Numpy 和线的交叉点 [英] Numpy and line intersections

问题描述

如何使用 numpy 计算两条线段的交点?

How would I use numpy to calculate the intersection between two line segments?

在代码中我有 segment1 = ((x1,y1),(x2,y2)) 和 segment2 = ((x1,y1),(x2,y2)).注意 segment1 不等于 segment2.因此，在我的代码中，我也一直在计算斜率和 y 截距，如果可以避免这种情况就好了，但我不知道如何做.

In the code I have segment1 = ((x1,y1),(x2,y2)) and segment2 = ((x1,y1),(x2,y2)). Note segment1 does not equal segment2. So in my code I've also been calculating the slope and y-intercept, it would be nice if that could be avoided but I don't know of a way how.

我一直将 Cramer 规则与我用 Python 编写的函数一起使用，但我想找到一种更快的方法.

I've been using Cramer's rule with a function I wrote up in Python but I'd like to find a faster way of doing this.

推荐答案

Stolen direct from https://web.archive.org/web/20111108065352/https://www.cs.mun.ca/~rod/2500/notes/numpy-arrays/numpy-arrays.html

Stolen directly from https://web.archive.org/web/20111108065352/https://www.cs.mun.ca/~rod/2500/notes/numpy-arrays/numpy-arrays.html

#
# line segment intersection using vectors
# see Computer Graphics by F.S. Hill
#
from numpy import *
def perp( a ) :
    b = empty_like(a)
    b[0] = -a[1]
    b[1] = a[0]
    return b

# line segment a given by endpoints a1, a2
# line segment b given by endpoints b1, b2
# return 
def seg_intersect(a1,a2, b1,b2) :
    da = a2-a1
    db = b2-b1
    dp = a1-b1
    dap = perp(da)
    denom = dot( dap, db)
    num = dot( dap, dp )
    return (num / denom.astype(float))*db + b1

p1 = array( [0.0, 0.0] )
p2 = array( [1.0, 0.0] )

p3 = array( [4.0, -5.0] )
p4 = array( [4.0, 2.0] )

print seg_intersect( p1,p2, p3,p4)

p1 = array( [2.0, 2.0] )
p2 = array( [4.0, 3.0] )

p3 = array( [6.0, 0.0] )
p4 = array( [6.0, 3.0] )

print seg_intersect( p1,p2, p3,p4)

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