matplotlib · tacaswell · Jun 17, 2020 · Oct 1, 2019 · Jun 17, 2020
diff --git a/lib/matplotlib/patches.py b/lib/matplotlib/patches.py
@@ -1592,14 +1592,12 @@ def draw(self, renderer):
            calculation much easier than doing rotated ellipse
            intersection directly).
 
-           This uses the "line intersecting a circle" algorithm
-           from:
+           This uses the "line intersecting a circle" algorithm from:
 
                Vince, John.  *Geometry for Computer Graphics: Formulae,
                Examples & Proofs.*  London: Springer-Verlag, 2005.
 
-        2. The angles of each of the intersection points are
-           calculated.
+        2. The angles of each of the intersection points are calculated.
 
         3. Proceeding counterclockwise starting in the positive
            x-direction, each of the visible arc-segments between the
@@ -1609,6 +1607,8 @@ def draw(self, renderer):
         """
         if not hasattr(self, 'axes'):
             raise RuntimeError('Arcs can only be used in Axes instances')
+        if not self.get_visible():
+            return
 
         self._recompute_transform()
 
@@ -1621,44 +1621,62 @@ def theta_stretch(theta, scale):
             theta = np.deg2rad(theta)
             x = np.cos(theta)
             y = np.sin(theta)
-            return np.rad2deg(np.arctan2(scale * y, x))
-        theta1 = theta_stretch(self.theta1, width / height)
-        theta2 = theta_stretch(self.theta2, width / height)
-
-        # Get width and height in pixels
-        width, height = self.get_transform().transform((width, height))
+            stheta = np.rad2deg(np.arctan2(scale * y, x))
+            # arctan2 has the range [-pi, pi], we expect [0, 2*pi]
+            return (stheta + 360) % 360
+
+        theta1 = self.theta1
+        theta2 = self.theta2
+
+        if (
+            # if we need to stretch the angles because we are distorted
+            width != height
+            # and we are not doing a full circle.
+            #
+            # 0 and 360 do not exactly round-trip through the angle
+            # stretching (due to both float precision limitations and
+            # the difference between the range of arctan2 [-pi, pi] and
+            # this method [0, 360]) so avoid doing it if we don't have to.
+            and not (theta1 != theta2 and theta1 % 360 == theta2 % 360)
+        ):
+            theta1 = theta_stretch(self.theta1, width / height)
+            theta2 = theta_stretch(self.theta2, width / height)
+
+        # Get width and height in pixels we need to use
+        # `self.get_data_transform` rather than `self.get_transform`
+        # because we want the transform from dataspace to the
+        # screen space to estimate how big the arc will be in physical
+        # units when rendered (the transform that we get via
+        # `self.get_transform()` goes from an idealized unit-radius
+        # space to screen space).
+        data_to_screen_trans = self.get_data_transform()
+        pwidth, pheight = (data_to_screen_trans.transform((width, height)) -
+                           data_to_screen_trans.transform((0, 0)))
         inv_error = (1.0 / 1.89818e-6) * 0.5
-        if width < inv_error and height < inv_error:
+
+        if pwidth < inv_error and pheight < inv_error:
             self._path = Path.arc(theta1, theta2)
             return Patch.draw(self, renderer)
 
