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Vectorize Arc.draw. #14694

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Merged
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Oct 1, 2019
Merged

Vectorize Arc.draw. #14694

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64 changes: 22 additions & 42 deletions lib/matplotlib/patches.py
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Original file line number Diff line number Diff line change
Expand Up @@ -1561,14 +1561,12 @@ 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
Expand Down Expand Up @@ -1601,33 +1599,25 @@ def theta_stretch(theta, scale):
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
Expand All @@ -1637,17 +1627,13 @@ 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.
# 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().inverted()
Expand All @@ -1656,16 +1642,10 @@ def iter_circle_intersect_on_line_seg(x0, y0, x1, y1):
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
theta = np.rad2deg(np.arctan2(y, x))
thetas.update(theta[(theta1 < theta) & (theta < theta2)])
thetas = sorted(thetas) + [theta2]

last_theta = theta1
Expand Down
40 changes: 40 additions & 0 deletions lib/matplotlib/tests/baseline_images/test_patches/large_arc.svg
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8 changes: 8 additions & 0 deletions lib/matplotlib/tests/test_patches.py
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Expand Up @@ -478,3 +478,11 @@ def test_fancyarrow_units():
fig, ax = plt.subplots()
arrow = FancyArrowPatch((0, dtime), (0.01, dtime))
ax.add_patch(arrow)


@image_comparison(["large_arc.svg"], style="mpl20")
def test_large_arc():
ax = plt.figure().add_subplot()
ax.set_axis_off()
# A large arc that crosses the axes view limits.
ax.add_patch(mpatches.Arc((-100, 0), 201, 201))