这是一个有点 hacky matplotlib 解决方案。主要的复杂性与使用 matplotlib 有关Path构建组合的对象Path.
#!/usr/bin/env python
import numpy as np
from matplotlib.path import Path
from matplotlib.patches import PathPatch, Polygon
from matplotlib.transforms import Bbox, BboxTransformTo
def side(a, b, c):
"On which side of line a-b is point c? Returns -1, 0, or 1."
return np.sign(np.linalg.det(np.c_[[a,b,c],[1,1,1]]))
def center((prev, curr, next), radius):
"Find center of arc approximating corner at curr."
p0, p1 = prev
c0, c1 = curr
n0, n1 = next
dp = radius * np.hypot(c1 - p1, c0 - p0)
dn = radius * np.hypot(c1 - n1, c0 - n0)
p = p1 * c0 - p0 * c1
n = n1 * c0 - n0 * c1
results = \
np.linalg.solve([[p1 - c1, c0 - p0],
[n1 - c1, c0 - n0]],
[[p - dp, p - dp, p + dp, p + dp],
[n - dn, n + dn, n - dn, n + dn]])
side_n = side(prev, curr, next)
side_p = side(next, curr, prev)
for r in results.T:
if (side(prev, curr, r), side(next, curr, r)) == (side_n, side_p):
return r
raise ValueError, "Cannot find solution"
def proj((prev, curr, next), center):
"Project center onto lines prev-curr and next-curr."
p0, p1 = prev = np.asarray(prev)
c0, c1 = curr = np.asarray(curr)
n0, n1 = next = np.asarray(next)
pc = curr - prev
nc = curr - next
pc2 = np.dot(pc, pc)
nc2 = np.dot(nc, nc)
return (prev + np.dot(center - prev, pc)/pc2 * pc,
next + np.dot(center - next, nc)/nc2 * nc)
def rad2deg(angle):
return angle * 180.0 / np.pi
def angle(center, point):
x, y = np.asarray(point) - np.asarray(center)
return np.arctan2(y, x)
def arc_path(center, start, end):
"Return a Path for an arc from start to end around center."
# matplotlib arcs always go ccw so we may need to mirror
mirror = side(center, start, end) < 0
if mirror:
start *= [1, -1]
center *= [1, -1]
end *= [1, -1]
return Path.arc(rad2deg(angle(center, start)),
rad2deg(angle(center, end))), \
mirror
def path(vertices, radii):
"Return a Path for a closed rounded polygon."
if np.isscalar(radii):
radii = np.repeat(radii, len(vertices))
else:
radii = np.asarray(radii)
pv = []
pc = []
first = True
for i in range(len(vertices)):
if i == 0:
seg = (vertices[-1], vertices[0], vertices[1])
elif i == len(vertices) - 1:
seg = (vertices[-2], vertices[-1], vertices[0])
else:
seg = vertices[i-1:i+2]
r = radii[i]
c = center(seg, r)
a, b = proj(seg, c)
arc, mirror = arc_path(c, a, b)
m = [1,1] if not mirror else [1,-1]
bb = Bbox([c, c + (r, r)])
iter = arc.iter_segments(BboxTransformTo(bb))
for v, c in iter:
if c == Path.CURVE4:
pv.extend([m * v[0:2], m * v[2:4], m * v[4:6]])
pc.extend([c, c, c])
elif c == Path.MOVETO:
pv.append(m * v)
if first:
pc.append(Path.MOVETO)
first = False
else:
pc.append(Path.LINETO)
pv.append([0,0])
pc.append(Path.CLOSEPOLY)
return Path(pv, pc)
if __name__ == '__main__':
from matplotlib import pyplot
fig = pyplot.figure()
ax = fig.add_subplot(111)
vertices = [[3,0], [5,2], [10,0], [6,9], [6,5], [3, 5], [0,2]]
patch = Polygon(vertices, edgecolor='red', facecolor='None',
linewidth=1)
ax.add_patch(patch)
patch = PathPatch(path(vertices, 0.5),
edgecolor='black', facecolor='blue', alpha=0.4,
linewidth=2)
ax.add_patch(patch)
ax.set_xlim(-1, 11)
ax.set_ylim(-1, 9)
fig.savefig('foo.pdf')
