如何检查一个点是否低于一条线?

2022-01-14 00:00:00 python geometry line math

问题描述

如何检查点是否低于线?

How can I check if a point is below a line or not ?

我有以下数据:

Line [ {x1,y1}, {x2,y2} ]
Points {xA,yA}, {xB,yB} ...

我需要在python中编写一个小算法来检测线的一侧和另一侧的点.

I need to write a small algorithm in python to detect points on one side and the other side of the line.

谢谢

解决方案

你可以尝试使用交叉产品 -- http://en.wikipedia.org/wiki/Cross_product.

You could try using a cross product -- http://en.wikipedia.org/wiki/Cross_product.

v1 = (x2-x1, y2-y1)   # Vector 1
v2 = (x2-xA, y2-yA)   # Vector 2
xp = v1[0]*v2[1] - v1[1]*v2[0]  # Cross product
if xp > 0:
    print('on one side')
elif xp < 0:
    print('on the other')
else:
    print('on the same line!')

您需要校准每一面的内容.如果您希望它位于下方"；或以上"您需要确保线上的点是水平排序的.

You'd need to calibrate what each side is. If you want it to be "below" or "above" you need to ensure the points on the line are sorted horizontally.

我还没有测试过.

编辑我最初输入了点积公式.:o

Edit I initially put in the dot product formula. :o

编辑 2 哦，我将坐标放入集合而不是元组.如果您运行的是相当现代的 Python 版本，则对向量使用 namedtuple('point', 'x y') 会很好.

Edit 2 D'oh, I was putting the coordinates into a set instead of a tuple. Using namedtuple('point', 'x y') for the vectors is nice if you're running a reasonably modern version of Python.

幸运的是，我发现计算二维向量的叉积.

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