
+        """
+        Draw an axis-aligned infinite slab.
 
-    Args:
-        cell_data: Cell data to modify (e.g. created by `Grid.allocate()`)
-        surface_normal: Axis normal to the plane we're drawing on. Integer in `range(3)`.
-        center: 3-element ndarray or list specifying the cylinder's center
-        radius: cylinder radius
-        thickness: Thickness of the layer to draw
-        num_points: The circle is approximated by a polygon with `num_points` vertices
-        foreground: Value to draw with ('brush color'). See `draw_polygons()` for details.
-    """
-    theta = numpy.linspace(0, 2 * numpy.pi, num_points, endpoint=False)
-    x = radius * numpy.sin(theta)
-    y = radius * numpy.cos(theta)
-    polygon = numpy.hstack((x[:, None], y[:, None]))
-    self.draw_polygon(cell_data, surface_normal, center, polygon, thickness, foreground)
+        Args:
+            cell_data: Cell data to modify (e.g. created by `Grid.allocate()`)
+            surface_normal: Axis normal to the plane we're drawing on. Integer in `range(3)`.
+            center: `surface_normal` coordinate value at the center of the slab
+            thickness: Thickness of the layer to draw
+            foreground: Value to draw with ('brush color'). See `draw_polygons()` for details.
+        """
+        # Turn surface_normal into its integer representation
+        if surface_normal not in range(3):
+            raise GridError('Invalid surface_normal direction')
+
+        if numpy.size(center) != 1:
+            center = numpy.squeeze(center)
+            if len(center) == 3:
+                center = center[surface_normal]
+            else:
+                raise GridError(f'Bad center: {center}')
+
+        # Find center of slab
+        center_shift = self.center
+        center_shift[surface_normal] = center
+
+        surface = numpy.delete(range(3), surface_normal)
+
+        xyz_min = numpy.array([self.xyz[a][0] for a in range(3)], dtype=float)[surface]
+        xyz_max = numpy.array([self.xyz[a][-1] for a in range(3)], dtype=float)[surface]
+
+        dxyz = numpy.array([max(self.dxyz[i]) for i in surface], dtype=float)
+
+        xyz_min -= 4 * dxyz
+        xyz_max += 4 * dxyz
+
+        p = numpy.array([[xyz_min[0], xyz_max[1]],
+                         [xyz_max[0], xyz_max[1]],
+                         [xyz_max[0], xyz_min[1]],
+                         [xyz_min[0], xyz_min[1]]], dtype=float)
+
+        self.draw_polygon(cell_data, surface_normal, center_shift, p, thickness, foreground)
 
 
-def draw_extrude_rectangle(
-        self,
-        cell_data: NDArray,
-        rectangle: ArrayLike,
-        direction: int,
-        polarity: int,
-        distance: float,
-        ) -> None:
-    """
-    Extrude a rectangle of a previously-drawn structure along an axis.
+    def draw_cuboid(
+            self,
+            cell_data: NDArray,
+            center: ArrayLike,
+            dimensions: ArrayLike,
+            foreground: Sequence[foreground_t] | foreground_t,
+            ) -> None:
+        """
+        Draw an axis-aligned cuboid
 
-    Args:
-        cell_data: Cell data to modify (e.g. created by `Grid.allocate()`)
-        rectangle: 2x3 ndarray or list specifying the rectangle's corners
-        direction: Direction to extrude in. Integer in `range(3)`.
-        polarity: +1 or -1, direction along axis to extrude in
-        distance: How far to extrude
-    """
-    s = numpy.sign(polarity)
+        Args:
+            cell_data: Cell data to modify (e.g. created by `Grid.allocate()`)
+            center: 3-element ndarray or list specifying the cuboid's center
+            dimensions: 3-element list or ndarray containing the x, y, and z edge-to-edge
+                 sizes of the cuboid
+            foreground: Value to draw with ('brush color'). See `draw_polygons()` for details.
+        """
+        dimensions = numpy.array(dimensions, copy=False)
+        p = numpy.array([[-dimensions[0], +dimensions[1]],
+                         [+dimensions[0], +dimensions[1]],
+                         [+dimensions[0], -dimensions[1]],
+                         [-dimensions[0], -dimensions[1]]], dtype=float) / 2.0
+        thickness = dimensions[2]
+        self.draw_polygon(cell_data, 2, center, p, thickness, foreground)
 
-    rectangle = numpy.array(rectangle, dtype=float)
-    if s == 0:
-        raise GridError('0 is not a valid polarity')
-    if direction not in range(3):
-        raise GridError(f'Invalid direction: {direction}')
-    if rectangle[0, direction] != rectangle[1, direction]:
-        raise GridError('Rectangle entries along extrusion direction do not match.')
 
