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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