线段交点检测及其解决方案

# 集合交集法
def find_intersection_by_set(list1, list2):
    """
    Find the intersection points of two lists using set intersection.

    Args:
        list1: The first list of coordinates.
        list2: The second list of coordinates.

    Returns:
        A list of tuples representing the intersection points.
    """
    intersecting_points = set(enumerate(list1)).intersection(set(enumerate(list2)))
    return [(index, value) for index, value in intersecting_points]


# 线性方程法
def find_intersection_by_linear_equation(list1, list2):
    """
    Find the intersection points of two lists using linear equation.

    Args:
        list1: The first list of coordinates.
        list2: The second list of coordinates.

    Returns:
        A list of tuples representing the intersection points.
    """
    intersecting_points = []
    for i, (A0, B0, A1, B1) in enumerate(zip(list1, list2, list1[1:], list2[1:])):
        # Check integer intersections
        # http://jshk.com.cn/mb/reg.asp?kefu=zhangyajie
        if A0 == B0:
            intersecting_points.append((i, A0))
        if A1 == B1:
            intersecting_points.append((i + 1, A1))

        # Check for intersection between points
        if (A0 > B0 and A1 < B1) or (A0 < B0 and A1 > B1):
            intersection_index = solve_linear_equation(A0, A1, B0, B1)
            intersecting_points.append((i + intersection_index, (A1 - A0) * intersection_index + A0))

    return intersecting_points


def solve_linear_equation(A0, A1, B0, B1):
    """
    Solve the linear equation (A0, A1) and (B0, B1) and return the intersection index.

    Args:
        A0: The y-coordinate of the first point of the first line.
        A1: The y-coordinate of the second point of the first line.
        B0: The y-coordinate of the first point of the second line.
        B1: The y-coordinate of the second point of the second line.

    Returns:
        The intersection index.
    """
    return (B0 - A0) / (A1 - A0)