python - how to use matplotlib PATH to draw polygon

Question

I have a problem when using python's matplotlib PATH modules I want to draw a close poly like this:

but I don't know exactly the sequence of the points to be connected and it turned out the result images can't meet my needs. How can I draw a polygon correctly without determining the sequence by myself but by the code?

here is my code:

import matplotlib
import matplotlib.pyplot as plt
import pandas
from matplotlib.path import Path
import matplotlib.patches as patches
#read data
info = pandas.read_csv('/Users/james/Desktop/nba.csv')
info.columns = ['number', 'team_id', 'player_id', 'x_loc', 'y_loc', 
'radius', 'moment', 'game_clock', 'shot_clock', 'player_name', 
'player_jersey']

#first_team_info
x_1 = info.x_loc[1:6]
y_1 = info.y_loc[1:6]
matrix= [x_1,y_1]
z_1 = list(zip(*matrix))
z_1.append(z_1[4])
n_1 = info.player_jersey[1:6]
verts = z_1
codes = [Path.MOVETO,
     Path.LINETO,
     Path.LINETO,
     Path.LINETO,
     Path.LINETO,
     Path.CLOSEPOLY,
     ]
     path = Path(verts, codes)
     fig = plt.figure()
     ax = fig.add_subplot(111)
     patch = patches.PathPatch(path, facecolor='orange', lw=2)
     ax.add_patch(patch)
     ax.set_xlim(0, 100)
     ax.set_ylim(0, 55)
     plt.show()

and I got this:

Answer 1

Matplotlib plots the points of a path in order they are given to patch. This can lead to undesired results, if there is no control over the order, like in the case from the question.

So the solution may be to

• (A) use a hull. Scipy provides scipy.spatial.ConvexHull to calculate the circonference of the points, which is automatically in the correct order. This gives good results in many cases, see first row, but may fail in other cases, because points inside the hull are ignored.
• (B) sort the points, e.g. counter clockwise around a certain point in the middle. In the example below I take the mean of all points for that. The sorting can be imagined like a radar scanner, points are sorted by their angle to the x axis. This solves e.g. the problem of the hull in the second row, but may of course also fail in more complicated shapes.

import numpy as np
import matplotlib.pyplot as plt
from scipy.spatial import ConvexHull

p = [(1,1), (2,1.6), (0.8,2.7), (1.7,3.2)]
p2 = [(0.7,1.3),(2,0.9),(1.4,1.5),(1.9,3.1),(0.6,2.5),(1.4,2.3)]

def convexhull(p):
    p = np.array(p)
    hull = ConvexHull(p)
    return p[hull.vertices,:]

def ccw_sort(p):
    p = np.array(p)
    mean = np.mean(p,axis=0)
    d = p-mean
    s = np.arctan2(d[:,0], d[:,1])
    return p[np.argsort(s),:]

fig, axes = plt.subplots(ncols=3, nrows=2, sharex=True, sharey=True)

axes[0,0].set_title("original")
poly = plt.Polygon(p, ec="k")
axes[0,0].add_patch(poly)

poly2 = plt.Polygon(p2, ec="k")
axes[1,0].add_patch(poly2)

axes[0,1].set_title("convex hull")
poly = plt.Polygon(convexhull(p), ec="k")
axes[0,1].add_patch(poly)

poly2 = plt.Polygon(convexhull(p2), ec="k")
axes[1,1].add_patch(poly2)

axes[0,2].set_title("ccw sort")
poly = plt.Polygon(ccw_sort(p), ec="k")
axes[0,2].add_patch(poly)

poly2 = plt.Polygon(ccw_sort(p2), ec="k")
axes[1,2].add_patch(poly2)


for ax in axes[0,:]:
    x,y = zip(*p)
    ax.scatter(x,y, color="k", alpha=0.6, zorder=3)
for ax in axes[1,:]:
    x,y = zip(*p2)
    ax.scatter(x,y, color="k", alpha=0.6, zorder=3)


axes[0,0].margins(0.1)
axes[0,0].relim()
axes[0,0].autoscale_view()
plt.show()