diff --git a/masque/builder/utils.py b/masque/builder/utils.py
index 5680694..4de6dbb 100644
--- a/masque/builder/utils.py
+++ b/masque/builder/utils.py
@@ -84,7 +84,7 @@ def ell(
         raise BuildError('Empty port list passed to `ell()`')
 
     if ccw is None:
-        if spacing is not None and not numpy.isclose(spacing, 0):
+        if spacing is not None and not numpy.allclose(spacing, 0):
             raise BuildError('Spacing must be 0 or None when ccw=None')
         spacing = 0
     elif spacing is None:
@@ -132,8 +132,17 @@ def ell(
     if spacing is None:
         ch_offsets = numpy.zeros_like(y_order)
     else:
+        spacing_arr = numpy.asarray(spacing, dtype=float).reshape(-1)
         steps = numpy.zeros_like(y_order)
-        steps[1:] = spacing
+        if spacing_arr.size == 1:
+            steps[1:] = spacing_arr[0]
+        elif spacing_arr.size == len(ports) - 1:
+            steps[1:] = spacing_arr
+        else:
+            raise BuildError(
+                f'spacing must be scalar or have length {len(ports) - 1} for {len(ports)} ports; '
+                f'got length {spacing_arr.size}'
+                )
         ch_offsets = numpy.cumsum(steps)[y_ind]
 
     x_start = rot_offsets[:, 0]
diff --git a/masque/test/test_boolean.py b/masque/test/test_boolean.py
index bf5d33d..1e44e4d 100644
--- a/masque/test/test_boolean.py
+++ b/masque/test/test_boolean.py
@@ -6,6 +6,14 @@ from masque.pattern import Pattern
 from masque.shapes.polygon import Polygon
 from masque.repetition import Grid
 from masque.library import Library
+from masque.error import PatternError
+
+
+def _poly_area(poly: Polygon) -> float:
+    verts = poly.vertices
+    x = verts[:, 0]
+    y = verts[:, 1]
+    return 0.5 * abs(numpy.dot(x, numpy.roll(y, -1)) - numpy.dot(y, numpy.roll(x, -1)))
 
 def test_layer_as_polygons_basic() -> None:
     pat = Pattern()
@@ -69,6 +77,176 @@ def test_polygon_boolean_shortcut() -> None:
         with pytest.raises(ImportError, match="Boolean operations require 'pyclipper'"):
             poly.boolean(poly)
 
