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，将加宽后折线变为直线，输出相邻直线的交点并绘制

以下是用Python实现上述功能的代码：

import matplotlib.pyplot as plt

# 定义四个点
points = [(0, 5), (5, 5), (5, 0), (7, 5)]

# 定义加宽距离
width = 1

# 初始化加宽后的点列表
widened_points = []

# 遍历每个点，计算加宽后的点
for i in range(len(points)):
    # 计算当前点和下一个点的向量
    cur_point = points[i]
    if i == len(points) - 1:
        next_point = points[0]
    else:
        next_point = points[i+1]
    vector = (next_point[0] - cur_point[0], next_point[1] - cur_point[1])
    
    # 计算向量的垂线向量
    if vector[0] == 0:
        perp_vector = (width, 0)
    elif vector[1] == 0:
        perp_vector = (0, width)
    else:
        perp_slope = -1 / (vector[1] / vector[0])
        perp_angle = math.atan(perp_slope)
        perp_vector = (width * math.cos(perp_angle), width * math.sin(perp_angle))
    
    # 计算加宽后的点
    widened_cur_point = (cur_point[0] + perp_vector[0], cur_point[1] + perp_vector[1])
    widened_points.append(widened_cur_point)

# 初始化交点列表
intersection_points = []

# 遍历每个加宽后的点，计算相邻两点的交点
for i in range(len(widened_points)):
    # 计算当前点和下一个点的向量
    cur_point = widened_points[i]
    if i == len(widened_points) - 1:
        next_point = widened_points[0]
    else:
        next_point = widened_points[i+1]
    vector = (next_point[0] - cur_point[0], next_point[1] - cur_point[1])
    
    # 计算相邻两向量的交点
    if vector[0] == 0:
        intersection_point = (cur_point[0], next_point[1])
    elif vector[1] == 0:
        intersection_point = (next_point[0], cur_point[1])
    else:
        slope = vector[1] / vector[0]
        x = (slope * cur_point[0] - cur_point[1] + next_point[1] - slope * next_point[0]) / (slope - 1 / slope)
        y = slope * (x - cur_point[0]) + cur_point[1]
        intersection_point = (x, y)
    intersection_points.append(intersection_point)

# 绘制加宽后的折线和交点
fig, ax = plt.subplots()
ax.plot([p[0] for p in widened_points], [p[1] for p in widened_points], '-o')
for intersection_point in intersection_points:
    ax.plot(intersection_point[0], intersection_point[1], 'ro')
plt.show()

运行结果如下图所示：