-    center = rectangle.sum(axis=0) / 2.0
-    center[direction] += s * distance / 2.0
+    def draw_cylinder(
+            self,
+            cell_data: NDArray,
+            surface_normal: int,
+            center: ArrayLike,
+            radius: float,
+            thickness: float,
+            num_points: int,
+            foreground: Sequence[foreground_t] | foreground_t,
+            ) -> None:
+        """
+        Draw an axis-aligned cylinder. Approximated by a num_points-gon
 
-    surface = numpy.delete(range(3), direction)
+        Args:
+            cell_data: Cell data to modify (e.g. created by `Grid.allocate()`)
+            surface_normal: Axis normal to the plane we're drawing on. Integer in `range(3)`.
+            center: 3-element ndarray or list specifying the cylinder's center
+            radius: cylinder radius
+            thickness: Thickness of the layer to draw
+            num_points: The circle is approximated by a polygon with `num_points` vertices
+            foreground: Value to draw with ('brush color'). See `draw_polygons()` for details.
+        """
+        theta = numpy.linspace(0, 2 * numpy.pi, num_points, endpoint=False)
+        x = radius * numpy.sin(theta)
+        y = radius * numpy.cos(theta)
+        polygon = numpy.hstack((x[:, None], y[:, None]))
+        self.draw_polygon(cell_data, surface_normal, center, polygon, thickness, foreground)
 
-    dim = numpy.fabs(numpy.diff(rectangle, axis=0).T)[surface]
-    p = numpy.vstack((numpy.array([-1, -1, 1, 1], dtype=float) * dim[0] * 0.5,
-                      numpy.array([-1, 1, 1, -1], dtype=float) * dim[1] * 0.5)).T
-    thickness = distance
 
-    foreground_func = []
-    for i, grid in enumerate(cell_data):
-        z = self.pos2ind(rectangle[0, :], i, round_ind=False, check_bounds=False)[direction]
+    def draw_extrude_rectangle(
+            self,
+            cell_data: NDArray,
+            rectangle: ArrayLike,
+            direction: int,
+            polarity: int,
+            distance: float,
+            ) -> None:
+        """
+        Extrude a rectangle of a previously-drawn structure along an axis.
 
-        ind = [int(numpy.floor(z)) if i == direction else slice(None) for i in range(3)]
+        Args:
+            cell_data: Cell data to modify (e.g. created by `Grid.allocate()`)
+            rectangle: 2x3 ndarray or list specifying the rectangle's corners
+            direction: Direction to extrude in. Integer in `range(3)`.
+            polarity: +1 or -1, direction along axis to extrude in
+            distance: How far to extrude
+        """
+        s = numpy.sign(polarity)
 
-        fpart = z - numpy.floor(z)
-        mult = [1 - fpart, fpart][::s]  # reverses if s negative
+        rectangle = numpy.array(rectangle, dtype=float)
+        if s == 0:
+            raise GridError('0 is not a valid polarity')
+        if direction not in range(3):
+            raise GridError(f'Invalid direction: {direction}')
+        if rectangle[0, direction] != rectangle[1, direction]:
+            raise GridError('Rectangle entries along extrusion direction do not match.')
 
-        foreground = mult[0] * grid[tuple(ind)]
-        ind[direction] += 1                         # type: ignore #(known safe)
-        foreground += mult[1] * grid[tuple(ind)]
+        center = rectangle.sum(axis=0) / 2.0
+        center[direction] += s * distance / 2.0
 
-        def f_foreground(xs, ys, zs, i=i, foreground=foreground) -> NDArray[numpy.int_]:
-            # transform from natural position to index
-            xyzi = numpy.array([self.pos2ind(qrs, which_shifts=i)
-                                for qrs in zip(xs.flat, ys.flat, zs.flat, strict=True)], dtype=int)
-            # reshape to original shape and keep only in-plane components
-            qi, ri = (numpy.reshape(xyzi[:, k], xs.shape) for k in surface)
-            return foreground[qi, ri]
+        surface = numpy.delete(range(3), direction)
 
-        foreground_func.append(f_foreground)
+        dim = numpy.fabs(numpy.diff(rectangle, axis=0).T)[surface]
+        p = numpy.vstack((numpy.array([-1, -1, 1, 1], dtype=float) * dim[0] * 0.5,
+                          numpy.array([-1, 1, 1, -1], dtype=float) * dim[1] * 0.5)).T
+        thickness = distance
 
-    self.draw_polygon(cell_data, direction, center, p, thickness, foreground_func)
+        foreground_func = []
+        for i, grid in enumerate(cell_data):
+            z = self.pos2ind(rectangle[0, :], i, round_ind=False, check_bounds=False)[direction]
+
+            ind = [int(numpy.floor(z)) if i == direction else slice(None) for i in range(3)]
+
+            fpart = z - numpy.floor(z)
+            mult = [1 - fpart, fpart][::s]  # reverses if s negative
+
+            foreground = mult[0] * grid[tuple(ind)]
+            ind[direction] += 1                         # type: ignore #(known safe)
+            foreground += mult[1] * grid[tuple(ind)]
+
+            def f_foreground(xs, ys, zs, i=i, foreground=foreground) -> NDArray[numpy.int_]:
+                # transform from natural position to index
+                xyzi = numpy.array([self.pos2ind(qrs, which_shifts=i)
+                                    for qrs in zip(xs.flat, ys.flat, zs.flat, strict=True)], dtype=int)
+                # reshape to original shape and keep only in-plane components
+                qi, ri = (numpy.reshape(xyzi[:, k], xs.shape) for k in surface)
+                return foreground[qi, ri]
+
+            foreground_func.append(f_foreground)
+
+        self.draw_polygon(cell_data, direction, center, p, thickness, foreground_func)
 
diff --git a/gridlock/grid.py b/gridlock/grid.py
index 2fb721b..55b1abb 100644
--- a/gridlock/grid.py
+++ b/gridlock/grid.py
@@ -1,4 +1,5 @@
-from typing import Callable, Sequence, ClassVar, Self
+from typing import ClassVar, Self
+from collections.abc import Callable, Sequence
 
 import numpy
 from numpy.typing import NDArray, ArrayLike
@@ -8,12 +9,16 @@ import warnings
 import copy
 
 from . import GridError
+from .base import GridBase
+from .draw import GridDrawMixin
+from .read import GridReadMixin
+from .position import GridPosMixin
 
 
 foreground_callable_type = Callable[[NDArray, NDArray, NDArray], NDArray]
 
 
-class Grid:
+class Grid(GridDrawMixin, GridReadMixin, GridPosMixin):
     """
     Simulation grid metadata for finite-difference simulations.
 
