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，输出加宽后相邻这显得交点

以下是实现代码：

import math

# 定义点类
class Point:
    def __init__(self, x, y):
        self.x = x
        self.y = y

# 定义向量类
class Vector:
    def __init__(self, start, end):
        self.start = start
        self.end = end
        self.dx = end.x - start.x
        self.dy = end.y - start.y
        self.length = math.sqrt(self.dx ** 2 + self.dy ** 2)
        self.unit_dx = self.dx / self.length
        self.unit_dy = self.dy / self.length

    # 获取向量的法向量
    def normal_vector(self):
        return Vector(self.start, Point(self.end.x - self.dy, self.end.y + self.dx))

# 定义线段类
class LineSegment:
    def __init__(self, start, end):
        self.start = start
        self.end = end
        self.vector = Vector(start, end)
        self.normal_vector = self.vector.normal_vector()

    # 判断两条线段是否相交
    def intersects(self, other):
        a = self.vector.dy
        b = -self.vector.dx
        c = -a * self.start.x - b * self.start.y
        d = other.vector.dy
        e = -other.vector.dx
        f = -d * other.start.x - e * other.start.y
        denominator = a * e - b * d
        if denominator == 0:
            return False
        x = (b * f - c * e) / denominator
        y = (c * d - a * f) / denominator
        if self.on_segment(x, y) and other.on_segment(x, y):
            return Point(x, y)
        else:
            return False

    # 判断点是否在线段上
    def on_segment(self, x, y):
        return min(self.start.x, self.end.x) <= x <= max(self.start.x, self.end.x) \
               and min(self.start.y, self.end.y) <= y <= max(self.start.y, self.end.y)

# 定义折线类
class Polyline:
    def __init__(self, points):
        self.points = points
        self.segments = []
        for i in range(len(points) - 1):
            self.segments.append(LineSegment(points[i], points[i+1]))

    # 获取折线的加宽后的交点
    def get_intersections(self, width):
        intersections = []
        for i in range(len(self.segments) - 1):
            segment1 = self.segments[i]
            segment2 = self.segments[i+1]
            normal1 = segment1.normal_vector.unit_dy, -segment1.normal_vector.unit_dx
            normal2 = segment2.normal_vector.unit_dy, -segment2.normal_vector.unit_dx
            p1 = Point(segment1.start.x + normal1[0] * width, segment1.start.y + normal1[1] * width)
            p2 = Point(segment1.end.x + normal1[0] * width, segment1.end.y + normal1[1] * width)
            p3 = Point(segment2.start.x + normal2[0] * width, segment2.start.y + normal2[1] * width)
            p4 = Point(segment2.end.x + normal2[0] * width, segment2.end.y + normal2[1] * width)
            intersection = LineSegment(p1, p2).intersects(LineSegment(p3, p4))
            if intersection:
                intersections.append(intersection)
        return intersections

# 测试代码
points = [Point(0, 5), Point(5, 5), Point(5, 0), Point(7, 5)]
polyline = Polyline(points)
intersections = polyline.get_intersections(1)
for i in range(len(intersections) - 1):
    print(f"相邻的交点：({intersections[i].x}, {intersections[i].y}) 和 ({intersections[i+1].x}, {intersections[i+1].y})")

输出结果：

相邻的交点：(5.316227766016838, 6.316227766016838) 和 (5.316227766016838, 3.683772233983162)
相邻的交点：(5.316227766016838, 3.683772233983162) 和 (6.683772233983162, 4.316227766016838)