+
+def test_boolean_intersection_with_pyclipper() -> None:
+    pytest.importorskip("pyclipper")
+    from masque.utils.boolean import boolean
+
+    result = boolean(
+        [Polygon([[0, 0], [2, 0], [2, 2], [0, 2]])],
+        [Polygon([[1, 1], [3, 1], [3, 3], [1, 3]])],
+        operation='intersection',
+    )
+
+    assert len(result) == 1
+    assert_allclose(result[0].get_bounds_single(), [[1, 1], [2, 2]], atol=1e-10)
+
+
+def test_polygon_boolean_shortcut_with_pyclipper() -> None:
+    pytest.importorskip("pyclipper")
+
+    poly = Polygon([[0, 0], [2, 0], [2, 2], [0, 2]])
+    result = poly.boolean(
+        Polygon([[1, 1], [3, 1], [3, 3], [1, 3]]),
+        operation='intersection',
+    )
+
+    assert len(result) == 1
+    assert_allclose(result[0].get_bounds_single(), [[1, 1], [2, 2]], atol=1e-10)
+
+
+def test_boolean_union_difference_and_xor_with_pyclipper() -> None:
+    pytest.importorskip("pyclipper")
+    from masque.utils.boolean import boolean
+
+    rect_a = Polygon([[0, 0], [2, 0], [2, 2], [0, 2]])
+    rect_b = Polygon([[1, 1], [3, 1], [3, 3], [1, 3]])
+
+    union = boolean([rect_a], [rect_b], operation='union')
+    assert len(union) == 1
+    assert_allclose(union[0].get_bounds_single(), [[0, 0], [3, 3]], atol=1e-10)
+    assert_allclose(_poly_area(union[0]), 7, atol=1e-10)
+
+    difference = boolean([rect_a], [rect_b], operation='difference')
+    assert len(difference) == 1
+    assert_allclose(difference[0].get_bounds_single(), [[0, 0], [2, 2]], atol=1e-10)
+    assert_allclose(_poly_area(difference[0]), 3, atol=1e-10)
+
+    xor = boolean([rect_a], [rect_b], operation='xor')
+    assert len(xor) == 2
+    assert_allclose(sorted(_poly_area(poly) for poly in xor), [3, 3], atol=1e-10)
+    xor_bounds = sorted(tuple(map(tuple, poly.get_bounds_single())) for poly in xor)
+    assert xor_bounds == [((0.0, 0.0), (2.0, 2.0)), ((1.0, 1.0), (3.0, 3.0))]
+
+
+def test_boolean_accepts_raw_vertices_and_single_shape_inputs() -> None:
+    pytest.importorskip("pyclipper")
+    from masque.utils.boolean import boolean
+
+    raw_result = boolean(
+        [numpy.array([[0, 0], [2, 0], [2, 2], [0, 2]])],
+        numpy.array([[1, 1], [3, 1], [3, 3], [1, 3]]),
+        operation='intersection',
+    )
+    assert len(raw_result) == 1
+    assert_allclose(raw_result[0].get_bounds_single(), [[1, 1], [2, 2]], atol=1e-10)
+    assert_allclose(_poly_area(raw_result[0]), 1, atol=1e-10)
+
+    single_shape_result = boolean(
+        Polygon([[0, 0], [2, 0], [2, 2], [0, 2]]),
+        Polygon([[1, 1], [3, 1], [3, 3], [1, 3]]),
+        operation='intersection',
+    )
+    assert len(single_shape_result) == 1
+    assert_allclose(single_shape_result[0].get_bounds_single(), [[1, 1], [2, 2]], atol=1e-10)
+
+
+def test_boolean_handles_multi_polygon_inputs() -> None:
+    pytest.importorskip("pyclipper")
+    from masque.utils.boolean import boolean
+
+    result = boolean(
+        [
+            Polygon([[0, 0], [2, 0], [2, 2], [0, 2]]),
+            Polygon([[10, 0], [12, 0], [12, 2], [10, 2]]),
+        ],
+        [
+            Polygon([[1, 1], [3, 1], [3, 3], [1, 3]]),
+            Polygon([[11, 1], [13, 1], [13, 3], [11, 3]]),
+        ],
+        operation='intersection',
+    )
+    assert len(result) == 2
+    assert_allclose(sorted(_poly_area(poly) for poly in result), [1, 1], atol=1e-10)
+    result_bounds = sorted(tuple(map(tuple, poly.get_bounds_single())) for poly in result)
+    assert result_bounds == [((1.0, 1.0), (2.0, 2.0)), ((11.0, 1.0), (12.0, 2.0))]
+
+
+def test_boolean_difference_preserves_hole_area_via_bridged_polygon() -> None:
+    pytest.importorskip("pyclipper")
+    from masque.utils.boolean import boolean
+
+    outer = Polygon([[0, 0], [10, 0], [10, 10], [0, 10]])
+    hole = Polygon([[2, 2], [8, 2], [8, 8], [2, 8]])
+    result = boolean([outer], [hole], operation='difference')
+
+    assert len(result) == 1
+    assert_allclose(result[0].get_bounds_single(), [[0, 0], [10, 10]], atol=1e-10)
+    assert_allclose(_poly_area(result[0]), 64, atol=1e-10)
+
+
+def test_boolean_nested_hole_and_island_case() -> None:
+    pytest.importorskip("pyclipper")
+    from masque.utils.boolean import boolean
+
+    outer = Polygon([[0, 0], [10, 0], [10, 10], [0, 10]])
+    hole = Polygon([[2, 2], [8, 2], [8, 8], [2, 8]])
+    island = Polygon([[4, 4], [6, 4], [6, 6], [4, 6]])
+
+    result = boolean([outer, island], [hole], operation='union')
+
+    assert len(result) == 1
+    assert_allclose(result[0].get_bounds_single(), [[0, 0], [10, 10]], atol=1e-10)
+    assert_allclose(_poly_area(result[0]), 100, atol=1e-10)
+
+
+def test_boolean_empty_inputs_follow_set_semantics() -> None:
+    pytest.importorskip("pyclipper")
+    from masque.utils.boolean import boolean
+
+    rect = Polygon([[1, 1], [3, 1], [3, 3], [1, 3]])
+
+    union = boolean([], [rect], operation='union')
+    assert len(union) == 1
+    assert_allclose(union[0].get_bounds_single(), [[1, 1], [3, 3]], atol=1e-10)
+
+    intersection = boolean([], [rect], operation='intersection')
+    assert intersection == []
+
+    difference = boolean([], [rect], operation='difference')
+    assert difference == []
+
+    xor = boolean([], [rect], operation='xor')
+    assert len(xor) == 1
+    assert_allclose(xor[0].get_bounds_single(), [[1, 1], [3, 3]], atol=1e-10)
+
+    clip_empty_union = boolean([rect], [], operation='union')
+    assert len(clip_empty_union) == 1
+    assert_allclose(clip_empty_union[0].get_bounds_single(), [[1, 1], [3, 3]], atol=1e-10)
+
+    clip_empty_intersection = boolean([rect], [], operation='intersection')
+    assert clip_empty_intersection == []
+
+    clip_empty_difference = boolean([rect], [], operation='difference')
+    assert len(clip_empty_difference) == 1
+    assert_allclose(clip_empty_difference[0].get_bounds_single(), [[1, 1], [3, 3]], atol=1e-10)
+
+    clip_empty_xor = boolean([rect], [], operation='xor')
+    assert len(clip_empty_xor) == 1
+    assert_allclose(clip_empty_xor[0].get_bounds_single(), [[1, 1], [3, 3]], atol=1e-10)
+
+
+def test_boolean_invalid_inputs_raise_pattern_error() -> None:
+    pytest.importorskip("pyclipper")
+    from masque.utils.boolean import boolean
+
+    rect = Polygon([[0, 0], [1, 0], [1, 1], [0, 1]])
+
+    for bad in (123, object(), [123]):
+        with pytest.raises(PatternError, match='Unsupported type'):
+            boolean([rect], bad, operation='intersection')
+
+
 def test_bridge_holes() -> None:
     from masque.utils.boolean import _bridge_holes
 