-        def iter_circle_intersect_on_line(x0, y0, x1, y1):
+        def line_circle_intersect(x0, y0, x1, y1):
             dx = x1 - x0
             dy = y1 - y0
             dr2 = dx * dx + dy * dy
             D = x0 * y1 - x1 * y0
             D2 = D * D
             discrim = dr2 - D2
-
-            # Single (tangential) intersection
-            if discrim == 0.0:
-                x = (D * dy) / dr2
-                y = (-D * dx) / dr2
-                yield x, y
-            elif discrim > 0.0:
-                # The definition of "sign" here is different from
-                # np.sign: we never want to get 0.0
-                if dy < 0.0:
-                    sign_dy = -1.0
-                else:
-                    sign_dy = 1.0
+            if discrim >= 0.0:
+                sign_dy = np.copysign(1, dy)  # +/-1, never 0.
                 sqrt_discrim = np.sqrt(discrim)
-                for sign in (1., -1.):
-                    x = (D * dy + sign * sign_dy * dx * sqrt_discrim) / dr2
-                    y = (-D * dx + sign * np.abs(dy) * sqrt_discrim) / dr2
-                    yield x, y
+                return np.array(
+                    [[(D * dy + sign_dy * dx * sqrt_discrim) / dr2,
+                      (-D * dx + abs(dy) * sqrt_discrim) / dr2],
+                     [(D * dy - sign_dy * dx * sqrt_discrim) / dr2,
+                      (-D * dx - abs(dy) * sqrt_discrim) / dr2]])
+            else:
+                return np.empty((0, 2))
 
-        def iter_circle_intersect_on_line_seg(x0, y0, x1, y1):
+        def segment_circle_intersect(x0, y0, x1, y1):
             epsilon = 1e-9
             if x1 < x0:
                 x0e, x1e = x1, x0
@@ -1668,40 +1686,34 @@ def iter_circle_intersect_on_line_seg(x0, y0, x1, y1):
                 y0e, y1e = y1, y0
             else:
                 y0e, y1e = y0, y1
-            x0e -= epsilon
-            y0e -= epsilon
-            x1e += epsilon
-            y1e += epsilon
-            for x, y in iter_circle_intersect_on_line(x0, y0, x1, y1):
-                if x0e <= x <= x1e and y0e <= y <= y1e:
-                    yield x, y
+            xys = line_circle_intersect(x0, y0, x1, y1)
+            xs, ys = xys.T
+            return xys[
+                (x0e - epsilon < xs) & (xs < x1e + epsilon)
+                & (y0e - epsilon < ys) & (ys < y1e + epsilon)
+            ]
 
         # Transforms the axes box_path so that it is relative to the unit
         # circle in the same way that it is relative to the desired ellipse.
-        box_path = Path.unit_rectangle()
         box_path_transform = (transforms.BboxTransformTo(self.axes.bbox)
-                              - self.get_transform())
-        box_path = box_path.transformed(box_path_transform)
+                              + self.get_transform().inverted())
+        box_path = Path.unit_rectangle().transformed(box_path_transform)
 
         thetas = set()
         # For each of the point pairs, there is a line segment
         for p0, p1 in zip(box_path.vertices[:-1], box_path.vertices[1:]):
-            x0, y0 = p0
-            x1, y1 = p1
-            for x, y in iter_circle_intersect_on_line_seg(x0, y0, x1, y1):
-                theta = np.arccos(x)
-                if y < 0:
-                    theta = 2 * np.pi - theta
-                # Convert radians to angles
-                theta = np.rad2deg(theta)
-                if theta1 < theta < theta2:
-                    thetas.add(theta)
+            xy = segment_circle_intersect(*p0, *p1)
+            x, y = xy.T
+            # arctan2 return [-pi, pi), the rest of our angles are in
+            # [0, 360], adjust as needed.
+            theta = (np.rad2deg(np.arctan2(y, x)) + 360) % 360
+            thetas.update(theta[(theta1 < theta) & (theta < theta2)])
         thetas = sorted(thetas) + [theta2]
-
         last_theta = theta1
         theta1_rad = np.deg2rad(theta1)
-        inside = box_path.contains_point((np.cos(theta1_rad),
-                                          np.sin(theta1_rad)))
+        inside = box_path.contains_point(
+            (np.cos(theta1_rad), np.sin(theta1_rad))
+        )
 
         # save original path
         path_original = self._path

diff --git a/lib/matplotlib/tests/baseline_images/test_axes/arc_angles.png b/lib/matplotlib/tests/baseline_images/test_axes/arc_angles.png