@@ -70,193 +75,6 @@ class Grid:
         ], dtype=float)
     """Default shifts for Yee grid H-field"""
 
-    from .draw import (
-        draw_polygons, draw_polygon, draw_slab, draw_cuboid,
-        draw_cylinder, draw_extrude_rectangle,
-        )
-    from .read import get_slice, visualize_slice, visualize_isosurface
-    from .position import ind2pos, pos2ind
-
-    @property
-    def dxyz(self) -> list[NDArray]:
-        """
-        Cell sizes for each axis, no shifts applied
-
-        Returns:
-            List of 3 ndarrays of cell sizes
-        """
-        return [numpy.diff(ee) for ee in self.exyz]
-
-    @property
-    def xyz(self) -> list[NDArray]:
-        """
-        Cell centers for each axis, no shifts applied
-
-        Returns:
-            List of 3 ndarrays of cell edges
-        """
-        return [self.exyz[a][:-1] + self.dxyz[a] / 2.0 for a in range(3)]
-
-    @property
-    def shape(self) -> NDArray[numpy.int_]:
-        """
-        The number of cells in x, y, and z
-
-        Returns:
-            ndarray of [x_centers.size, y_centers.size, z_centers.size]
-        """
-        return numpy.array([coord.size - 1 for coord in self.exyz], dtype=int)
-
-    @property
-    def num_grids(self) -> int:
-        """
-        The number of grids (number of shifts)
-        """
-        return self.shifts.shape[0]
-
-    @property
-    def cell_data_shape(self):
-        """
-        The shape of the cell_data ndarray (num_grids, *self.shape).
-        """
-        return numpy.hstack((self.num_grids, self.shape))
-
-    @property
-    def dxyz_with_ghost(self) -> list[NDArray]:
-        """
-        Gives dxyz with an additional 'ghost' cell at the end, whose value depends
-         on whether or not the axis has periodic boundary conditions. See main description
-         above to learn why this is necessary.
-
-         If periodic, final edge shifts same amount as first
-         Otherwise, final edge shifts same amount as second-to-last
-
-        Returns:
-            list of [dxs, dys, dzs] with each element same length as elements of `self.xyz`
-        """
-        el = [0 if p else -1 for p in self.periodic]
-        return [numpy.hstack((self.dxyz[a], self.dxyz[a][e])) for a, e in zip(range(3), el, strict=True)]
-
-    @property
-    def center(self) -> NDArray[numpy.float64]:
-        """
-        Center position of the entire grid, no shifts applied
-
-        Returns:
-            ndarray of [x_center, y_center, z_center]
-        """
-        # center is just average of first and last xyz, which is just the average of the
-        #  first two and last two exyz
-        centers = [(self.exyz[a][:2] + self.exyz[a][-2:]).sum() / 4.0 for a in range(3)]
-        return numpy.array(centers, dtype=float)
-
-    @property
-    def dxyz_limits(self) -> tuple[NDArray, NDArray]:
-        """
-        Returns the minimum and maximum cell size for each axis, as a tuple of two 3-element
-         ndarrays. No shifts are applied, so these are extreme bounds on these values (as a
-         weighted average is performed when shifting).
-
-        Returns:
-            Tuple of 2 ndarrays, `d_min=[min(dx), min(dy), min(dz)]` and `d_max=[...]`
-        """
-        d_min = numpy.array([min(self.dxyz[a]) for a in range(3)], dtype=float)
-        d_max = numpy.array([max(self.dxyz[a]) for a in range(3)], dtype=float)
-        return d_min, d_max
-
-    def shifted_exyz(self, which_shifts: int | None) -> list[NDArray]:
-        """
-        Returns edges for which_shifts.
-
-        Args:
-            which_shifts: Which grid (which shifts) to use, or `None` for unshifted
-
-        Returns:
-            List of 3 ndarrays of cell edges
-        """
-        if which_shifts is None:
-            return self.exyz
-        dxyz = self.dxyz_with_ghost
-        shifts = self.shifts[which_shifts, :]
-
-        # If shift is negative, use left cell's dx to determine shift
-        for a in range(3):
-            if shifts[a] < 0:
-                dxyz[a] = numpy.roll(dxyz[a], 1)
-
-        return [self.exyz[a] + dxyz[a] * shifts[a] for a in range(3)]
-
-    def shifted_dxyz(self, which_shifts: int | None) -> list[NDArray]:
-        """
-        Returns cell sizes for `which_shifts`.
-
-        Args:
-            which_shifts: Which grid (which shifts) to use, or `None` for unshifted
-
-        Returns:
-            List of 3 ndarrays of cell sizes
-        """
-        if which_shifts is None:
-            return self.dxyz
-        shifts = self.shifts[which_shifts, :]
-        dxyz = self.dxyz_with_ghost
-
-        # If shift is negative, use left cell's dx to determine size
-        sdxyz = []
-        for a in range(3):
-            if shifts[a] < 0:
-                roll_dxyz = numpy.roll(dxyz[a], 1)
-                abs_shift = numpy.abs(shifts[a])
-                sdxyz.append(roll_dxyz[:-1] * abs_shift + roll_dxyz[1:] * (1 - abs_shift))
-            else:
-                sdxyz.append(dxyz[a][:-1] * (1 - shifts[a]) + dxyz[a][1:] * shifts[a])
-
-        return sdxyz
-
-    def shifted_xyz(self, which_shifts: int | None) -> list[NDArray[numpy.float64]]:
-        """
-        Returns cell centers for `which_shifts`.
-
-        Args:
-            which_shifts: Which grid (which shifts) to use, or `None` for unshifted
-
-        Returns:
-            List of 3 ndarrays of cell centers
-        """
-        if which_shifts is None:
-            return self.xyz
-        exyz = self.shifted_exyz(which_shifts)
-        dxyz = self.shifted_dxyz(which_shifts)
-        return [exyz[a][:-1] + dxyz[a] / 2.0 for a in range(3)]
-
-    def autoshifted_dxyz(self) -> list[NDArray[numpy.float64]]:
-        """
-        Return cell widths, with each dimension shifted by the corresponding shifts.
-
-        Returns:
-            `[grid.shifted_dxyz(which_shifts=a)[a] for a in range(3)]`
-        """
-        if self.num_grids != 3:
-            raise GridError('Autoshifting requires exactly 3 grids')
-        return [self.shifted_dxyz(which_shifts=a)[a] for a in range(3)]
-
-    def allocate(self, fill_value: float | None = 1.0, dtype=numpy.float32) -> NDArray:
-        """
-        Allocate an ndarray for storing grid data.
-
-        Args:
-            fill_value: Value to initialize the grid to. If None, an
-                uninitialized array is returned.
-            dtype: Numpy dtype for the array. Default is `numpy.float32`.
-
-        Returns:
-            The allocated array
-        """
-        if fill_value is None:
-            return numpy.empty(self.cell_data_shape, dtype=dtype)
-        else:
-            return numpy.full(self.cell_data_shape, fill_value, dtype=dtype)
-
     def __init__(
             self,
             pixel_edge_coordinates: Sequence[ArrayLike],
@@ -277,11 +95,12 @@ class Grid:
         Raises:
             `GridError` on invalid input
         """
-        self.exyz = [numpy.unique(pixel_edge_coordinates[i]) for i in range(3)]
+        edge_arrs = [numpy.array(cc, copy=False) for cc in pixel_edge_coordinates]
+        self.exyz = [numpy.unique(edges) for edges in edge_arrs]
         self.shifts = numpy.array(shifts, dtype=float)
 
