From cf9dece8f269384ba06e966348f7d19308ff1ed8 Mon Sep 17 00:00:00 2001
From: Behdad Esfahbod <behdad@behdad.org>
Date: Fri, 3 Feb 2023 09:54:43 -0700
Subject: [PATCH] [transform] Add Transform.toDecomposed()

---
 Lib/fontTools/misc/transform.py | 38 +++++++++++++++++++++++++++++++++
 Tests/misc/transform_test.py    |  8 +++++++
 2 files changed, 46 insertions(+)

diff --git a/Lib/fontTools/misc/transform.py b/Lib/fontTools/misc/transform.py
index 1e5c8693e..101652969 100644
--- a/Lib/fontTools/misc/transform.py
+++ b/Lib/fontTools/misc/transform.py
@@ -349,6 +349,44 @@ class Transform(NamedTuple):
         """
         return "[%s %s %s %s %s %s]" % self
 
+    def toDecomposed(self) -> "DecomposedTransform":
+        """Decompose into a DecomposedTransform."""
+        # Adapted from an answer on
+        # https://math.stackexchange.com/questions/13150/extracting-rotation-scale-values-from-2d-transformation-matrix
+        a, b, c, d, x, y = self
+        delta = a * d - b * c
+
+        rotation = 0
+        scaleX = scaleY = 0
+        skewX = skewY = 0
+
+        # Apply the QR-like decomposition.
+        if a != 0 or b != 0:
+            r = math.sqrt(a * a + b * b)
+            rotation = math.acos(a / r) if b > 0 else -math.acos(a / r)
+            scaleX, scaleY = (r, delta / r)
+            skewX, skewY = (math.atan((a * c + b * d) / (r * r)), 0)
+        elif c != 0 or d != 0:
+            s = math.sqrt(c * c + d * d)
+            rotation = math.pi / 2 - (math.acos(-c / s) if d > 0 else -math.acos(c / s))
+            scaleX, scaleY = (delta / s, s)
+            skewX, skewY = (0, math.atan((a * c + b * d) / (s * s)))
+        else:
+            # a = b = c = d = 0
+            pass
+
+        return DecomposedTransform(
+            x,
+            y,
+            math.degrees(rotation),
+            scaleX,
+            scaleY,
+            -math.degrees(skewX),
+            math.degrees(skewY),
+            0,
+            0,
+        )
+
     def __bool__(self):
         """Returns True if transform is not identity, False otherwise.
 
diff --git a/Tests/misc/transform_test.py b/Tests/misc/transform_test.py
index 0e978cd2b..3c9b57cfd 100644
--- a/Tests/misc/transform_test.py
+++ b/Tests/misc/transform_test.py
@@ -115,6 +115,14 @@ class TransformTest(object):
         assert Scale(2) == Transform(2, 0, 0, 2, 0, 0)
         assert Scale(1, 2) == Transform(1, 0, 0, 2, 0, 0)
 
+    def test_decompose(self):
+        t = Transform(2, 0, 0, 3, 5, 7)
+        d = t.toDecomposed()
+        assert d.scaleX == 2
+        assert d.scaleY == 3
+        assert d.translateX == 5
+        assert d.translateY == 7
+
 
 class DecomposedTransformTest(object):
     def test_identity(self):