diff --git a/pyproject.toml b/pyproject.toml
index 9011310..61ca403 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -18,5 +18,6 @@ build-backend = "flit_core.buildapi"
 [dependency-groups]
 dev = [
     "black>=25.1.0",
+    "ipykernel>=6.30.1",
     "pytest>=8.4.1",
 ]
diff --git a/src/load_distribution/load_distribution.py b/src/load_distribution/load_distribution.py
index f1ee0bd..9f30871 100644
--- a/src/load_distribution/load_distribution.py
+++ b/src/load_distribution/load_distribution.py
@@ -1,4 +1,6 @@
 from __future__ import annotations
+from collections import Counter
+import math
 from typing import Optional
 from dataclasses import dataclass
 import numpy.typing as npt
@@ -180,23 +182,41 @@ def singularities_to_polygon(los: list[Singularity], xy: bool = False) -> Polygo
     x_acc = []
     prev_x = None
     n = None
+    # Create a list of the x-ordinates required
+    # Always starts on 0.0
+    x_acc.append(0.0)
     for idx, sing in enumerate(sorted_sings):
         n = sing.precision
         eps = 10 ** (-2 * n)
         if prev_x != sing.x0 and prev_x is not None:
             x_acc.append(prev_x + eps)
-        x_acc.append(sing.x0)
+        if prev_x is not None and not math.isclose(prev_x, sing.x0):
+            x_acc.append(sing.x0)
         x_acc.append(sing.x0 + eps)
-        if idx == len(sorted_sings) - 1:
-            x_acc.append(sing.x1 - eps)
-        x_acc.append(sing.x1)
+        x_acc.append(sing.x1 - eps)
         prev_x = sing.x1
-        if idx == len(sorted_sings) - 1:  # Last iteration of actual iterations
-            x_acc.append(sing.x1)
 
+    # There are two scenarios: sing functions that describe trapezoids/triangles
+    # and sing functions that describe step functions (rectangles). To ensure
+    # we get enough points to fully describe each, we end up getting too many
+    # x ordinates in some cases. The below is a filter to look for the unnecessary
+    # duplicate x-ordinates. The goal is to have the minimum amount to describe the
+    # required shape, even if that means the exact x value is omitted (because we are
+    # keeping the value immediately to the left and immediately to the right instead).
     x_acc = sorted(list(set(x_acc)))
+    x_ord_count = Counter([round(x, 6) for x in x_acc])
+    to_filter = []
+    for key, count in x_ord_count.items():
+        if count == 3:
+            to_filter.append(key)
+    for filter_val in to_filter:
+        index = x_acc.index(filter_val)
+        x_acc.pop(index)
+
+    # Now, for every x value, compute the corresponding y value
     y_acc = [sum([sing(x) for sing in sorted_sings]) for x in x_acc[:-1]]
-    y_acc += [0.0]
+    # Always ends on 0.0
+    y_acc.append(0.0)
     if xy:
         return x_acc, y_acc
     else:
diff --git a/tests/test_load_distribution.py b/tests/test_load_distribution.py
index 199a7f4..7707697 100644
--- a/tests/test_load_distribution.py
+++ b/tests/test_load_distribution.py
@@ -175,25 +175,26 @@ def test_singularities_to_polygon():
 
     assert (
         ld.singularities_to_polygon(square_45_sings[0] + square_45_sings[1]).wkt
-        == "POLYGON ((0 0, 0 0, 5 10, 5 10, 10 0, 10 0, 0 0))"
+        == "POLYGON ((0 0, 0 0, 5 10, 5 10, 10 0, 0 0))"
+        # == "POLYGON ((0 0, 5 10, 5 10, 10 0, 10 0, 0 0))"
     )
     assert (
         ld.singularities_to_polygon(
             square_pac_man_sings[0] + square_pac_man_sings[1]
         ).wkt
-        == "POLYGON ((0 0, 0 10, 5 10, 5 10, 10 0, 10 0, 10 0, 0 0))"
+        == "POLYGON ((0 0, 0 10, 5 10, 5 10, 10 0, 10 0, 0 0))"
     )
     assert (
         ld.singularities_to_polygon(
             square_bow_tie_sings[0] + square_bow_tie_sings[1]
         ).wkt
-        == "POLYGON ((0 0, 0 0, 4 10, 4 10, 6 10, 6 10, 10 0, 10 0, 10 0, 0 0))"
+        == "POLYGON ((0 0, 0 0, 4 10, 4 10, 6 10, 6 10, 10 0, 10 0, 0 0))"
     )
     assert (
         ld.singularities_to_polygon(
             square_with_L_hole_sings[0] + square_with_L_hole_sings[1]
         ).wkt
-        == "POLYGON ((0 0, 0 10, 2 10, 2 4, 4 4, 4 8, 8 8, 8 8, 8 10, 10 10, 10 0, 0 0))"
+        == "POLYGON ((0 0, 0 10, 2 10, 2 4, 4 4, 4 8, 8 8, 8 10, 10 10, 10 0, 0 0))"
     )
 
 
diff --git a/uv.lock b/uv.lock
index 096e313..52d563e 100644
--- a/uv.lock
+++ b/uv.lock
@@ -1,6 +1,24 @@
 version = 1
 requires-python = ">=3.11"
 
