Merge pull request matplotlib#31844 from SharadhNaidu/fix-arc-winding-snap

FIX: snap near-integer arc windings to a full circle on polar plots (matplotlib#20388, matplotlib#26972)

Author: timhoffm

lib/matplotlib/path.py

@@ -978,6 +978,10 @@ def arc(cls, theta1, theta2, n=None, is_wedge=False):
         That is, if *theta2* > *theta1* + 360, the arc will be from *theta1* to
         *theta2* - 360 and not a full circle plus some extra overlap.
 
+        As a special case, if the span *theta2* - *theta1* is within
+        floating-point tolerance of a whole number of turns, a complete circle
+        is drawn.
+
         If *n* is provided, it is the number of spline segments to make.
         If *n* is not provided, the number of spline segments is
         determined based on the delta between *theta1* and *theta2*.
@@ -989,11 +993,20 @@ def arc(cls, theta1, theta2, n=None, is_wedge=False):
         halfpi = np.pi * 0.5
 
         eta1 = theta1
-        eta2 = theta2 - 360 * np.floor((theta2 - theta1) / 360)
-        # Ensure 2pi range is not flattened to 0 due to floating-point errors,
-        # but don't try to expand existing 0 range.
-        if theta2 != theta1 and eta2 <= eta1:
-            eta2 += 360
+        n_turns = (theta2 - theta1) / 360
+        nearest_turn = np.rint(n_turns)
+        is_full_circle = nearest_turn != 0 and abs(n_turns - nearest_turn) <= 1e-12
+        # We unwrap *theta2* to the shortest arc within 360 degrees.
+        # Full circles need special handling as floating point errors can
+        # make a full circle have 360° + eps, which would be unwrapped
+        # to eps only, i.e. collapsing the full circle to an infinitesimal arc.
+        # The threshold of 1e-12 is a defensive choice: Much larger than
+        # numeric precision errors (~1e-15) but still smaller than any
+        # expected real-world arcs.
+        if is_full_circle:
+            eta2 = theta1 + 360
+        else:
+            eta2 = theta2 - 360 * np.floor(n_turns)
         eta1, eta2 = np.deg2rad([eta1, eta2])
 
         # number of curve segments to make

lib/matplotlib/tests/test_path.py

@@ -511,6 +511,42 @@ def test_full_arc(offset):
     np.testing.assert_allclose(maxs, 1)
 
 
+@pytest.mark.parametrize('theta2', [
+    360, 720, 360 * 5,                       # exact whole turns
+    np.nextafter(360, 1e6),                  # +1 ulp: realistic float noise
+    np.nextafter(360, 0),                    # -1 ulp
+    np.nextafter(720, 1e6),
+])
+def test_arc_full_circle_snap(theta2):
+    # A span within floating-point tolerance of a whole number of turns must
+    # draw a complete circle, not collapse to a near-empty arc.
+    np.testing.assert_allclose(Path.arc(0, theta2).vertices,
+                               Path.arc(0, 360).vertices)
+
+
+@pytest.mark.parametrize('theta1, theta2', [(0, -360), (0, -720), (360, 0),
+                                            (10, -350)])
+def test_arc_negative_full_circle(theta1, theta2):
+    # An exact negative multiple of 360 must draw a complete circle.
+    # The result is the same complete circle as the equivalent positive turn
+    # starting from *theta1* (so the assertion holds for non-cardinal starts).
+    np.testing.assert_allclose(Path.arc(theta1, theta2).vertices,
+                               Path.arc(theta1, theta1 + 360).vertices)
+
+
+def test_arc_unwrap_partial_turn():
+    # A span comfortably more than a whole number of turns (not near-integer)
+    # is unwrapped to the equivalent shortest arc within 360 degrees.
+    np.testing.assert_allclose(Path.arc(0, 410).vertices,
+                               Path.arc(0, 50).vertices)
+    np.testing.assert_allclose(Path.arc(0, 540).vertices,
+                               Path.arc(0, 180).vertices)
+    # A span a clear fraction of a degree past a full turn is the caller's
+    # explicit request and must NOT be snapped to a circle (tolerance guard).
+    np.testing.assert_allclose(Path.arc(0, 360.001).vertices,
+                               Path.arc(0, 0.001).vertices)
+
+
 def test_disjoint_zero_length_segment():
     this_path = Path(
         np.array([

lib/matplotlib/tests/test_polar.py

@@ -328,6 +328,28 @@ def test_polar_gridlines():
     assert ax.yaxis.majorTicks[0].gridline.get_alpha() == .2
 
 
+@pytest.mark.parametrize('theta_zero_location, theta_offset', [
+    (("N", 20), None),
+    (("N", 30), None),
+    (None, 1.570796327),
+])
+def test_polar_outer_spine_not_collapsed(theta_zero_location, theta_offset):
+    # The polar outer spine spans a full turn via Path.arc.  For some theta
+    # offsets/directions, floating-point error left the span just short of a
+    # full 360 degrees and the spine collapsed to a near-empty arc.  Check it
+    # still occupies a sensible area.
+    fig, ax = plt.subplots(subplot_kw={'projection': 'polar'})
+    if theta_zero_location is not None:
+        ax.set_theta_direction(-1)
+        ax.set_theta_zero_location(*theta_zero_location)
+    if theta_offset is not None:
+        ax.set_theta_offset(theta_offset)
+    fig.canvas.draw()
+    # A collapsed spine has a near-zero (~1e-13) bounding box; a healthy one is
+    # hundreds of points across.
+    assert ax.spines['polar'].get_tightbbox().size.min() > 1
+
+
 def test_get_tightbbox_polar():
     fig, ax = plt.subplots(subplot_kw={'projection': 'polar'})
     fig.canvas.draw()