如何顺时针或者逆时针记录多边形的每个点

问题定义：

按照顺时针或者逆时针提取多边形的各个顶点

问题解决：

针对一个凸多边形，假设多边形的中心为C，多边形的任意一个顶点为A

做一个辅助点，假设有一条水平线通过中心点C，并在c点右边设一个B点

这样，可以通过 与 的夹角确定A点的角度，这样根据不同位置的顶点就能得到其夹角。

具体python实现：

# -*- coding: utf-8 -*-
 
import numpy as np
import cv2
import cv2 as cv
from sklearn.cluster import DBSCAN
import copy
 
def obtain_corners(mask):
    dst = cv.cornerHarris(mask,5,5,0.04)
    # 设置阈值，将角点绘制出来，阈值根据图像进行选择
    pos = np.where(dst>0.001*dst.max())
    x = pos[1]
    y = pos[0]
    epsilon = 2
    min_samples=1
    ou = np.concatenate((x.reshape(-1,1),y.reshape(-1,1)), axis=1)
    db = DBSCAN(eps=epsilon, min_samples=min_samples).fit(ou)
    _labels = db.labels_
    points_poly = np.zeros([0,2], dtype=np.float32)
    for i in range(_labels.max()+1):
        vv = np.mean(ou[np.where(_labels == i)[0], :], 0)
        points_poly = np.concatenate((points_poly, vv.reshape(1,2)), axis=0)
    return points_poly
 
 
def dot_product_angle(v1, v2):
    if np.linalg.norm(v1) == 0 or np.linalg.norm(v2) == 0:
        print("Zero magnitude vector!")
    else:
        vector_dot_product = np.dot(v1, v2)
        arccos = np.arccos(vector_dot_product / (np.linalg.norm(v1) * np.linalg.norm(v2)))
        angle = np.degrees(arccos)
        return angle
    return 0
 
def obtain_vector(a, b, center):
    aa = copy.deepcopy(a)
    bb = copy.deepcopy(b)
    aa[0] = center[0] - aa[0]
    aa[1] = center[1] - aa[1]
    bb[0] = center[0] - bb[0]
    bb[1] = center[1] - bb[1]
    return aa, bb   
 
 
# load image
large = cv2.imread('ss_big.png', 0)
 
# obtain corners 
points_poly = obtain_corners(large)
_, temp_bin = cv2.threshold(large, 126, 255, cv2.THRESH_BINARY)
num_labels, labels, stats, centroids = cv2.connectedComponentsWithStats(temp_bin, connectivity=8)
 
# obtain the center
center = centroids[1, :]
 
# save angle
angle = []
b = np.array([center[0] + 10, center[1]], dtype=np.float32)
for i in range(points_poly.shape[0]):
    aa, bb = obtain_vector(points_poly[i,:], b, center)
    angle_ = dot_product_angle(aa, bb)
    #print(points_poly[i,:])
    if points_poly[i,1] > center[1]:
        angle_ += 180
    angle.append(angle_)
 
index_ = np.argsort(np.array(angle, dtype=np.float32))
 
# sorted by angle 
pos_poly = points_poly[index_,:]
print(pos_poly)
 

 结果：

[[1761.5         651.125     ]
 [1562.43636364  592.49090909]
 [1489.41666667  514.9375    ]
 [1527.11111111  310.44444444]
 [1499.36363636  272.04545455]
 [1261.42857143  219.03571429]
 [1224.15        234.15      ]
 [1180.          416.66666667]
 [ 890.18181818  395.42424242]
 [1638.48484848 1105.84848485]
 [1432.53061224 1043.44897959]
 [1360.25       1078.85      ]
 [1303.54166667 1246.16666667]
 [1240.48       1267.46      ]
 [ 965.09090909 1175.6969697 ]
 [1015.73076923 1001.42307692]
 [ 978.5         904.55555556]
 [ 793.65714286  833.8       ]]