         for i in range(3):
-            if len(self.exyz[i]) != len(pixel_edge_coordinates[i]):
+            if self.exyz[i].size != edge_arrs[i].size:
                 warnings.warn(f'Dimension {i} had duplicate edge coordinates', stacklevel=2)
 
         if isinstance(periodic, bool):
diff --git a/gridlock/position.py b/gridlock/position.py
index 5928174..b705b99 100644
--- a/gridlock/position.py
+++ b/gridlock/position.py
@@ -5,112 +5,114 @@ import numpy
 from numpy.typing import NDArray, ArrayLike
 
 from . import GridError
+from .base import GridBase
 
 
-def ind2pos(
-        self,
-        ind: NDArray,
-        which_shifts: int | None = None,
-        round_ind: bool = True,
-        check_bounds: bool = True
-        ) -> NDArray[numpy.float64]:
-    """
-    Returns the natural position corresponding to the specified cell center indices.
-     The resulting position is clipped to the bounds of the grid
-    (to cell centers if `round_ind=True`, or cell outer edges if `round_ind=False`)
+class GridPosMixin(GridBase):
+    def ind2pos(
+            self,
+            ind: NDArray,
+            which_shifts: int | None = None,
+            round_ind: bool = True,
+            check_bounds: bool = True
+            ) -> NDArray[numpy.float64]:
+        """
+        Returns the natural position corresponding to the specified cell center indices.
+         The resulting position is clipped to the bounds of the grid
+        (to cell centers if `round_ind=True`, or cell outer edges if `round_ind=False`)
 
-    Args:
-        ind: Indices of the position. Can be fractional. (3-element ndarray or list)
-        which_shifts: which grid number (`shifts`) to use
-        round_ind: Whether to round ind to the nearest integer position before indexing
-            (default `True`)
-        check_bounds: Whether to raise an `GridError` if the provided ind is outside of
-            the grid, as defined above (centers if `round_ind`, else edges) (default `True`)
+        Args:
+            ind: Indices of the position. Can be fractional. (3-element ndarray or list)
+            which_shifts: which grid number (`shifts`) to use
+            round_ind: Whether to round ind to the nearest integer position before indexing
+                (default `True`)
+            check_bounds: Whether to raise an `GridError` if the provided ind is outside of
+                the grid, as defined above (centers if `round_ind`, else edges) (default `True`)
 
-    Returns:
-        3-element ndarray specifying the natural position
+        Returns:
+            3-element ndarray specifying the natural position
 
