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，将加宽后的折线延长，输出加宽后折线与折线的交点并并绘制

以下是Python代码：

import matplotlib.pyplot as plt
import numpy as np

# 折线的四个点
points = [(0, 5), (5, 5), (5, 0), (7, 5)]

# 把每一段折线加宽
width = 1
new_points = []
for i in range(len(points)-1):
    p1 = points[i]
    p2 = points[i+1]
    dx = p2[0] - p1[0]
    dy = p2[1] - p1[1]
    length = np.sqrt(dx**2 + dy**2)
    if length > 0:
        ux = width * dy / length
        uy = -width * dx / length
        p1_new = (p1[0]+ux, p1[1]+uy)
        p2_new = (p2[0]+ux, p2[1]+uy)
        new_points.append((p1_new, p2_new))

# 计算加宽后折线与折线的交点
intersects = []
for i in range(len(new_points)-1):
    for j in range(i+1, len(new_points)):
        p11, p12 = new_points[i]
        p21, p22 = new_points[j]
        dx1 = p12[0] - p11[0]
        dy1 = p12[1] - p11[1]
        dx2 = p22[0] - p21[0]
        dy2 = p22[1] - p21[1]
        det = dx1 * dy2 - dx2 * dy1
        if det != 0:
            t1 = (dx2 * (p11[1]-p21[1]) - dy2 * (p11[0]-p21[0])) / det
            t2 = (dx1 * (p11[1]-p21[1]) - dy1 * (p11[0]-p21[0])) / det
            if 0 <= t1 <= 1 and 0 <= t2 <= 1:
                x = p11[0] + t1 * dx1
                y = p11[1] + t1 * dy1
                intersects.append((x, y))

# 绘制加宽后的折线和交点
fig, ax = plt.subplots()
for p1, p2 in new_points:
    ax.plot([p1[0], p2[0]], [p1[1], p2[1]], 'b')
for x, y in intersects:
    ax.plot(x, y, 'ro')
ax.axis('equal')
plt.show()

运行结果：