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pythonmathgeometry
mclafee
mclafee

Reputation: 1426

Find point-B on line by distance from point-A

I have line-equation, point-A and distance, and need to find point-B at the edge of the distance, on the line. I have 2 equations:

distance = math.sqrt((pt1[0] - pt2[0])**2 + (pt1[1] - pt2[1])**2)
pt2[1] = m*pt2[0] + n

distance, pt1, m and n are known.

How can I implement this calculation in Python? Maybe there is a Python library that can do this for me?

Upvotes: 1

Views: 3769

Answers (2)

Steven Liao
Steven Liao

Reputation: 3787

Given the line y=mx+b, the slope m tells us the ratio between the change in x (dx) and the change in y (dy).

Math:

// Given
point_b = (point_a[0]+dx,point_a[1]+dy)
other_possible_point_b = (point_a[0]-dx,point_a[1]-dy)
dy = m*dx
x**2 + y**2 = distance

// Calculations
dx**2 + (m*dx)**2 = distance
(m**2+1)(dx**2) = distance
dx = sqrt(distance/(m**2+1))
dy = m*sqrt(distance/(m**2+1))

Python solution:

from math import sqrt

point_b = (point_a[0]+dx(distance,m), point_a[1]+dy(distance,m))
other_possible_point_b = (point_a[0]-dx(distance,m), point_a[1]-dy(distance,m)) # going the other way

def dy(distance, m):
    return m*dx(distance, m)

def dx(distance, m):
    return sqrt(distance/(m**2+1))

Upvotes: 4

Abhishek Bansal
Abhishek Bansal

Reputation: 12715

I am assuming that point A is not on the line. ( Even if it is, the solution will not be different) You need to find the intersection between a circle and a line. It may have 1, 2 or 0 solutions.

(x1-x2)^2 + (y1-y2)^2 = d^2
y2 = m*x2 + c

The simplest solution would be: Replace y2 by (m*x2 + c) in the first equation and solve the quadratic for x2.

Upvotes: 1

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