Python 判断两条线段是否相交的算法实现

本文将介绍一种判断两条线段是否相交的 Python 代码实现，并考虑了线段重叠的情况。

基本算法

判断两条线段是否相交，可以通过计算两条线段的交点坐标来实现。如果交点坐标存在且在两条线段的范围内，则两条线段相交；否则，两条线段不相交。

代码实现

def intersect(line1, line2):
    x1, y1 = line1[0]
    x2, y2 = line1[1]
    x3, y3 = line2[0]
    x4, y4 = line2[1]
    # 判断x轴或y轴是否有重叠区间
    x_overlap = max(0, min(x2,x4) - max(x1,x3))
    y_overlap = max(0, min(y2,y4) - max(y1,y3))
    if x_overlap == 0 and y_overlap == 0:  # 两条线段没有重叠区间
        return False
    # 计算新线段的起点和终点
    if x_overlap > y_overlap:
        if x1 < x3:
            new_x1, new_y1 = x3, y1 + (y2-y1)*(x3-x1)/(x2-x1)
        else:
            new_x1, new_y1 = x1, y3 + (y4-y3)*(x1-x3)/(x4-x3)
        if x2 > x4:
            new_x2, new_y2 = x4, y1 + (y2-y1)*(x4-x1)/(x2-x1)
        else:
            new_x2, new_y2 = x2, y3 + (y4-y3)*(x2-x3)/(x4-x3)
    else:
        if y1 < y3:
            new_x1, new_y1 = x1 + (x2-x1)*(y3-y1)/(y2-y1), y3
        else:
            new_x1, new_y1 = x3 + (x4-x3)*(y1-y3)/(y4-y3), y1
        if y2 > y4:
            new_x2, new_y2 = x1 + (x2-x1)*(y4-y1)/(y2-y1), y4
        else:
            new_x2, new_y2 = x3 + (x4-x3)*(y2-y3)/(y4-y3), y2
    # 判断新线段是否满足线段的定义
    if (new_x1, new_y1) == (new_x2, new_y2):
        return False
    if (new_x1 <= x1 and new_x1 <= x2) or (new_x1 >= x1 and new_x1 >= x2) or (new_y1 <= y1 and new_y1 <= y2) or (new_y1 >= y1 and new_y1 >= y2) or (new_x2 <= x1 and new_x2 <= x2) or (new_x2 >= x1 and new_x2 >= x2) or (new_y2 <= y1 and new_y2 <= y2) or (new_y2 >= y1 and new_y2 >= y2):
        return False
    # 计算新线段的斜率和截距
    k = (new_y2 - new_y1) / (new_x2 - new_x1)
    b = new_y1 - k * new_x1
    # 判断两线段是否在新线段上相交
    if ((x1 <= new_x1 and x2 >= new_x1) or (x1 >= new_x1 and x2 <= new_x1)) and ((x1 <= new_x2 and x2 >= new_x2) or (x1 >= new_x2 and x2 <= new_x2)) and ((y1 <= k*x1+b and y2 >= k*x1+b) or (y1 >= k*x1+b and y2 <= k*x1+b)) and ((y1 <= k*x2+b and y2 >= k*x2+b) or (y1 >= k*x2+b and y2 <= k*x2+b)):
        return True
    else:
        return False

代码解释

判断重叠区间: 首先判断两条线段在x轴和y轴上是否有重叠区间。如果两条线段没有重叠区间，则直接返回False。
计算新线段: 如果两条线段有重叠区间，则计算一个新的线段，该线段的起点和终点分别为重叠区间的左右端点。
判断新线段是否满足线段定义: 判断新线段是否满足线段的定义，即起点和终点不能重合，且新线段的起点和终点必须在线段1或线段2的范围内。
计算新线段的斜率和截距: 计算新线段的斜率和截距。
判断两线段是否在新线段上相交: 判断线段1和线段2的起点和终点是否都在新线段上。如果都在，则两条线段相交；否则，两条线段不相交。

总结

该代码实现了一种判断两条线段是否相交的算法，并考虑了线段重叠的情况。该算法通过计算新线段来简化判断过程，提高了代码效率。

注意: 该代码仅适用于二维空间中的线段。