diff --git a/autoarray/structures/triangles/abstract.py b/autoarray/structures/triangles/abstract.py
index 463d1017..c0efd2fe 100644
--- a/autoarray/structures/triangles/abstract.py
+++ b/autoarray/structures/triangles/abstract.py
@@ -252,7 +252,7 @@ def containing_indices(self, shape: Shape) -> np.ndarray:
 
         Returns
         -------
-        The triangles that intersect the shape.
+        The indices of triangles that intersect the shape.
         """
 
     @abstractmethod
diff --git a/autoarray/structures/triangles/abstract_coordinate_array.py b/autoarray/structures/triangles/abstract_coordinate_array.py
index 0a5a36b2..72267275 100644
--- a/autoarray/structures/triangles/abstract_coordinate_array.py
+++ b/autoarray/structures/triangles/abstract_coordinate_array.py
@@ -10,7 +10,7 @@ class AbstractCoordinateArray(ABC):
     def __init__(
         self,
         coordinates: np.ndarray,
-        side_length: float,
+        side_length: float = 1.0,
         x_offset: float = 0.0,
         y_offset: float = 0.0,
         flipped: bool = False,
@@ -140,23 +140,18 @@ def for_limits_and_scale(
         scale: float = 1.0,
         **_,
     ):
+        x_shift = int(2 * x_min / scale)
+        y_shift = int(y_min / (HEIGHT_FACTOR * scale))
+
         coordinates = []
-        x = x_min
-        while x < x_max:
-            y = y_min
-            while y < y_max:
-                coordinates.append([x, y])
-                y += scale
-            x += scale
 
-        x_mean = (x_min + x_max) / 2
-        y_mean = (y_min + y_max) / 2
+        for x in range(x_shift, int(2 * x_max / scale) + 1):
+            for y in range(y_shift - 1, int(y_max / (HEIGHT_FACTOR * scale)) + 2):
+                coordinates.append([x, y])
 
         return cls(
             coordinates=np.array(coordinates),
             side_length=scale,
-            x_offset=x_mean,
-            y_offset=y_mean,
         )
 
     @property
diff --git a/autoarray/structures/triangles/coordinate_array.py b/autoarray/structures/triangles/coordinate_array.py
index e45f3eed..9551885e 100644
--- a/autoarray/structures/triangles/coordinate_array.py
+++ b/autoarray/structures/triangles/coordinate_array.py
@@ -5,6 +5,7 @@
     AbstractCoordinateArray,
 )
 from autoarray.structures.triangles.array import ArrayTriangles
+from autoarray.structures.triangles.shape import Shape
 from autoconf import cached_property
 
 
@@ -88,7 +89,9 @@ def neighborhood(self) -> "CoordinateArrayTriangles":
     def _vertices_and_indices(self):
         flat_triangles = self.triangles.reshape(-1, 2)
         vertices, inverse_indices = np.unique(
-            flat_triangles, axis=0, return_inverse=True
+            flat_triangles,
+            axis=0,
+            return_inverse=True,
         )
         indices = inverse_indices.reshape(-1, 3)
         return vertices, indices
@@ -131,3 +134,18 @@ def for_indexes(self, indexes: np.ndarray) -> "CoordinateArrayTriangles":
             x_offset=self.x_offset,
             flipped=self.flipped,
         )
+
+    def containing_indices(self, shape: Shape) -> np.ndarray:
+        """
+        Find the triangles that insect with a given shape.
+
+        Parameters
+        ----------
+        shape
+            The shape
+
+        Returns
+        -------
+        The indices of triangles that intersect the shape.
+        """
+        return self.with_vertices(self.vertices).containing_indices(shape)
diff --git a/autoarray/structures/triangles/jax_coordinate_array.py b/autoarray/structures/triangles/jax_coordinate_array.py
index ce3e9e0d..2e1dd3c0 100644
--- a/autoarray/structures/triangles/jax_coordinate_array.py
+++ b/autoarray/structures/triangles/jax_coordinate_array.py
@@ -146,6 +146,8 @@ def _vertices_and_indices(self):
             axis=0,
             return_inverse=True,
             size=3 * self.coordinates.shape[0],
+            equal_nan=True,
+            fill_value=np.nan,
         )
         indices = inverse_indices.reshape(-1, 3)
         return vertices, indices
diff --git a/test_autoarray/structures/triangles/test_coordinate_implementation.py b/test_autoarray/structures/triangles/test_coordinate_implementation.py
index d7c7a338..96b040b2 100644
--- a/test_autoarray/structures/triangles/test_coordinate_implementation.py
+++ b/test_autoarray/structures/triangles/test_coordinate_implementation.py
@@ -4,6 +4,7 @@
 
 from autoarray.structures.triangles.abstract import HEIGHT_FACTOR
 from autoarray.structures.triangles.coordinate_array import CoordinateArrayTriangles
+from autoarray.structures.triangles.shape import Point
 
 
 @pytest.fixture
@@ -269,3 +270,47 @@ def test_for_limits_and_scale():
 
 def test_means(one_triangle):
     assert np.all(one_triangle.means == [[0.0, -0.14433756729740643]])
+
+
+@pytest.mark.parametrize(
+    "x, y",
+    [
+        (0.0, 0.0),
+        (-0.5, -HEIGHT_FACTOR / 2),
+        (0.5, -HEIGHT_FACTOR / 2),
+        (0.0, HEIGHT_FACTOR / 2),
+    ],
+)
+def test_containment(one_triangle, x, y):
+    assert one_triangle.containing_indices(Point(x, y)) == [0]
+
+
+def test_triangles_touch():
+    triangles = CoordinateArrayTriangles(
+        np.array([[0, 0], [2, 0]]),
+    )
+
+    assert max(triangles.triangles[0][:, 0]) == min(triangles.triangles[1][:, 0])
+
+    triangles = CoordinateArrayTriangles(
+        np.array([[0, 0], [0, 1]]),
+    )
+    assert max(triangles.triangles[0][:, 1]) == min(triangles.triangles[1][:, 1])
+
+
+def test_from_grid_regression():
+    triangles = CoordinateArrayTriangles.for_limits_and_scale(
+        x_min=-4.75,
+        x_max=4.75,
+        y_min=-4.75,
+        y_max=4.75,
+        scale=0.5,
+    )
+
+    x = triangles.vertices[:, 0]
+    assert min(x) <= -4.75
+    assert max(x) >= 4.75
+
+    y = triangles.vertices[:, 1]
+    assert min(y) <= -4.75
+    assert max(y) >= 4.75