arc transform fixed (#98)

* arc transform fixed

* Update svgpathtools/path.py

Co-authored-by: Matthijs Kooijman <matthijs@stdin.nl>

* Fixed rotation bug in transformation of arcs

* Made compatible with python2.7

Changed the shorthand @ for np matrix multiplication to matmul

Co-authored-by: vrroom <vrroomc@github.com>
Co-authored-by: Matthijs Kooijman <matthijs@stdin.nl>

svgpathtools/path.py

@@ -13,6 +13,7 @@ from warnings import warn
 from operator import itemgetter
 import numpy as np
 from itertools import tee
+from functools import reduce
 
 # these imports were originally from math and cmath, now are from numpy
 # in order to encourage code that generalizes to vector inputs
@@ -288,7 +289,6 @@ def scale(curve, sx, sy=None, origin=0j):
         raise TypeError("Input `curve` should be a Path, Line, "
                         "QuadraticBezier, CubicBezier, or Arc object.")
 
-
 def transform(curve, tf):
     """Transforms the curve by the homogeneous transformation matrix tf"""
     def to_point(p):
@@ -310,13 +310,32 @@ def transform(curve, tf):
     elif isinstance(curve, Arc):
         new_start = to_complex(tf.dot(to_point(curve.start)))
         new_end = to_complex(tf.dot(to_point(curve.end)))
-        new_radius = to_complex(tf.dot(to_vector(curve.radius)))
-        if tf[0][0] * tf[1][1] >= 0.0:
-            new_sweep = curve.sweep
+        
+        # Based on https://math.stackexchange.com/questions/2349726/compute-the-major-and-minor-axis-of-an-ellipse-after-linearly-transforming-it
+        rx2 = curve.radius.real ** 2
+        ry2 = curve.radius.imag ** 2
+
+        Q = np.array([[1/rx2, 0], [0, 1/ry2]])
+        invT = np.linalg.inv(tf[:2,:2])
+        D = reduce(np.matmul, [invT.T, Q, invT])
+
+        eigvals, eigvecs = np.linalg.eig(D)
+
+        rx = 1 / np.sqrt(eigvals[0])
+        ry = 1 / np.sqrt(eigvals[1])
+
+        new_radius = complex(rx, ry)
+
+        xeigvec = eigvecs[:, 0]
+        rot = np.degrees(np.arccos(xeigvec[0]))
+
+        if new_radius.real == 0 or new_radius.imag == 0 :
+            return Line(new_start, new_end)
         else : 
-            new_sweep = not curve.sweep
-        return Arc(new_start, radius=new_radius, rotation=curve.rotation,
-                   large_arc=curve.large_arc, sweep=new_sweep, end=new_end)
+            return Arc(new_start, radius=new_radius, rotation=curve.rotation + rot,
+                       large_arc=curve.large_arc, sweep=curve.sweep, end=new_end,
+                       autoscale_radius=False)
+
     else:
         raise TypeError("Input `curve` should be a Path, Line, "
                         "QuadraticBezier, CubicBezier, or Arc object.")