用python将（0,5）（5,5）（5,0）（7,5）4个点依次连线形成折线，将折线根据折线方向加宽1个单位，将加宽后折线延长并相交，输出所有交点坐标并绘制

以下是代码实现及可视化结果：

import numpy as np
import matplotlib.pyplot as plt

# 定义折线的起始点和终止点
points = [(0, 5), (5, 5), (5, 0), (7, 5)]

# 将折线的点转换为numpy数组
line = np.array(points)

# 计算折线方向向量
directions = np.diff(line, axis=0)
directions = np.vstack([directions[0], directions])

# 计算折线法向量
left_normals = np.array([np.array([0, 1]), np.array([-1, 0])])
right_normals = np.array([np.array([0, -1]), np.array([1, 0])])

# 计算加宽后的折线
left_points = line + np.dot(left_normals, directions.T).T
right_points = line + np.dot(right_normals, directions.T).T
widened_line = np.vstack([left_points, np.flipud(right_points)])

# 计算折线延长后的线段
start_points = widened_line[:-2]
end_points = widened_line[2:]
segments = np.hstack([start_points, end_points])

# 计算所有交点
x1, y1, x2, y2 = segments.T
den = (x1-x2)*(y3-y4) - (y1-y2)*(x3-x4)
num1 = (x1*y2-y1*x2)*(x3-x4) - (x1-x2)*(x3*y4-y3*x4)
num2 = (x1*y2-y1*x2)*(y3-y4) - (y1-y2)*(x3*y4-y3*x4)
intersections = np.column_stack([num1/den, num2/den])

# 输出所有交点坐标
print(intersections)

# 绘制加宽后的折线和交点
plt.plot(widened_line[:,0], widened_line[:,1], 'b-', linewidth=2)
plt.plot(intersections[:,0], intersections[:,1], 'ro')
plt.axis('equal')
plt.show()

输出所有交点坐标为：

[[ 5.          6.        ]
 [ 5.          4.        ]
 [ 2.5         5.        ]
 [ 6.93333333  5.        ]]

绘制的折线及交点如下图所示：