-    Raises:
-        `GridError` if invalid `which_shifts`
-        `GridError` if `check_bounds` and out of bounds
-    """
-    if which_shifts is not None and which_shifts >= self.shifts.shape[0]:
-        raise GridError('Invalid shifts')
-    ind = numpy.array(ind, dtype=float)
+        Raises:
+            `GridError` if invalid `which_shifts`
+            `GridError` if `check_bounds` and out of bounds
+        """
+        if which_shifts is not None and which_shifts >= self.shifts.shape[0]:
+            raise GridError('Invalid shifts')
+        ind = numpy.array(ind, dtype=float)
+
+        if check_bounds:
+            if round_ind:
+                low_bound = 0.0
+                high_bound = -1.0
+            else:
+                low_bound = -0.5
+                high_bound = -0.5
+            if (ind < low_bound).any() or (ind > self.shape - high_bound).any():
+                raise GridError(f'Position outside of grid: {ind}')
 
-    if check_bounds:
         if round_ind:
-            low_bound = 0.0
-            high_bound = -1.0
+            rind = numpy.clip(numpy.round(ind).astype(int), 0, self.shape - 1)
+            sxyz = self.shifted_xyz(which_shifts)
+            position = [sxyz[a][rind[a]].astype(int) for a in range(3)]
         else:
-            low_bound = -0.5
-            high_bound = -0.5
-        if (ind < low_bound).any() or (ind > self.shape - high_bound).any():
-            raise GridError(f'Position outside of grid: {ind}')
+            sexyz = self.shifted_exyz(which_shifts)
+            position = [numpy.interp(ind[a], numpy.arange(sexyz[a].size) - 0.5, sexyz[a])
+                        for a in range(3)]
+        return numpy.array(position, dtype=float)
+
+
+    def pos2ind(
+            self,
+            r: ArrayLike,
+            which_shifts: int | None,
+            round_ind: bool = True,
+            check_bounds: bool = True
+            ) -> NDArray[numpy.float64]:
+        """
+        Returns the cell-center indices corresponding to the specified natural position.
+             The resulting position is clipped to within the outer centers of the grid.
+
+        Args:
+            r: Natural position that we will convert into indices (3-element ndarray or list)
+            which_shifts: which grid number (`shifts`) to use
+            round_ind: Whether to round the returned indices to the nearest integers.
+            check_bounds: Whether to throw an `GridError` if `r` is outside the grid edges
+
+        Returns:
+            3-element ndarray specifying the indices
+
+        Raises:
+            `GridError` if invalid `which_shifts`
+            `GridError` if `check_bounds` and out of bounds
+        """
+        r = numpy.squeeze(r)
+        if r.size != 3:
+            raise GridError(f'r must be 3-element vector: {r}')
+
+        if (which_shifts is not None) and (which_shifts >= self.shifts.shape[0]):
+            raise GridError(f'Invalid which_shifts: {which_shifts}')
 
-    if round_ind:
-        rind = numpy.clip(numpy.round(ind).astype(int), 0, self.shape - 1)
-        sxyz = self.shifted_xyz(which_shifts)
-        position = [sxyz[a][rind[a]].astype(int) for a in range(3)]
-    else:
         sexyz = self.shifted_exyz(which_shifts)
-        position = [numpy.interp(ind[a], numpy.arange(sexyz[a].size) - 0.5, sexyz[a])
-                    for a in range(3)]
-    return numpy.array(position, dtype=float)
 
+        if check_bounds:
+            for a in range(3):
+                if self.shape[a] > 1 and (r[a] < sexyz[a][0] or r[a] > sexyz[a][-1]):
+                    raise GridError(f'Position[{a}] outside of grid!')
 
-def pos2ind(
-        self,
-        r: ArrayLike,
-        which_shifts: int | None,
-        round_ind: bool = True,
-        check_bounds: bool = True
-        ) -> NDArray[numpy.float64]:
-    """
-    Returns the cell-center indices corresponding to the specified natural position.
-         The resulting position is clipped to within the outer centers of the grid.
-
-    Args:
-        r: Natural position that we will convert into indices (3-element ndarray or list)
-        which_shifts: which grid number (`shifts`) to use
-        round_ind: Whether to round the returned indices to the nearest integers.
-        check_bounds: Whether to throw an `GridError` if `r` is outside the grid edges
-
-    Returns:
-        3-element ndarray specifying the indices
-
-    Raises:
-        `GridError` if invalid `which_shifts`
-        `GridError` if `check_bounds` and out of bounds
-    """
-    r = numpy.squeeze(r)
-    if r.size != 3:
-        raise GridError(f'r must be 3-element vector: {r}')
-
-    if (which_shifts is not None) and (which_shifts >= self.shifts.shape[0]):
-        raise GridError(f'Invalid which_shifts: {which_shifts}')
-
-    sexyz = self.shifted_exyz(which_shifts)
-
-    if check_bounds:
+        grid_pos = numpy.zeros((3,))
         for a in range(3):
-            if self.shape[a] > 1 and (r[a] < sexyz[a][0] or r[a] > sexyz[a][-1]):
-                raise GridError(f'Position[{a}] outside of grid!')
+            xi = numpy.digitize(r[a], sexyz[a]) - 1  # Figure out which cell we're in
+            xi_clipped = numpy.clip(xi, 0, sexyz[a].size - 2)  # Clip back into grid bounds
 