+[[package]]
+name = "appnope"
+version = "0.1.4"
+source = { registry = "https://pypi.org/simple" }
+sdist = { url = "https://files.pythonhosted.org/packages/35/5d/752690df9ef5b76e169e68d6a129fa6d08a7100ca7f754c89495db3c6019/appnope-0.1.4.tar.gz", hash = "sha256:1de3860566df9caf38f01f86f65e0e13e379af54f9e4bee1e66b48f2efffd1ee", size = 4170 }
+wheels = [
+    { url = "https://files.pythonhosted.org/packages/81/29/5ecc3a15d5a33e31b26c11426c45c501e439cb865d0bff96315d86443b78/appnope-0.1.4-py2.py3-none-any.whl", hash = "sha256:502575ee11cd7a28c0205f379b525beefebab9d161b7c964670864014ed7213c", size = 4321 },
+]
+
+[[package]]
+name = "asttokens"
+version = "3.0.0"
+source = { registry = "https://pypi.org/simple" }
+sdist = { url = "https://files.pythonhosted.org/packages/4a/e7/82da0a03e7ba5141f05cce0d302e6eed121ae055e0456ca228bf693984bc/asttokens-3.0.0.tar.gz", hash = "sha256:0dcd8baa8d62b0c1d118b399b2ddba3c4aff271d0d7a9e0d4c1681c79035bbc7", size = 61978 }
+wheels = [
+    { url = "https://files.pythonhosted.org/packages/25/8a/c46dcc25341b5bce5472c718902eb3d38600a903b14fa6aeecef3f21a46f/asttokens-3.0.0-py3-none-any.whl", hash = "sha256:e3078351a059199dd5138cb1c706e6430c05eff2ff136af5eb4790f9d28932e2", size = 26918 },
+]
+
 [[package]]
 name = "black"
 version = "25.1.0"
@@ -29,6 +47,51 @@ wheels = [
     { url = "https://files.pythonhosted.org/packages/09/71/54e999902aed72baf26bca0d50781b01838251a462612966e9fc4891eadd/black-25.1.0-py3-none-any.whl", hash = "sha256:95e8176dae143ba9097f351d174fdaf0ccd29efb414b362ae3fd72bf0f710717", size = 207646 },
 ]
 
+[[package]]
+name = "cffi"
+version = "1.17.1"
+source = { registry = "https://pypi.org/simple" }
+dependencies = [
+    { name = "pycparser" },
+]
+sdist = { url = "https://files.pythonhosted.org/packages/fc/97/c783634659c2920c3fc70419e3af40972dbaf758daa229a7d6ea6135c90d/cffi-1.17.1.tar.gz", hash = "sha256:1c39c6016c32bc48dd54561950ebd6836e1670f2ae46128f67cf49e789c52824", size = 516621 }
+wheels = [
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+    { url = "https://files.pythonhosted.org/packages/6c/f5/6c3a8efe5f503175aaddcbea6ad0d2c96dad6f5abb205750d1b3df44ef29/cffi-1.17.1-cp311-cp311-macosx_11_0_arm64.whl", hash = "sha256:30c5e0cb5ae493c04c8b42916e52ca38079f1b235c2f8ae5f4527b963c401caf", size = 178651 },
+    { url = "https://files.pythonhosted.org/packages/94/dd/a3f0118e688d1b1a57553da23b16bdade96d2f9bcda4d32e7d2838047ff7/cffi-1.17.1-cp311-cp311-manylinux_2_12_i686.manylinux2010_i686.manylinux_2_17_i686.manylinux2014_i686.whl", hash = "sha256:f75c7ab1f9e4aca5414ed4d8e5c0e303a34f4421f8a0d47a4d019ceff0ab6af4", size = 445259 },
+    { url = "https://files.pythonhosted.org/packages/2e/ea/70ce63780f096e16ce8588efe039d3c4f91deb1dc01e9c73a287939c79a6/cffi-1.17.1-cp311-cp311-manylinux_2_17_aarch64.manylinux2014_aarch64.whl", hash = "sha256:a1ed2dd2972641495a3ec98445e09766f077aee98a1c896dcb4ad0d303628e41", size = 469200 },
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+]
+
 [[package]]
 name = "click"
 version = "8.2.1"
@@ -50,6 +113,54 @@ wheels = [
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