import matplotlib.pyplot as plt
import math
import sklearn.datasets as datasets
"""
使用Graham扫描法计算凸包
网上的代码好多运行效果并不好
算法参见《算法导论》第三版 第605页
"""
def get_bottom_point(points):
"""
返回points中纵坐标最小的点的索引，如果有多个纵坐标最小的点则返回其中横坐标最小的那个
:param points:
:return:
"""
min_index = 0
n = len(points)
for i in range(0, n):
if points[i][1] < points[min_index][1] or (points[i][1] == points[min_index][1] and points[i][0] < points[min_index][0]):
min_index = i
return min_index
def sort_polar_angle_cos(points, center_point):
"""
按照与中心点的极角进行排序，使用的是余弦的方法
:param points: 需要排序的点
:param center_point: 中心点
:return:
"""
n = len(points)
cos_value = []
rank = []
norm_list = []
for i in range(0, n):
point_ = points[i]
point = [point_[0]-center_point[0], point_[1]-center_point[1]]
rank.append(i)
norm_value = math.sqrt(point[0]*point[0] + point[1]*point[1])
norm_list.append(norm_value)
if norm_value == 0:
cos_value.append(1)
else:
cos_value.append(point[0] / norm_value)
for i in range(0, n-1):
index = i + 1
while index > 0:
if cos_value[index] > cos_value[index-1] or (cos_value[index] == cos_value[index-1] and norm_list[index] > norm_list[index-1]):
temp = cos_value[index]
temp_rank = rank[index]
temp_norm = norm_list[index]
cos_value[index] = cos_value[index-1]
rank[index] = rank[index-1]
norm_list[index] = norm_list[index-1]
cos_value[index-1] = temp
rank[index-1] = temp_rank
norm_list[index-1] = temp_norm
index = index-1
else:
break
sorted_points = []
for i in rank:
sorted_points.append(points[i])
return sorted_points
def vector_angle(vector):
"""
返回一个向量与向量 [1, 0]之间的夹角， 这个夹角是指从[1, 0]沿逆时针方向旋转多少度能到达这个向量
:param vector:
:return:
"""
norm_ = math.sqrt(vector[0]*vector[0] + vector[1]*vector[1])
if norm_ == 0:
return 0
angle = math.acos(vector[0]/norm_)
if vector[1] >= 0:
return angle
else:
return 2*math.pi - angle
def coss_multi(v1, v2):
"""
计算两个向量的叉乘
:param v1:
:param v2:
:return:
"""
return v1[0]*v2[1] - v1[1]*v2[0]
def graham_scan(points):
# print("Graham扫描法计算凸包")
bottom_index = get_bottom_point(points)
bottom_point = points.pop(bottom_index)
sorted_points = sort_polar_angle_cos(points, bottom_point)
m = len(sorted_points)
if m < 2:
print("点的数量过少，无法构成凸包")
return
stack = []
stack.append(bottom_point)
stack.append(sorted_points[0])
stack.append(sorted_points[1])
for i in range(2, m):
length = len(stack)
top = stack[length-1]
next_top = stack[length-2]
v1 = [sorted_points[i][0]-next_top[0], sorted_points[i][1]-next_top[1]]
v2 = [top[0]-next_top[0], top[1]-next_top[1]]
while coss_multi(v1, v2) >= 0:
stack.pop()
length = len(stack)
top = stack[length-1]
next_top = stack[length-2]
v1 = [sorted_points[i][0] - next_top[0], sorted_points[i][1] - next_top[1]]
v2 = [top[0] - next_top[0], top[1] - next_top[1]]
stack.append(sorted_points[i])
return stack
def test1():
points = [[1.1, 3.6],
[2.1, 5.4],
[2.5, 1.8],
[3.3, 3.98],
[4.8, 6.2],
[4.3, 4.1],
[4.2, 2.4],
[5.9, 3.5],
[6.2, 5.3],
[6.1, 2.56],
[7.4, 3.7],
[7.1, 4.3],
[7, 4.1]]
for point in points:
plt.scatter(point[0], point[1], marker='o', c='y')
result = graham_scan(points)
length = len(result)
for i in range(0, length-1):
plt.plot([result[i][0], result[i+1][0]], [result[i][1], result[i+1][1]], c='r')
plt.plot([result[0][0], result[length-1][0]], [result[0][1], result[length-1][1]], c='r')
plt.show()
def test2():
"""
使用复杂一些的数据测试程序运行效果
:return:
"""
iris = datasets.load_iris()
data = iris.data
points_ = data[:, 0:2]
points__ = points_[0:50, :]
points = points__.tolist()
temp_index = 0
for point in points:
plt.scatter(point[0], point[1], marker='o', c='y')
index_str = str(temp_index)
plt.annotate(index_str, (point[0], point[1]))
temp_index = temp_index + 1
result = graham_scan(points)
print(result)
length = len(result)
for i in range(0, length-1):
plt.plot([result[i][0], result[i+1][0]], [result[i][1], result[i+1][1]], c='r')
plt.plot([result[0][0], result[length-1][0]], [result[0][1], result[length-1][1]], c='r')
# for i in range(0, len(rank)):
plt.show()
if __name__ == "__main__":
test2()
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版权声明：本文为CSDN博主「麦克斯韦的妖精」的原创文章，遵循 CC 4.0 BY-SA 版权协议，转载请附上原文出处链接及本声明。
原文链接：https://blog.csdn.net/john_bian/article/details/85221039