Convexity

convex and nonconvex
sets and functions



In [1]:

    
import numpy as np
import matplotlib.path as mpath
import matplotlib.patches as mpatches
import matplotlib.pyplot as plt

%matplotlib inline



In [2]:

    
# shape copied from matplotlib example
fig, ax = plt.subplots()

Path = mpath.Path
path_data = [
    (Path.MOVETO, (1.58, -2.57)),
    (Path.CURVE4, (0.35, -1.1)),
    (Path.CURVE4, (-1.75, 2.0)),
    (Path.CURVE4, (0.375, 2.0)),
    (Path.LINETO, (0.85, 1.15)),
    (Path.CURVE4, (2.2, 3.2)),
    (Path.CURVE4, (3, 0.05)),
    (Path.CURVE4, (2.0, -0.5)),
    (Path.CLOSEPOLY, (1.58, -2.57)),
    ]
codes, verts = zip(*path_data)
path = mpath.Path(verts, codes)
patch = mpatches.PathPatch(path, facecolor='r', alpha=0.5)
ax.add_patch(patch)
ax.axis('equal')

plt.savefig('nonconvex-set.pdf')



In [3]:

    
fig, ax = plt.subplots()

Path = mpath.Path
path_data = [
    (Path.MOVETO, (0,0)),
    (Path.CURVE4, (2,3)),
    (Path.CURVE4, (1,6)),
    (Path.CURVE4, (-2,5)),
    (Path.LINETO, (-3,1)),
    (Path.CLOSEPOLY, (0,0)),
    ]
codes, verts = zip(*path_data)
path = mpath.Path(verts, codes)
patch = mpatches.PathPatch(path, facecolor='g', alpha=0.5)
ax.add_patch(patch)
ax.axis('equal')

plt.savefig('convex-set.pdf')



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