From 27d2e85573be14e28a17a031c09a157276ee1155 Mon Sep 17 00:00:00 2001
From: lee <205592689+jkhahe72-sh3@users.noreply.github.com>
Date: Mon, 9 Mar 2026 18:12:33 +0100
Subject: [PATCH 1/4] Add point to plane distance using Hesse normal form

Adds a function to compute the distance between a point and a plane in 3D using the Hesse normal form.
---
 geometry/point_to_plane_distance.py | 25 +++++++++++++++++++++++++
 1 file changed, 25 insertions(+)
 create mode 100644 geometry/point_to_plane_distance.py

diff --git a/geometry/point_to_plane_distance.py b/geometry/point_to_plane_distance.py
new file mode 100644
index 000000000000..b7c5adb28bad
--- /dev/null
+++ b/geometry/point_to_plane_distance.py
@@ -0,0 +1,25 @@
+from math import sqrt
+
+
+def point_to_plane_distance(
+    x: float, y: float, z: float, a: float, b: float, c: float, d: float
+) -> float:
+    """
+    Return the distance between a point (x, y, z) and the plane ax + by + cz + d = 0 using the Hesse normal form.
+
+    Reference:
+    https://en.wikipedia.org/wiki/Hesse_normal_form
+
+    >>> point_to_plane_distance(1, 2, 3, 1, 0, 0, -1)
+    0.0
+    >>> point_to_plane_distance(3, 2, 1, 1, 0, 0, -1)
+    2.0
+    >>> point_to_plane_distance(1, 2, 3, 0, 0, 0, 4)
+    Traceback (most recent call last):
+        ...
+    ValueError: Normal vector cannot be zero.
+    """
+    if a == 0 and b == 0 and c == 0:
+        raise ValueError("Normal vector cannot be zero.")
+    
+    return abs(a * x + b * y + c * z + d) / sqrt(a**2 + b**2 + c**2)
\ No newline at end of file

From b0936781ce23e7776f762de0ca815b95c2e05d40 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Mon, 9 Mar 2026 17:26:49 +0000
Subject: [PATCH 2/4] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 geometry/point_to_plane_distance.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/geometry/point_to_plane_distance.py b/geometry/point_to_plane_distance.py
index b7c5adb28bad..1c9106f78ed6 100644
--- a/geometry/point_to_plane_distance.py
+++ b/geometry/point_to_plane_distance.py
@@ -21,5 +21,5 @@ def point_to_plane_distance(
     """
     if a == 0 and b == 0 and c == 0:
         raise ValueError("Normal vector cannot be zero.")
-    
-    return abs(a * x + b * y + c * z + d) / sqrt(a**2 + b**2 + c**2)
\ No newline at end of file
+
+    return abs(a * x + b * y + c * z + d) / sqrt(a**2 + b**2 + c**2)

From 710a359203a2d1e176975146856836eca5d922b3 Mon Sep 17 00:00:00 2001
From: lee <205592689+jkhahe72-sh3@users.noreply.github.com>
Date: Mon, 9 Mar 2026 18:32:58 +0100
Subject: [PATCH 3/4] Fix line length in docstring

---
 geometry/point_to_plane_distance.py | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/geometry/point_to_plane_distance.py b/geometry/point_to_plane_distance.py
index b7c5adb28bad..35ab8c35a00b 100644
--- a/geometry/point_to_plane_distance.py
+++ b/geometry/point_to_plane_distance.py
@@ -5,7 +5,8 @@ def point_to_plane_distance(
     x: float, y: float, z: float, a: float, b: float, c: float, d: float
 ) -> float:
     """
-    Return the distance between a point (x, y, z) and the plane ax + by + cz + d = 0 using the Hesse normal form.
+    Return the distance between a point (x, y, z) and the plane
+    ax + by + cz + d = 0 using the Hesse normal form.
 
     Reference:
     https://en.wikipedia.org/wiki/Hesse_normal_form

From 204ba41bb092ad58fd3139e77fcd863326668619 Mon Sep 17 00:00:00 2001
From: lee <205592689+jkhahe72-sh3@users.noreply.github.com>
Date: Mon, 9 Mar 2026 18:57:34 +0100
Subject: [PATCH 4/4] Use descriptive parameter names

---
 geometry/point_to_plane_distance.py | 17 ++++++++++++++---
 1 file changed, 14 insertions(+), 3 deletions(-)

diff --git a/geometry/point_to_plane_distance.py b/geometry/point_to_plane_distance.py
index 26a3cca7a2fd..6969803033d6 100644
--- a/geometry/point_to_plane_distance.py
+++ b/geometry/point_to_plane_distance.py
@@ -2,7 +2,13 @@
 
 
 def point_to_plane_distance(
-    x: float, y: float, z: float, a: float, b: float, c: float, d: float
+    point_x: float,
+    point_y: float,
+    point_z: float,
+    normal_x: float,
+    normal_y: float,
+    normal_z: float,
+    plane_constant: float
 ) -> float:
     """
     Return the distance between a point (x, y, z) and the plane
@@ -20,7 +26,12 @@ def point_to_plane_distance(
         ...
     ValueError: Normal vector cannot be zero.
     """
-    if a == 0 and b == 0 and c == 0:
+    if normal_x == 0 and normal_y == 0 and normal_z == 0:
         raise ValueError("Normal vector cannot be zero.")
 
-    return abs(a * x + b * y + c * z + d) / sqrt(a**2 + b**2 + c**2)
+    return abs(
+        normal_x * point_x
+        + normal_y * point_y
+        + normal_z * point_z
+        + plane_constant
+    ) / sqrt(normal_x**2 + normal_y**2 + normal_z**2)