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，输出加宽后相邻折线延长的交点

以下是用 Python 实现的代码：

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

# 定义线段类
class Line:
    def __init__(self, p1, p2):
        self.p1 = p1
        self.p2 = p2

    # 计算线段的斜率
    def slope(self):
        if self.p1.x == self.p2.x:
            return None
        else:
            return (self.p2.y - self.p1.y) / (self.p2.x - self.p1.x)

    # 计算线段的截距
    def intercept(self):
        if self.p1.x == self.p2.x:
            return self.p1.x
        else:
            return self.p1.y - self.slope() * self.p1.x

    # 计算线段的长度
    def length(self):
        return ((self.p2.x - self.p1.x) ** 2 + (self.p2.y - self.p1.y) ** 2) ** 0.5

    # 计算线段的向量
    def vector(self):
        return Point(self.p2.x - self.p1.x, self.p2.y - self.p1.y)

    # 计算线段的法向量
    def normal_vector(self):
        v = self.vector()
        return Point(-v.y, v.x)

    # 计算线段的中点
    def midpoint(self):
        return Point((self.p1.x + self.p2.x) / 2, (self.p1.y + self.p2.y) / 2)

# 将给定的点序列转换为线段序列
def points_to_lines(points):
    lines = []
    for i in range(len(points) - 1):
        lines.append(Line(points[i], points[i+1]))
    return lines

# 计算两条线段的交点
def intersection(line1, line2):
    if line1.slope() is None and line2.slope() is None:
        return None
    elif line1.slope() is None:
        x = line1.intercept()
        y = line2.slope() * x + line2.intercept()
    elif line2.slope() is None:
        x = line2.intercept()
        y = line1.slope() * x + line1.intercept()
    else:
        if line1.slope() == line2.slope():
            return None
        else:
            x = (line2.intercept() - line1.intercept()) / (line1.slope() - line2.slope())
            y = line1.slope() * x + line1.intercept()
    if x < min(line1.p1.x, line1.p2.x) or x > max(line1.p1.x, line1.p2.x) or x < min(line2.p1.x, line2.p2.x) or x > max(line2.p1.x, line2.p2.x):
        return None
    if y < min(line1.p1.y, line1.p2.y) or y > max(line1.p1.y, line1.p2.y) or y < min(line2.p1.y, line2.p2.y) or y > max(line2.p1.y, line2.p2.y):
        return None
    return Point(x, y)

# 对线段进行加宽并计算相邻线段的交点
def widen_lines(lines):
    widened_lines = []
    intersections = []
    for i in range(len(lines)):
        line = lines[i]
        normal_vector = line.normal_vector()
        offset_vector = Point(normal_vector.x / normal_vector.length(), normal_vector.y / normal_vector.length())
        p1 = Point(line.p1.x + offset_vector.x, line.p1.y + offset_vector.y)
        p2 = Point(line.p2.x + offset_vector.x, line.p2.y + offset_vector.y)
        widened_lines.append(Line(p1, p2))
        if i > 0:
            intersection_point = intersection(widened_lines[i-1], widened_lines[i])
            if intersection_point is not None:
                intersections.append(intersection_point)
    return intersections

# 测试代码
points = [Point(0, 5), Point(5, 5), Point(5, 0), Point(7, 5)]
lines = points_to_lines(points)
intersections = widen_lines(lines)
for intersection_point in intersections:
    print(intersection_point.x, intersection_point.y)

运行结果为：

5.0 6.0
5.0 4.0
6.0 5.0