在另一条线的一点上绘制固定长度的垂直线 [英] Draw perpendicular line of fixed length at a point of another line

问题描述

我有两个点A(10,20)和B(15,30).这些点生成线AB.我需要在Python中的点B上绘制一条长度为6(每个方向为3个单位)的垂直线CD.

I have two points A (10,20) and B (15,30). The points generate a line AB. I need to draw a perpendicular line, CD, on point B with a length of 6 (each direction 3 units) in Python.

我已经具有使用以下代码的AB行的某些属性:

I already have some properties of line AB using the following code:

from scipy import stats
x = [10,15]
y = [20,30]
slope, intercept, r_value, p_value, std_err = stats.linregress(x,y)

如何计算C和D的位置.我需要它们的X和Y值.

How can I calculate the location of C and D. I need their X and Y value.

使用Shapely库将C和D的值用于完成另一个目标.

The value of C and D will be used for accomplishing another objective using the Shapely library.

推荐答案

如果 slope 是AB的斜率，则CD的斜率是 -1/slope .这等于水平变化的垂直变化: dy/dx = -1/slope .这样得出 dx = -slope * dx .根据勾股定理，您有 3 ** 2 = dy ** 2 + dx ** 2 .替换 dx ，您会得到

If slope is the slope of AB, then the slope of CD is -1/slope. This is equal to vertical change over horizontal change: dy/dx = -1/slope. This gives that dx = -slope*dx. And by Pythagorean Theorem, you have 3**2 = dy**2+dx**2. Substitute for dx, and you get

3 ** 2 =(-slope * dy)** 2 + dy ** 2
3 ** 2 =(斜率** 2 + 1)* dy ** 2
dy ** 2 = 3 ** 2/(坡度** 2 + 1)
dy = math.sqrt(3 ** 2/(slope ** 2 + 1))

然后您将获得 dx = -slope * dy .最后，您可以使用 dx 和 dy 来获取C和D.因此，代码为:

Then you can get dx = -slope*dy. Finally, you can use dx and dy to get C and D. So the code would be:

import math
dy = math.sqrt(3**2/(slope**2+1))
dx = -slope*dy
C[0] = B[0] + dx
C[1] = B[1] + dy
D[0] = B[0] - dx
D[1] = B[1] - dy

(请注意，尽管 math.sqrt 仅返回一个数字，但通常存在正负平方根.C对应于正平方根，D对应于负).

(Note that although math.sqrt returns only one number, in general there is a positive and negative square root. C corresponds to the positive square root, and D to the negative).

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