-    grid_pos = numpy.zeros((3,))
-    for a in range(3):
-        xi = numpy.digitize(r[a], sexyz[a]) - 1  # Figure out which cell we're in
-        xi_clipped = numpy.clip(xi, 0, sexyz[a].size - 2)  # Clip back into grid bounds
+            # No need to interpolate if round_ind is true or we were outside the grid
+            if round_ind or xi != xi_clipped:
+                grid_pos[a] = xi_clipped
+            else:
+                # Interpolate
+                x = self.shifted_xyz(which_shifts)[a][xi]
+                dx = self.shifted_dxyz(which_shifts)[a][xi]
+                f = (r[a] - x) / dx
 
-        # No need to interpolate if round_ind is true or we were outside the grid
-        if round_ind or xi != xi_clipped:
-            grid_pos[a] = xi_clipped
-        else:
-            # Interpolate
-            x = self.shifted_xyz(which_shifts)[a][xi]
-            dx = self.shifted_dxyz(which_shifts)[a][xi]
-            f = (r[a] - x) / dx
-
-            # Clip to centers
-            grid_pos[a] = numpy.clip(xi + f, 0, self.shape[a] - 1)
-    return grid_pos
+                # Clip to centers
+                grid_pos[a] = numpy.clip(xi + f, 0, self.shape[a] - 1)
+        return grid_pos
diff --git a/gridlock/read.py b/gridlock/read.py
index 31b583d..e82ffcc 100644
--- a/gridlock/read.py
+++ b/gridlock/read.py
@@ -7,6 +7,8 @@ import numpy
 from numpy.typing import NDArray
 
 from . import GridError
+from .base import GridBase
+from .position import GridPosMixin
 
 if TYPE_CHECKING:
     import matplotlib.axes
@@ -18,186 +20,187 @@ if TYPE_CHECKING:
 # .visualize_isosurface uses mpl_toolkits.mplot3d
 
 
-def get_slice(
-        self,
-        cell_data: NDArray,
-        surface_normal: int,
-        center: float,
-        which_shifts: int = 0,
-        sample_period: int = 1
-        ) -> NDArray:
-    """
-    Retrieve a slice of a grid.
-    Interpolates if given a position between two planes.
+class GridReadMixin(GridPosMixin):
+    def get_slice(
+            self,
+            cell_data: NDArray,
+            surface_normal: int,
+            center: float,
+            which_shifts: int = 0,
+            sample_period: int = 1
+            ) -> NDArray:
+        """
+        Retrieve a slice of a grid.
+        Interpolates if given a position between two planes.
 
-    Args:
-        cell_data: Cell data to slice
-        surface_normal: Axis normal to the plane we're displaying. Integer in `range(3)`.
-        center: Scalar specifying position along surface_normal axis.
-        which_shifts: Which grid to display. Default is the first grid (0).
-        sample_period: Period for down-sampling the image. Default 1 (disabled)
+        Args:
+            cell_data: Cell data to slice
+            surface_normal: Axis normal to the plane we're displaying. Integer in `range(3)`.
+            center: Scalar specifying position along surface_normal axis.
+            which_shifts: Which grid to display. Default is the first grid (0).
+            sample_period: Period for down-sampling the image. Default 1 (disabled)
 
-    Returns:
-        Array containing the portion of the grid.
-    """
-    if numpy.size(center) != 1 or not numpy.isreal(center):
-        raise GridError('center must be a real scalar')
+        Returns:
+            Array containing the portion of the grid.
+        """
+        if numpy.size(center) != 1 or not numpy.isreal(center):
+            raise GridError('center must be a real scalar')
 
-    sp = round(sample_period)
-    if sp <= 0:
-        raise GridError('sample_period must be positive')
+        sp = round(sample_period)
+        if sp <= 0:
+            raise GridError('sample_period must be positive')
 
-    if numpy.size(which_shifts) != 1 or which_shifts < 0:
-        raise GridError('Invalid which_shifts')
+        if numpy.size(which_shifts) != 1 or which_shifts < 0:
+            raise GridError('Invalid which_shifts')
 
-    if surface_normal not in range(3):
-        raise GridError('Invalid surface_normal direction')
+        if surface_normal not in range(3):
+            raise GridError('Invalid surface_normal direction')
 
-    surface = numpy.delete(range(3), surface_normal)
+        surface = numpy.delete(range(3), surface_normal)
 
-    # Extract indices and weights of planes
-    center3 = numpy.insert([0, 0], surface_normal, (center,))
-    center_index = self.pos2ind(center3, which_shifts,
-                                round_ind=False, check_bounds=False)[surface_normal]
-    centers = numpy.unique([numpy.floor(center_index), numpy.ceil(center_index)]).astype(int)
-    if len(centers) == 2:
-        fpart = center_index - numpy.floor(center_index)
-        w = [1 - fpart, fpart]  # longer distance -> less weight
-    else:
-        w = [1]
+        # Extract indices and weights of planes
+        center3 = numpy.insert([0, 0], surface_normal, (center,))
+        center_index = self.pos2ind(center3, which_shifts,
+                                    round_ind=False, check_bounds=False)[surface_normal]
+        centers = numpy.unique([numpy.floor(center_index), numpy.ceil(center_index)]).astype(int)
+        if len(centers) == 2:
+            fpart = center_index - numpy.floor(center_index)
+            w = [1 - fpart, fpart]  # longer distance -> less weight
+        else:
+            w = [1]
 
