如何在python中计算点和相交线之间的距离？

Question

I am rusty in my math, not sure how to calculate the distrance from the highest point H to the intersection between the 2 lowest points in the middle for the N point.

import matplotlib.pyplot as plt
from scipy import interpolate
import numpy as np

y= [10.5,10,12,13,10,11,16,10,9,13,10]
x= np.linspace(1, len(y), len(y), endpoint=True)
dist = np.linalg.norm(y-x)

print dst

fig, ax = plt.subplots(figsize=(8, 6))
ax.plot(x, y, color='red')

Answer 1

import heapq
import operator
import math


y = [10.5,10,12,13,10,11,16,10,9,13,10]
x= np.linspace(1, len(y), len(y), endpoint=True)

y1,y2 = heapq.nsmallest(2, enumerate(y), key=operator.itemgetter(1))
x1,y1 = y1
x1 = x[x1]

x2,y2 = y2
x2 = x[x2]

m = (y2-y1)/(x2-x1)
print("Equation of line: y = {}(x-{}) + {}".format(m, x1, y1))

apexPoint = (5,4)  # or wherever the apex point is    
X,Y = apexPoint
M = 1/m
print("Equation of perpendicular line: y = {}(x-{}) + {}".format(M, X, Y))

intersect_x = ((M*X)+Y-(m*x1)-y1)/(M-m)
intersect_y = m*(intersect_x - x1) + y1

dist = math.sqrt((X - intersect_x)**2 + (Y - intersect_y)**2)  # this is your answer

Answer 2

I looked at your chart. The line is not perpendicular. It is a vertical line from a point to a line segment.

Assuming your apex point is (x0,y0) and your base points are (x1,y1) and (x2,y2):

The equation of the line joining 2 points (x1,y1) and (x2,y2) is:

y = (y2-y1)/(x2-x1) * x + (y2 * (x2-x1) - x1 * (y2-y1)) / (x2-x1)

Get the y intercept on the the line:

ymid = (y2-y1)/(x2-x1) * x0 + (y2 * (x2-x1) - x1 * (y2-y1)) / (x2-x1)

Your distance is:

y0 - ymid

See http://pythonfiddle.com/SO-33162756/

Answer 3

This doesn't answer your question directly but perhaps you would want to checkout the awesome python module shapely .

You can create geometric objects such as LineStrings , Points using the module.

And a simple call to:

object.project(other[, normalized=False])

Returns the distance along this geometric object to a point nearest the other object.

will give you your answer.

Here's its documentation: Shapely Documentation