Метод 1:
Определите центральную точку, вычислите угол между каждой координатой и центральной точкой, затем упорядочите их по углу:
import pandas as pd
# Define function to compute angle between vectors
import math
def clockwiseangle_and_distance(point, origin = [0,0], refvec = [1,0]):
# Vector between point and the origin: v = p - o
vector = [point[0]-origin[0], point[1]-origin[1]]
# Length of vector: ||v||
lenvector = math.hypot(vector[0], vector[1])
# If length is zero there is no angle
if lenvector == 0:
return -math.pi, 0
# Normalize vector: v/||v||
normalized = [vector[0]/lenvector, vector[1]/lenvector]
dotprod = normalized[0]*refvec[0] + normalized[1]*refvec[1] # x1*x2 + y1*y2
diffprod = refvec[1]*normalized[0] - refvec[0]*normalized[1] # x1*y2 - y1*x2
angle = math.atan2(diffprod, dotprod)
# Negative angles represent counter-clockwise angles so we need to subtract them
# from 2*pi (360 degrees)
if angle < 0:
return 2*math.pi+angle, lenvector
# I return first the angle because that's the primary sorting criterium
# but if two vectors have the same angle then the shorter distance should come first.
return angle, lenvector
import pandas as pd
# Compute the center point
center = pts.mean(axis=0)
angle = []
for i in range(len(pts)):
ang, dist = clockwiseangle_and_distance(pts[i,:] - center, origin=[0,0], refvec=[1,0])
angle.append(ang)
df = pd.DataFrame(pts)
df['angle'] = np.degrees(angle)
df = df.sort_values(by='angle')
df['clockwise_order'] = np.arange(len(df))
import matplotlib.pyplot as plt
# Create plot to show the ordering of the points
plt.figure()
df.plot(kind='scatter', x=0, y=1, s=100, alpha=0.5)
plt.title('Points by clockwise order')
for idx, row in df.iterrows():
plt.gca().annotate('{:.0f}'.format(row['clockwise_order']), (row[0], row[1]),
ha='center', va='center_baseline', fontsize=6, color='k', fontweight='bold')
plt.gca().annotate('Center', center,
ha='center', va='center')
Если этот порядок по часовой стрелке не дает того, что вы хотите, попробуйте метод 2.
Метод 2:
Чтобы отсортировать точки для данной геометрии по часовой стрелке так, чтобы они образовали замкнутое кольцо, вы можете сделать следующее:
- Разделить набор данных на квадранты
- Выберите центральную точку так, чтобы оставшиеся точки квадранта лежали на дуге окружности с центром в центральной точке
- Упорядочите каждый квадрант по часовой стрелке
- Поместите каждый квадрантпо часовой стрелке
# Compute the center point
center = pts.mean(axis=0)
df = pd.DataFrame(pts)
# Group points into quadrants
df['quadrant'] = 0
df.loc[(df[0] > center[0]) & (df[1] > center[1]), 'quadrant'] = 0
df.loc[(df[0] > center[0]) & (df[1] < center[1]), 'quadrant'] = 1
df.loc[(df[0] < center[0]) & (df[1] < center[1]), 'quadrant'] = 2
df.loc[(df[0] < center[0]) & (df[1] > center[1]), 'quadrant'] = 3
quadrant = {}
for i in range(4):
quadrant[i] = df[df.quadrant == i]
# Intelligently choose the quadrant centers
x = 35
y = 5
subcenter = [[ x, y],
[ x, -y],
[-x, -y],
[-x, y]]
# Compute the angle between each quadrant and respective center point
angle = {}
points = {}
df_sub = {}
for j in range(len(quadrant)):
angle[j] = []
points[j] = quadrant[j][[0,1]]
for i in range(len(points[j])):
ang, dist = clockwiseangle_and_distance(points[j].values[i,:] - subcenter[j], origin=[0,0], refvec=[1,0])
angle[j].append(ang)
df_sub[j] = quadrant[j]
df_sub[j]['angle'] = np.degrees(angle[j])
df_sub[j] = df_sub[j].sort_values(by='angle')
# Combine the data frames
df = pd.concat(df_sub)
df['clockwise_order'] = np.arange(len(df))
# Plot the points by clockwise order
import matplotlib.pyplot as plt
# Create plot to show the ordering of the points
fig, axis = plt.subplots()
df[[0,1]].plot(x=0, y=1, ax=axis, c='lightblue', legend=False, clip_on=False)
df.plot(kind='scatter', x=0, y=1, s=100, ax=axis, c='lightblue', clip_on=False)
plt.title('Points by quadrant in clockwise order')
plt.axis('off')
for idx, row in df.iterrows():
plt.gca().annotate('{:.0f}'.format(row['clockwise_order']), (row[0], row[1]),
ha='center', va='center_baseline', fontsize=6, color='k', fontweight='bold')
plt.gca().annotate('Center', center,
ha='center', va='center')
for i in range(len(subcenter)):
plt.scatter(subcenter[i][0], subcenter[i][1], alpha=0.5, s=80, marker='s')
plt.gca().annotate('Quadrant \n'+str(i)+'\n', subcenter[i],
ha='center', va='center_baseline', color='k', fontsize=8)
# Plot with axis equally-spaced
df2 = df[[0,1]].reset_index(drop=True)
df2.loc[len(df2),:] = df2.loc[0,:]
df2.plot(x=0, y=1, c='k', legend=False, clip_on=False)
plt.axis('equal')
plt.axis('off')
Если этоне дает вам то, что вы хотите, возможно, вам придется заказывать координаты вручную.