How to extend a line segment in both directions

Question

I've been stuck on this annoying problems for eons. I'm trying to write code so that I can scale a line segment meaning if the amount that I was to scale by(for example) is 2 and the current length of the line is 33 it will increase the entire length to 67. Meaning I add half to the beginning and half to the end... new front ---a--------b--- new back... But I'm having trouble translating it into code. Here is an example of the code.. The endpoints method should return the endpoints in a tuple such as (p1, p2)

from point import Point
import math

class Line:
def __init__(self,aPoint=Point(), bPoint=Point()):
    self.firstPoint = aPoint
    self.secondPoint = bPoint

def getEndPoints(self):
    return (self.firstPoint, self.secondPoint)

def scale(self,factor):
    if factor < 1:
       x1 = self.firstPoint.x +(self.secondPoint.x - self.firstPoint.x) * (factor)
       x2 = self.secondPoint.x +(self.firstPoint.x  - self.secondPoint.x) * (factor)
       print(str(x1))
       y1 = self.firstPoint.y +(self.secondPoint.y - self.firstPoint.y) * (factor)
       y2 = self.secondPoint.y +(self.firstPoint.y  - self.secondPoint.y) * (factor)
    else:
       x1 = -(self.firstPoint.x +(self.secondPoint.x - self.firstPoint.x) * (factor))
       x2 = -(self.secondPoint.x +(self.firstPoint.x  - self.secondPoint.x) * (factor))
       y1 = self.firstPoint.y +(self.secondPoint.y - self.firstPoint.y) * (factor)
       y2  = self.secondPoint.y +(self.firstPoint.y  - self.secondPoint.y) * (factor)
    self.firstPoint = Point(x1, y1)
    self.secondPoint = Point(x2, y2)

if __name__ == "__main__":
    p1 = Point(5,5)
    p2 = Point(20,35)
    l1 = Line(p1,p2)
    l1.scale(2)
    p5 = Point(-2.5,-10)
    p6 = Point(27.5,50)
    assert l1.getEndPoints() == (p5,p6)

These tests are not working correctly but the above are.. I'm getting a(5.0, 5.0) and b(20.0, 35.0)

---

    l1.scale(0.5)

    p5 = Point(8.75,12.5)
    p6 = Point(16.25,27.5)

---

class Point:
'''Point class represents and manipulates
x,y coordinates.'''

def __init__(self,x=0,y=0):
    '''Create a new point with default
    x,y coordinates at 0,0.'''
    self.x = x
    self.y = y

def distanceTo(self,aPoint):
    return ((self.x-aPoint.x) ** 2 + (self.y-aPoint.y) ** 2)** .5 

Answer 1

not sure if I get it right but

1. use linear interpolation (parametric line equation)

   You got line defined by endpoints p0,p1 in form of vectors so any point on it is defined as:

   p(t)=p0+(p1-p0)*t
   

   where p(t) is the point (vector) and t is scalar parameter in range

   t=<0.0,1.0>
   

   if you do not know the vector math then rewrite it to scalars

   x(t)=x0+(x1-x0)*t
   y(t)=y0+(y1-y0)*t
   

   so if t=0 then you get the point p0 and if t=1 then you get the point p1

2. Now just rescale the t range

   so you have scale s

   t0=0.5-(0.5*s)` ... move from half of line by scale towards p0
   t1=0.5+(0.5*s)` ... move from half of line by scale towards p1
   

   so new endpoints are

   q0=p0+(p1-p0)*t0
   q1=p0+(p1-p0)*t1
   

[edit1] I see it like this

def scale(self,factor):
 t0=0.5*(1.0-factor)
 t1=0.5*(1.0+factor)
 x1 = self.firstPoint.x +(self.secondPoint.x - self.firstPoint.x) * t0
 y1 = self.firstPoint.y +(self.secondPoint.y - self.firstPoint.y) * t0
 x2 = self.firstPoint.x +(self.secondPoint.x - self.firstPoint.x) * t1
 y2 = self.firstPoint.y +(self.secondPoint.y - self.firstPoint.y) * t1
 self.firstPoint = Point(x1, y1)
 self.secondPoint = Point(x2, y2)

Take in mind I do not code in python so handle with prejudice ...

Answer 2

For a scale factor s, the coordinates of the new points are given by

Xa' = Xa (1+s)/2 + Xb (1-s)/2
Ya' = Ya (1+s)/2 + Yb (1-s)/2


Xb' = Xb (1+s)/2 + Xa (1-s)/2
Yb' = Yb (1+s)/2 + Ya (1-s)/2

Answer 3

With the common metrik, you only need to adjust each dimension seperately.

I rewrote some parts of the code, to fit it better to the usual Python style

You might want to work through the things, you are unfamiliar with to save yourself a lot of time in the future.

class Line:
    def __init__(self, point_one, point_two):
        self.point_one = point_one
        self.point_two = point_two

    def __str__(self):
        return 'Line(p1:{},p2:{})'.format(self.point_one, self.point_two)

    @property
    def points(self):
        return self.point_one, self.point_two

    @property
    def length(self):
        return ((self.point_one.x - self.point_two.x)**2 + (self.point_one.y - self.point_two.y)**2)**0.5

    def scale(self, factor):
        self.point_one.x, self.point_two.x = Line.scale_dimension(self.point_one.x, self.point_two.x, factor)
        self.point_one.y, self.point_two.y = Line.scale_dimension(self.point_one.y, self.point_two.y, factor)

    @staticmethod
    def scale_dimension(dim1, dim2, factor):
        base_length = dim2 - dim1
        ret1 = dim1 - (base_length * (factor-1) / 2)
        ret2 = dim2 + (base_length * (factor-1) / 2)
        return ret1, ret2


class Point:
    def __init__(self, x=0, y=0):
        self.x = x
        self.y = y

    def __str__(self):
        return 'Point(x={},y={})'.format(self.x, self.y)

    def __eq__(self, other):
        return self.x == other.x and self.y == other.y


if __name__ == "__main__":
    p1 = Point(5, 5)
    p2 = Point(20, 35)
    l1 = Line(p1, p2)
    print(l1)
    print(l1.length)
    l1.scale(2)
    print(l1)
    print(l1.length)
    p5 = Point(-2.5, -10)
    p6 = Point(27.5, 50)
    assert l1.points == (p5, p6)

Note, that the scale method modifies the orginal line and points. If you want to get a new line, the method should be:

def scale(self, factor):
    x1, x2 = Line.scale_dimension(self.point_one.x, self.point_two.x, factor)
    y1, y2 = Line.scale_dimension(self.point_one.y, self.point_two.y, factor)
    return Line(Point(x1, y1), Point(x2, y2))