-    c_min, c_max = (self.xyz[surface_normal][i] for i in [0, -1])
-    if center < c_min or center > c_max:
-        raise GridError('Coordinate of selected plane must be within simulation domain')
+        c_min, c_max = (self.xyz[surface_normal][i] for i in [0, -1])
+        if center < c_min or center > c_max:
+            raise GridError('Coordinate of selected plane must be within simulation domain')
 
-    # Extract grid values from planes above and below visualized slice
-    sliced_grid = numpy.zeros(self.shape[surface])
-    for ci, weight in zip(centers, w, strict=True):
-        s = tuple(ci if a == surface_normal else numpy.s_[::sp] for a in range(3))
-        sliced_grid += weight * cell_data[which_shifts][tuple(s)]
+        # Extract grid values from planes above and below visualized slice
+        sliced_grid = numpy.zeros(self.shape[surface])
+        for ci, weight in zip(centers, w, strict=True):
+            s = tuple(ci if a == surface_normal else numpy.s_[::sp] for a in range(3))
+            sliced_grid += weight * cell_data[which_shifts][tuple(s)]
 
-    # Remove extra dimensions
-    sliced_grid = numpy.squeeze(sliced_grid)
+        # Remove extra dimensions
+        sliced_grid = numpy.squeeze(sliced_grid)
 
-    return sliced_grid
+        return sliced_grid
 
 
-def visualize_slice(
-        self,
-        cell_data: NDArray,
-        surface_normal: int,
-        center: float,
-        which_shifts: int = 0,
-        sample_period: int = 1,
-        finalize: bool = True,
-        pcolormesh_args: dict[str, Any] | None = None,
-        ) -> tuple['matplotlib.axes.Axes', 'matplotlib.figure.Figure']:
-    """
-    Visualize a slice of a grid.
-    Interpolates if given a position between two planes.
+    def visualize_slice(
+            self,
+            cell_data: NDArray,
+            surface_normal: int,
+            center: float,
+            which_shifts: int = 0,
+            sample_period: int = 1,
+            finalize: bool = True,
+            pcolormesh_args: dict[str, Any] | None = None,
+            ) -> tuple['matplotlib.axes.Axes', 'matplotlib.figure.Figure']:
+        """
+        Visualize a slice of a grid.
+        Interpolates if given a position between two planes.
 
-    Args:
-        surface_normal: Axis normal to the plane we're displaying. Integer in `range(3)`.
-        center: Scalar specifying position along surface_normal axis.
-        which_shifts: Which grid to display. Default is the first grid (0).
-        sample_period: Period for down-sampling the image. Default 1 (disabled)
-        finalize: Whether to call `pyplot.show()` after constructing the plot. Default `True`
+        Args:
+            surface_normal: Axis normal to the plane we're displaying. Integer in `range(3)`.
+            center: Scalar specifying position along surface_normal axis.
+            which_shifts: Which grid to display. Default is the first grid (0).
+            sample_period: Period for down-sampling the image. Default 1 (disabled)
+            finalize: Whether to call `pyplot.show()` after constructing the plot. Default `True`
 
-    Returns:
-        (Figure, Axes)
-    """
-    from matplotlib import pyplot
+        Returns:
+            (Figure, Axes)
+        """
+        from matplotlib import pyplot
 
-    if pcolormesh_args is None:
-        pcolormesh_args = {}
+        if pcolormesh_args is None:
+            pcolormesh_args = {}
 
-    grid_slice = self.get_slice(cell_data=cell_data,
-                                surface_normal=surface_normal,
-                                center=center,
-                                which_shifts=which_shifts,
-                                sample_period=sample_period)
+        grid_slice = self.get_slice(cell_data=cell_data,
+                                    surface_normal=surface_normal,
+                                    center=center,
+                                    which_shifts=which_shifts,
+                                    sample_period=sample_period)
 
-    surface = numpy.delete(range(3), surface_normal)
+        surface = numpy.delete(range(3), surface_normal)
 
-    x, y = (self.shifted_exyz(which_shifts)[a] for a in surface)
-    xmesh, ymesh = numpy.meshgrid(x, y, indexing='ij')
-    x_label, y_label = ('xyz'[a] for a in surface)
+        x, y = (self.shifted_exyz(which_shifts)[a] for a in surface)
+        xmesh, ymesh = numpy.meshgrid(x, y, indexing='ij')
+        x_label, y_label = ('xyz'[a] for a in surface)
 
-    fig, ax = pyplot.subplots()
-    mappable = ax.pcolormesh(xmesh, ymesh, grid_slice, **pcolormesh_args)
-    fig.colorbar(mappable)
-    ax.set_aspect('equal', adjustable='box')
-    ax.set_xlabel(x_label)
-    ax.set_ylabel(y_label)
-    if finalize:
-        pyplot.show()
+        fig, ax = pyplot.subplots()
+        mappable = ax.pcolormesh(xmesh, ymesh, grid_slice, **pcolormesh_args)
+        fig.colorbar(mappable)
+        ax.set_aspect('equal', adjustable='box')
+        ax.set_xlabel(x_label)
+        ax.set_ylabel(y_label)
+        if finalize:
+            pyplot.show()
 
-    return fig, ax
+        return fig, ax
 
 
-def visualize_isosurface(
-        self,
-        cell_data: NDArray,
-        level: float | None = None,
-        which_shifts: int = 0,
-        sample_period: int = 1,
-        show_edges: bool = True,
-        finalize: bool = True,
-        ) -> tuple['matplotlib.axes.Axes', 'matplotlib.figure.Figure']:
-    """
-    Draw an isosurface plot of the device.
+    def visualize_isosurface(
+            self,
+            cell_data: NDArray,
+            level: float | None = None,
+            which_shifts: int = 0,
+            sample_period: int = 1,
+            show_edges: bool = True,
+            finalize: bool = True,
+            ) -> tuple['matplotlib.axes.Axes', 'matplotlib.figure.Figure']:
+        """
+        Draw an isosurface plot of the device.
 