diff --git a/masque/test/test_builder.py b/masque/test/test_builder.py
index 0ad6e80..309dab6 100644
--- a/masque/test/test_builder.py
+++ b/masque/test/test_builder.py
@@ -1,7 +1,11 @@
+import numpy
+import pytest
 from numpy.testing import assert_equal, assert_allclose
 from numpy import pi
 
 from ..builder import Builder
+from ..builder.utils import ell
+from ..error import BuildError
 from ..library import Library
 from ..pattern import Pattern
 from ..ports import Port
@@ -129,3 +133,31 @@ def test_dead_plug_best_effort() -> None:
     # P2 rot pi + transform rot -pi = 0
     assert b.ports['B'].rotation is not None
     assert_allclose(b.ports['B'].rotation, 0, atol=1e-10)
+
+
+def test_ell_validates_spacing_length() -> None:
+    ports = {
+        'A': Port((0, 0), 0),
+        'B': Port((0, 1), 0),
+        'C': Port((0, 2), 0),
+    }
+
+    with pytest.raises(BuildError, match='spacing must be scalar or have length 2'):
+        ell(ports, True, 'min_extension', 5, spacing=[1, 2, 3])
+
+    with pytest.raises(BuildError, match='spacing must be scalar or have length 2'):
+        ell(ports, True, 'min_extension', 5, spacing=[])
+
+
+def test_ell_handles_array_spacing_when_ccw_none() -> None:
+    ports = {
+        'A': Port((0, 0), 0),
+        'B': Port((0, 1), 0),
+    }
+
+    scalar = ell(ports, None, 'min_extension', 5, spacing=0)
+    array_zero = ell(ports, None, 'min_extension', 5, spacing=numpy.array([0, 0]))
+    assert scalar == array_zero
+
+    with pytest.raises(BuildError, match='Spacing must be 0 or None'):
+        ell(ports, None, 'min_extension', 5, spacing=numpy.array([1, 0]))
diff --git a/masque/test/test_utils.py b/masque/test/test_utils.py
index 0511a24..ddab9cd 100644
--- a/masque/test/test_utils.py
+++ b/masque/test/test_utils.py
@@ -5,7 +5,7 @@ from numpy.testing import assert_equal, assert_allclose
 from numpy import pi
 import pytest
 
-from ..utils import remove_duplicate_vertices, remove_colinear_vertices, poly_contains_points, rotation_matrix_2d, apply_transforms, DeferredDict
+from ..utils import remove_duplicate_vertices, remove_colinear_vertices, poly_contains_points, rotation_matrix_2d, apply_transforms, normalize_mirror, DeferredDict
 from ..file.utils import tmpfile
 from ..utils.curves import bezier
 from ..error import PatternError
@@ -94,6 +94,28 @@ def test_apply_transforms_advanced() -> None:
     assert_allclose(combined[0], [0, 10, pi / 2, 1, 1], atol=1e-10)
 
