From ea761eb0c43ba515c827b138136e66aa44bf1e9f Mon Sep 17 00:00:00 2001
From: Joe Wallwork <joe.wallwork@outlook.com>
Date: Sat, 15 Jun 2024 09:35:29 +0100
Subject: [PATCH] #79: Sympylify plane calculation

---
 movement/math.py | 34 +++++++++++-----------------------
 pyproject.toml   |  2 +-
 2 files changed, 12 insertions(+), 24 deletions(-)

diff --git a/movement/math.py b/movement/math.py
index 022057d..2f74a37 100644
--- a/movement/math.py
+++ b/movement/math.py
@@ -1,4 +1,5 @@
 import numpy as np
+import sympy
 
 __all__ = []
 
@@ -52,25 +53,12 @@ def _equation_of_plane(a, b, c):
     :returns: a function of three variables representing the plane
     :rtype: :class:`~.Callable`
     """
-    assert len(a) == 3
-    assert len(b) == 3
-    assert len(c) == 3
-    a = np.array(a)
-    b = np.array(b)
-    c = np.array(c)
-    n = np.cross(b - a, c - a)
-
-    # Colinear case
-    if np.allclose(n, 0):
-        return None
-
-    def f(x, y, z):
-        return x * n[0] + y * n[1] + z * n[2] - np.dot(n, a)
-
-    assert np.isclose(f(*a), 0)
-    assert np.isclose(f(*b), 0)
-    assert np.isclose(f(*c), 0)
-    return f
+    plane = sympy.Plane(sympy.Point3D(a), sympy.Point3D(b), sympy.Point3D(c))
+
+    def equation(x, y, z):
+        return plane.distance(sympy.Point3D((x, y, z)))
+
+    return equation
 
 
 def equation_of_plane(*points):
@@ -87,8 +75,8 @@ def equation_of_plane(*points):
     while len(indices) >= 3:
         np.random.shuffle(indices)
         i, j, k = indices[:3]
-        f = _equation_of_plane(points[i], points[j], points[k])
-        if f is not None:
-            return f
-        indices.pop(0)
+        try:
+            return _equation_of_plane(points[i], points[j], points[k])
+        except ValueError:
+            indices.pop(0)
     raise ValueError("Could not determine a plane for the provided points.")
diff --git a/pyproject.toml b/pyproject.toml
index a73926c..0d7b416 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -4,7 +4,7 @@ requires = ["setuptools"]
 [project]
 name = "movement"
 version = "0.2"
-dependencies = ["cffconvert", "pre-commit", "ruff"]
+dependencies = ["cffconvert", "pre-commit", "ruff", "sympy"]
 authors = [
   {name = "Joseph G. Wallwork", email = "joe.wallwork@outlook.com"},
   {name = "Stephan C. Kramer"},