From 4e1c8f9a965f2d85e4c3b53b176cb2dfda34c681 Mon Sep 17 00:00:00 2001
From: Simon Cozens <simon@simon-cozens.org>
Date: Tue, 11 Jun 2024 09:25:38 +0100
Subject: [PATCH] Add the denominator to curvature checks

---
 beziers/cubicbezier.py     | 2 +-
 beziers/quadraticbezier.py | 8 ++++++++
 2 files changed, 9 insertions(+), 1 deletion(-)

diff --git a/beziers/cubicbezier.py b/beziers/cubicbezier.py
index f973c4a..4eed4c2 100644
--- a/beziers/cubicbezier.py
+++ b/beziers/cubicbezier.py
@@ -209,7 +209,7 @@ def curvatureAtTime(self, t: float) -> float:
         return (
             d.pointAtTime(t).x * d2.pointAtTime(t).y
             - d.pointAtTime(t).y * d2.pointAtTime(t).x
-        )
+        ) / ((d.pointAtTime(t).x ** 2 + d.pointAtTime(t).y ** 2) ** 1.5)
 
     @property
     def tunniPoint(self) -> Point:
diff --git a/beziers/quadraticbezier.py b/beziers/quadraticbezier.py
index ad6ba2c..0a40ec3 100644
--- a/beziers/quadraticbezier.py
+++ b/beziers/quadraticbezier.py
@@ -112,6 +112,14 @@ def findExtremes(self):
         """Returns a list of time `t` values for extremes of the curve."""
         return self._findDRoots()
 
+    def curvatureAtTime(self, t: float) -> float:
+        """Returns the C curvature at time `t`."""
+        d = self.derivative()
+        d2 = self.end - self.start  # A constant
+        return (d.pointAtTime(t).x * d2.y - d.pointAtTime(t).y * d2.x) / (
+            (d.pointAtTime(t).x ** 2 + d.pointAtTime(t).y ** 2) ** 1.5
+        )
+
     @property
     def area(self):
         """Returns the signed area between the curve and the y-axis"""