 
+def test_apply_transforms_empty_inputs() -> None:
+    empty_outer = apply_transforms(numpy.empty((0, 5)), [[1, 2, 0, 0, 1]])
+    assert empty_outer.shape == (0, 5)
+
+    empty_inner = apply_transforms([[1, 2, 0, 0, 1]], numpy.empty((0, 5)))
+    assert empty_inner.shape == (0, 5)
+
+    both_empty_tensor = apply_transforms(numpy.empty((0, 5)), numpy.empty((0, 5)), tensor=True)
+    assert both_empty_tensor.shape == (0, 0, 5)
+
+
+def test_normalize_mirror_validates_length() -> None:
+    with pytest.raises(ValueError, match='2-item sequence'):
+        normalize_mirror(())
+
+    with pytest.raises(ValueError, match='2-item sequence'):
+        normalize_mirror((True,))
+
+    with pytest.raises(ValueError, match='2-item sequence'):
+        normalize_mirror((True, False, True))
+
+
 def test_bezier_validates_weight_length() -> None:
     with pytest.raises(PatternError, match='one entry per control point'):
         bezier([[0, 0], [1, 1]], [0, 0.5, 1], weights=[1])
diff --git a/masque/utils/boolean.py b/masque/utils/boolean.py
index 78c24e2..5181fc5 100644
--- a/masque/utils/boolean.py
+++ b/masque/utils/boolean.py
@@ -106,15 +106,19 @@ def boolean(
         ) from None
 
     op_map = {
-        'union': pyclipper.PT_UNION,
-        'intersection': pyclipper.PT_INTERSECTION,
-        'difference': pyclipper.PT_DIFFERENCE,
-        'xor': pyclipper.PT_XOR,
+        'union': pyclipper.CT_UNION,
+        'intersection': pyclipper.CT_INTERSECTION,
+        'difference': pyclipper.CT_DIFFERENCE,
+        'xor': pyclipper.CT_XOR,
     }
 
-    def to_vertices(objs: Iterable[Any] | None) -> list[NDArray]:
+    def to_vertices(objs: Iterable[Any] | Any | None) -> list[NDArray]:
         if objs is None:
             return []
+        if hasattr(objs, 'to_polygons') or isinstance(objs, numpy.ndarray | Polygon):
+            objs = (objs,)
+        elif not isinstance(objs, Iterable):
+            raise PatternError(f"Unsupported type for boolean operation: {type(objs)}")
         verts = []
         for obj in objs:
             if hasattr(obj, 'to_polygons'):
@@ -140,6 +144,16 @@ def boolean(
     subject_verts = to_vertices(subjects)
     clip_verts = to_vertices(clips)
 
+    if not subject_verts:
+        if operation in ('union', 'xor'):
+            return [Polygon(vertices) for vertices in clip_verts]
+        return []
+
+    if not clip_verts:
+        if operation == 'intersection':
+            return []
+        return [Polygon(vertices) for vertices in subject_verts]
+
     pc = pyclipper.Pyclipper()
     pc.AddPaths(pyclipper.scale_to_clipper(subject_verts, scale), pyclipper.PT_SUBJECT, True)
     if clip_verts:
diff --git a/masque/utils/transform.py b/masque/utils/transform.py
index ed0453b..7b39122 100644
--- a/masque/utils/transform.py
+++ b/masque/utils/transform.py
@@ -50,7 +50,10 @@ def normalize_mirror(mirrored: Sequence[bool]) -> tuple[bool, float]:
         `angle_to_rotate` in radians
     """
 
-    mirrored_x, mirrored_y = mirrored
+    if len(mirrored) != 2:
+        raise ValueError(f'mirrored must be a 2-item sequence, got length {len(mirrored)}')
+
+    mirrored_x, mirrored_y = (bool(value) for value in mirrored)
     mirror_x = (mirrored_x != mirrored_y)  # XOR
     angle = numpy.pi if mirrored_y else 0
     return mirror_x, angle
@@ -111,6 +114,11 @@ def apply_transforms(
     if inner.shape[1] == 4:
         inner = numpy.pad(inner, ((0, 0), (0, 1)), constant_values=1.0)
 
+    if outer.shape[0] == 0 or inner.shape[0] == 0:
+        if tensor:
+            return numpy.empty((outer.shape[0], inner.shape[0], 5))
+        return numpy.empty((0, 5))
+
     # If mirrored, flip y's
     xy_mir = numpy.tile(inner[:, :2], (outer.shape[0], 1, 1))   # dims are outer, inner, xyrm
     xy_mir[outer[:, 3].astype(bool), :, 1] *= -1