Rotate line with two points

Question

I have line with two points

(x1, y1) (x2, y2)

and I am working on x+, y+ plane only

and say this line is vertical say

(320, 320) (320, 160)

How do I rotate it by 90 degrees to get

(320, 320) (480, 320)  [90 deg rotated by bottom point (320, 320)]
(320, 160) (480, 160)  [90 deg rotated by top point (320, 160)]

Remember I would need in same form—i.e,

(x1, y1) (x2, y2)

By the way, these lines can only be vertical or horizontal, so the slope is either undefined or zero.

Answer 1

To rotate B 90 degrees around A:

diff = B-A
B_new = A + array([-diff[1],diff[0]])

To be more general, you do this:

def rot_origin(p, ang):
    return array([p[0]*cos(ang)-p[1]*sin(ang),p[0]*sin(ang)+p[1]*cos(ang)])

def rot_around(p, p0, ang):
    return p0 + rot_origin(p-p0, ang)

Then, your case would be B_new = rot_around(A, B, pi/2), since 90 degrees is pi/2 radians.

Edit: Just to make it completely explicit for your example. To rotate by 90 degrees around point 1, you would get:

(x1,y1) (x1-(y2-y1),y1+(x2-x1))

To rotate around point 2, you would get:

(x2-(y1-y2),y2+(x1-x2)) (x2,y2)

Answer 2

To get what you put as example:

1. Get the distance between top and bottom points. In your example, d = sqrt((x2 - x1)^2 + (y2-y1)^2).
2. For a 90 degrees rotation by bottom point, simply use (x2,y2) and (x2+d, y2) as end points.
3. For a 90 degrees rotation by top point, simply use (x1,y1) and (x1+d, y1) as end points.

This can be easily generalized to any line, not only a vertical one, and any rotation angle.