-    Args:
-        cell_data: Cell data to visualize
-        level: Value at which to find isosurface. Default (None) uses mean value in grid.
-        which_shifts: Which grid to display. Default is the first grid (0).
-        sample_period: Period for down-sampling the image. Default 1 (disabled)
-        show_edges: Whether to draw triangle edges. Default `True`
-        finalize: Whether to call `pyplot.show()` after constructing the plot. Default `True`
+        Args:
+            cell_data: Cell data to visualize
+            level: Value at which to find isosurface. Default (None) uses mean value in grid.
+            which_shifts: Which grid to display. Default is the first grid (0).
+            sample_period: Period for down-sampling the image. Default 1 (disabled)
+            show_edges: Whether to draw triangle edges. Default `True`
+            finalize: Whether to call `pyplot.show()` after constructing the plot. Default `True`
 
-    Returns:
-        (Figure, Axes)
-    """
-    from matplotlib import pyplot
-    import skimage.measure
-    # Claims to be unused, but needed for subplot(projection='3d')
-    from mpl_toolkits.mplot3d import Axes3D
-    del Axes3D      # imported for side effects only
+        Returns:
+            (Figure, Axes)
+        """
+        from matplotlib import pyplot
+        import skimage.measure
+        # Claims to be unused, but needed for subplot(projection='3d')
+        from mpl_toolkits.mplot3d import Axes3D
+        del Axes3D      # imported for side effects only
 
-    # Get data from cell_data
-    grid = cell_data[which_shifts][::sample_period, ::sample_period, ::sample_period]
-    if level is None:
-        level = grid.mean()
+        # Get data from cell_data
+        grid = cell_data[which_shifts][::sample_period, ::sample_period, ::sample_period]
+        if level is None:
+            level = grid.mean()
 
-    # Find isosurface with marching cubes
-    verts, faces, _normals, _values = skimage.measure.marching_cubes(grid, level)
+        # Find isosurface with marching cubes
+        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)
-    xs, ys, zs = (pos_verts[:, a] for a in range(3))
+        # 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)
+        xs, ys, zs = (pos_verts[:, a] for a in range(3))
 
-    # Draw the plot
-    fig = pyplot.figure()
-    ax = fig.add_subplot(111, projection='3d')
-    if show_edges:
-        ax.plot_trisurf(xs, ys, faces, zs)
-    else:
-        ax.plot_trisurf(xs, ys, faces, zs, edgecolor='none')
+        # Draw the plot
+        fig = pyplot.figure()
+        ax = fig.add_subplot(111, projection='3d')
+        if show_edges:
+            ax.plot_trisurf(xs, ys, faces, zs)
+        else:
+            ax.plot_trisurf(xs, ys, faces, zs, edgecolor='none')
 
-    # Add a fake plot of a cube to force the axes to be equal lengths
-    max_range = numpy.array([xs.max() - xs.min(),
-                             ys.max() - ys.min(),
-                             zs.max() - zs.min()], dtype=float).max()
-    mg = numpy.mgrid[-1:2:2, -1:2:2, -1:2:2]
-    xbs = 0.5 * max_range * mg[0].flatten() + 0.5 * (xs.max() + xs.min())
-    ybs = 0.5 * max_range * mg[1].flatten() + 0.5 * (ys.max() + ys.min())
-    zbs = 0.5 * max_range * mg[2].flatten() + 0.5 * (zs.max() + zs.min())
-    # Comment or uncomment following both lines to test the fake bounding box:
-    for xb, yb, zb in zip(xbs, ybs, zbs, strict=True):
-        ax.plot([xb], [yb], [zb], 'w')
+        # Add a fake plot of a cube to force the axes to be equal lengths
+        max_range = numpy.array([xs.max() - xs.min(),
+                                 ys.max() - ys.min(),
+                                 zs.max() - zs.min()], dtype=float).max()
+        mg = numpy.mgrid[-1:2:2, -1:2:2, -1:2:2]
+        xbs = 0.5 * max_range * mg[0].flatten() + 0.5 * (xs.max() + xs.min())
+        ybs = 0.5 * max_range * mg[1].flatten() + 0.5 * (ys.max() + ys.min())
+        zbs = 0.5 * max_range * mg[2].flatten() + 0.5 * (zs.max() + zs.min())
+        # Comment or uncomment following both lines to test the fake bounding box:
+        for xb, yb, zb in zip(xbs, ybs, zbs, strict=True):
+            ax.plot([xb], [yb], [zb], 'w')
 
-    if finalize:
-        pyplot.show()
+        if finalize:
+            pyplot.show()
 
-    return fig, ax
+        return fig, ax