import numpy as np


def find_offset_points(x1, y1, x2, y2, distance=5):
    # 计算线段上五分之一处的点
    x_p = x1 + (x2 - x1) / 5
    y_p = y1 + (y2 - y1) / 5

    # 计算线段的斜率
    m = (y2 - y1) / (x2 - x1)

    # 计算法线的斜率
    m_perp = -1 / m if m != 0 else np.inf  # 防止除以零

    # 如果斜率为无穷大，则法线为垂直线
    if np.isinf(m_perp):
        x_offset = x_p
        y_offset_1 = y_p + distance
        y_offset_2 = y_p - distance
        return [(x_offset, y_offset_1), (x_offset, y_offset_2)]

    # 法线方程 y - y_p = m_perp(x - x_p)
    # 改写为标准形式 m_perp*x - y + y_p - m_perp*x_p = 0
    A = m_perp
    B = -1
    C = y_p - m_perp * x_p

    # 平行线方程 Ax + By + C_offset = 0
    # 距离公式 d = |Ax + By + C| / sqrt(A^2 + B^2) = distance
    # |Ax + By + C_offset| = distance * sqrt(A^2 + B^2)
    # C_offset = C +/- distance * sqrt(A^2 + B^2)
    sqrt_AB = np.sqrt(A ** 2 + B ** 2)
    C_offset_1 = C + distance * sqrt_AB
    C_offset_2 = C - distance * sqrt_AB

    # 解方程找到平行线上的点
    # m_perp*x - y + C_offset = 0 => y = m_perp*x + C_offset
    def solve_for_y(x, C_offset):
        return m_perp * x + C_offset

    # 选择线段AB上的一个点进行代入求解，比如选择x1或x2
    # 这里选择x1，也可以选择x2
    x_test = x1  # 或者 x_test = x2
    y1_offset = solve_for_y(x_test, C_offset_1)
    y2_offset = solve_for_y(x_test, C_offset_2)

    # 计算对应的x坐标
    x1_offset = (y1_offset - C_offset_1) / m_perp
    x2_offset = (y2_offset - C_offset_2) / m_perp

    # 返回两个坐标点
    return [(x1_offset, y1_offset), (x2_offset, y2_offset)]


# 示例使用
x1, y1 = 0, 0
x2, y2 = 10, 10
points = find_offset_points(x1, y1, x2, y2)
print(points)